We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ∼30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing.

Unsourced random access emerged as a novel wireless paradigm enabling massive device connectivity on the uplink. We consider quasi-static Rayleigh fading wherein the access point has multiple receive antennas and every mobile device a single transmit antenna. The objective is to construct a coding scheme that minimizes the energy-per-bit subject to a maximum probability of error given a fixed message length and a prescribed number of channel uses. Every message is partitioned into two parts: the first determines pilot values and spreading sequences; the remaining bits are encoded using a polar code. The transmitted signal contains two distinct sections. The first features pilots and the second is composed of spread modulated symbols. The receiver has three modules: an energy detector, tasked with recovering the set of active pilot sequences; a bank of Minimum Mean Square Error (MMSE) estimators acting on measurements at the receiver; and a polar list-decoder, which seeks to retrieve the coded information bits. A successive cancellation step is applied to subtract recovered codewords, before the residual signal is fed back to the decoder. Empirical evidence suggests that an appropriate combination of these ideas can outperform state-of-the-art coding techniques when the number of active users exceeds one hundred.

We consider the approximate support recovery (ASR) task of inferring the support of a$K$-sparse vector$\mathrm{x}\in \mathbb{R}^{n}$from$m$noisy measurements. We examine the case where$n$is large, which precludes the application of standard compressed sensing solvers, thereby necessitating solutions with lower complexity. We design a scheme for ASR by leveraging techniques developed for unsourced multiple access. We present two decoding algorithms with computational complexities$\mathcal{O}(K^{2}\log n+ K\log n\log\log n)$and$\mathcal{O}(K^{3}+K^{2}\log n+K\log n\log \log n)$per iteration, respectively. When$K\ll n$, this is much lower than the complexity of approximate message passing with a minimum mean squared error denoiser, which requires$\mathcal{O}(mn)$operations per iteration. This gain comes at a slight performance cost. Our findings suggest that notions from multiple access can play an important role in the design of measurement schemes for ASR.

Color-shift keying (CSK) is a modulation scheme used in visible light communication (VLC) to transmit data by varying the intensity of red, green, and blue LEDs. We study the channel coding for VLC using CSK under constraints of no color shift and no illumination flicker during transmission and design codes over newly introduced symmetric symbol constellations over a triangle intensity plane. One class of codes contains the transmitted sequence based on finite-state machines, and the other is based on the concept of trellis-coded modulation for mitigating color shifts during transmission. The codes have a trellis structure which allows optimal soft-decision decoding using the Viterbi algorithm providing asymptotic coding gain improvements of 1.5 to 3.5 dB with respect to the uncoded transmission while complying with the color shift and flicker constraints.

We analyze the asymptotic average and effective throughputs of a multiuser diversity scheme for a secondary multiuser network consisting of multiple secondary users (transmitters) and one secondary receiver. Considering a transmit power adaptation strategy at the secondary users to satisfy the instantaneous interference constraint at the primary receiver, the secondary receiver selects the k-th best secondary user for transmission, namely, the one with the k-th highest signal-to-noise ratio (SNR). We use extreme value theory to show that the k-th highest SNR converges uniformly in distribution to an inverse gamma random variable for a fixed k and large number of secondary users. We use this result to derive closed-form asymptotic expressions for the average and effective throughputs of the k-th best secondary user.

The effective rate is an important metric that takes delay quality of service (QoS) requirements into consideration while analyzing the performance of wireless systems. In this paper we analyze the effective rate of multiple-input single-output (MISO) systems with transmit antenna selection (TAS) subject to Rayleigh fading. Specifically, we derive an analytical expression for the effective rate of MISO/TAS systems and closed form expressions for the effective rate in asymptotically high and low signal-to-noise ratio (SNR) regimes. Furthermore, we analyze the effective rate of MISO/TAS systems with large number of transmit antennas and derive an asymptotic analytical expression for it.

We analyze the asymptotic average throughput of a multiuser diversity (MD) scheme, in the limit of large number of users, for free space optical (FSO) communication systems over a gamma-gamma fading channel. It is assumed that the FSO system consists of an optical transmitter (central node) equipped with K transmit apertures to serve K users (one transmit aperture for each user). It is also assumed that each user is equipped with N receive apertures and equal gain combining (EGC) is employed at the user's receiver. In MD, the central node serves only one user which has the largest channel gain among the K users, while other users remain silent. Using extreme value theory (EVT), we derive a simple and tight upper bound on the asymptotic average throughput of the considered FSO system. Moreover, the asymptotic average bit error rate (BER) is investigated and a closed form approximation for the average BER of the FSO system with MD#x002F;EGC scheme is obtained.

The IEEE 802.15.7 standard for visible light communication (VLC) includes the use of run-length-limited codes to mitigate modulation-induced flickering and the further use of coding to improve bit error rate performance. In this paper, we introduce algorithms to design codes using finite-state machines, which provide simultaneously a coding gain while also mitigating flicker. The codes have the additional advantage of being optimally soft-decision decodable using the Viterbi algorithm. To compare the flicker mitigation performance of different codes, we further introduce a mathematical measure of flicker based on the power spectrum of the transmitted signals. We discuss tradeoffs between flicker mitigation, code rate, and coding gain, design several codes, and compare their error rate and flicker mitigation performance to some codes in the VLC standard.

The IEEE 802.15.7 standard on visible light communications (VLC) proposes color-shift-keying (CSK) as a way to increase data rate while keeping a constant optical power. In this paper, we propose two algorithms to design codes by finite state machines (FSM) using newly introduced CSK constellations. These codes ensure a constant perceived color eliminating the use of the scrambler proposed by the standard. Furthermore, they achieve about 1 to 3 dB of coding gain compared with the standard constellations and are optimally and efficiently softdecision decodable using the Viterbi algorithm.

In this paper, we present a methodology employing statistical analysis and stochastic geometry to study geometric routing schemes in wireless ad hoc networks. In particular, we analyze the network-layer performance of one such scheme, the random [ 1/ 2]disk routing scheme, which is a localized geometric routing scheme in which each node chooses the next relay randomly among the nodes within its transmission range and in the general direction of the destination. The techniques developed in this paper enable us to establish the asymptotic connectivity and the convergence results for the mean and variance of the routing path lengths generated by geometric routing schemes in random wireless networks. In particular, we approximate the progress of the routing path toward the destination by a Markov process and determine the sufficient conditions that ensure the asymptotic connectivity for both dense and large-scale ad hoc networks deploying the random [ 1/ 2]disk routing scheme. Furthermore, using this Markov characterization, we show that the expected length (hop count) of the path generated by the random [ 1/ 2]disk routing scheme normalized by the length of the path generated by the ideal direct-line routing, converges to 3π/4 asymptotically. Moreover, we show that the variance-to-mean ratio of the routing path length converges to 9π2/64-1 asymptotically. Through simulation, we show that the aforementioned asymptotic statistics are in fact quite accurate even for finite granularity and size of the network.

In this paper we consider a cognitive radio network with access to N licensed primary frequency bands and their usage statistics, where the decentralized secondary users are subject to certain inter-network interference constraint. In particular, to limit the interference to the primary network, secondary users are equipped with spectrum sensors and are capable of sensing and accessing a limited number of channels at the same time due to hardware limitations. We consider both the error-free and erroneous spectrum sensing scenarios, and establish the jointly optimal random sensing and access scheme, which maximizes the secondary network expected sum throughput while honoring the primary interference constraint. We show that under certain conditions the optimal sensing and access scheme is independent of the primary frequency bandwidths and usage statistics; otherwise, they follow water-filling-like strategies. Moreover, we show that the performance of the secondary network depends on the ratio between the “opportunity-detection” probability and the “mis-detection” probability if the former is larger; otherwise, it depends on the ratio between the “false-alarm” probability and the “detection” probability. Finally, we demonstrate a binary behavior for the optimal access scheme at each channel, depending on whether the opportunity-detection probability or mis-detection probability is larger in that channel.

In beamforming, channel state information (CSI) is used to design the beamforming vector (or matrix). Since in a practical system the CSI always needs to be estimated, channel estimation (CE) errors are inevitable, which could severely affect the performance of a beamforming scheme. In this paper, we present a novel beamforming method for two-way relay (TWR) systems that is robust against CE errors. The proposed method obtains a sub-optimal solution for the associated non-convex robust optimization problem by solving a set of closed-form linear equations. Simulations show a considerable performance gain over the rank-one relaxation-based semidefinite programming (SDP) solutions, especially for the cases where the relaxed problem becomes infeasible. In addition, there is significant reduction in complexity, making this method very attractive for practical implementation.

We study the asymptotic performance of two multi-hop overlaid ad-hoc networks that utilize the same temporal, spectral, and spatial resources based on random access schemes. The primary network consists of Poisson distributed legacy users with density λ(p)and the secondary network consists of Poisson distributed cognitive radio users with density λ(s)= (λ(p))β(β > 0, β ≠ 1) that utilize the spectrum opportunistically. Both networks are decentralized and employ ALOHA medium access protocols where the secondary nodes are additionally equipped with range-limited perfect spectrum sensors to monitor and protect primary transmissions. We study the problem in two distinct regimes, namely β > 1 and 01. On the contrary, spectrum sensing turns out to be unnecessary when β <; 1 and employing spectrum sensors cannot improve the network performances.

Cognitive radio systems are a promising solution to the spectrum scarcity problem but accurate modeling of both primary and secondary user activity, spectrum utilization, and system throughput are vital to achieve good performance in such systems. In this paper, we consider a set of primary users that are distributed in space based on a Poisson point process and demand for the available spectrum. We assess the effect of these demands on primary user activity, spectrum occupancy, and total system throughput under various subcarrier-request distributions and fading environments. The asymptotic mean number of active primary users and occupied subcarriers are analytically derived and evaluated further considering the primary network traffic and the average probability of miss-detection of an occupied subcarrier by a single sensing secondary user. It is seen that the average probability of miss-detection is a function of system traffic and the subcarrier-request distribution of primary users and that for extreme primary user traffic, the applied subcarrier-request distribution and total number of provided subcarriers cannot improve further the asymptotic sensing accuracy of the secondary user. Finally, the primary network and the secondary user throughputs in the presence of mutual interference due to imperfect detection of secondary users are investigated and their asymptotic values for large primary network traffic, primary user transmit power, and secondary user transmit power are analytically derived. The results are critically investigated, formulated as theorems and compared with simulations. It is observed that analytical and simulation results are in perfect agreement. It is shown that increasing the primary network transmit power benefits both the primary network and the secondary user throughputs.

The concept of channel capacity per unit cost was introduced by Verdu in 1990 to study the limits of cost-efficient wide-band communication. It was shown that orthogonal signaling can achieve the channel capacity per unit cost of memoryless stationary channels with a zero-cost input letter. This paper introduces a concept of secrecy capacity per unit cost to study cost-efficient wide-band secrecy communication. For degraded memoryless stationary wiretap channels, it is shown that an orthogonal coding scheme with randomized pulse position and constant pulse shape achieves the secrecy capacity per unit cost with a zero-cost input letter. For general memoryless stationary wiretap channels, the performance of orthogonal codes is studied, and the benefit of further randomizing the pulse shape is demonstrated via a simple example.

This paper presents the design of a robust beamforming scheme for a two-way relay network, composed of one multi-antenna relay and two single-antenna terminals, with the consideration of channel estimation errors. Given the assumption that the channel estimation error is within a certain range, we aim to minimize the transmit power at the multi-antenna relay and guarantee that the signal to interference and noise ratios (SINRs) at the two terminals are larger than a predefined value. Such a robust beamforming matrix design problem is formulated as a non-convex optimization problem, which is then converted into a semi-definite programming (SDP) problem by the S-procedure and rank one relaxation. The robust beamforming matrix is then derived from a principle eigenvector based rank-one reconstruction algorithm. We further propose a hybrid approach based on the best-effort principle to improve the outage probability performance, which is defined as the probability that one of two resulting terminal SINRs is less than the predefined value. Simulation results are presented to show that the robust design leads to better outage performance than the traditional non-robust approaches.

Cognitive Radio systems are a promising solution to the spectrum scarcity problem, but precise modeling of spectrum utilization is vital to the analysis and design of such systems. In this paper, we mathematically derive the Probability Mass Function (PMF) of the fraction of available subcarriers for the secondary users in an OFDMA based cognitive radio system for different requesting distributions. The PMF of the total number of requested subcarriers from all primary users is derived and the effect of the requesting distribution on the asymptotic spectrum availability for secondary users is studied. It is shown that if a requesting distribution is undesired, providing more subcarriers will not increase the spectrum availability for the secondary network.

Recently, there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as “secret writing on dirty paper”) to within half a bit.

Recently there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as “secret writing on dirty paper”) to within (1/2) log 3 bits.

We consider the problem of establishing reliable unicast connections across a communication network with nonuniform edge capacities. Our goal is to provide instantaneous recovery from single edge failures. With instantaneous recovery, the destination node can decode the packets sent by the source node even if one of the network edges fails, without the need of retransmission or rerouting. It has been recognized that the network coding technique offers significant advantages for this problem over standard solutions such as disjoint path routing and diversity coding. We focus on two cases of practical interest: 1) backup protection of a single flow that can be split into two subflows; and 2) shared backup protection of two unicast flows. We present an efficient network coding algorithm that operates over a small finite field (GF(2)). The small size of the underlying field results in a significant reduction in the computational and communication overhead associated with the practical implementation of the network coding technique. Our algorithm exploits the unique structure of minimum coding networks, i.e., networks that do not contain redundant edges. We also consider the related capacity reservation problem and present an approximation algorithm that finds a solution whose cost is at most two times more than the optimum.

Theindex codingproblem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks. An instance of the index coding problem includes a sender that holds a set of information messagesX={x1,...,xk}and a set of receiversR. Each receiver(x,H)inRneeds to obtain a messagex Xand has priorside informationconsisting of a subsetHofX. The sender uses a noiseless communication channel to broadcast encoding of messages inXto all clients. The objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers. In this paper, we analyze the relation between the index coding problem, the more general network coding problem, and the problem of finding a linear representation of a matroid. In particular, we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem. Our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem. Specifically, we show thatvector linear codesoutperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions.

Cognitive radios have a great potential to improve spectrum utilization by enabling secondary (unlicensed) users to opportunistically access the spectrum without disturbing the primary (licensed) users' communication. However, to assure acceptable QoS for secondary users without interfering with primary users several challenges must be overcome under physical constraints. Because of hardware constraints, secondary users can only sense a limited number of spectrum channels. Therefore a secondary user must wisely select the channels to be sensed to increase it's likelihood for successful data transmission. However if a secondary user takes up a greedy approach and disregards other secondary users in its channel selection, the whole secondary network would suffer in terms of aggregate throughput. Also because of the autonomous nature of secondary users, the search policy must be as decentralized as possible, i.e. secondary users should need almost no information of one another to operate. In this work we propose a search policy for secondary users in a cell based ad-hoc network and evaluate its performance (total primary and secondary throughput) as a function of different system parameters.

The concept of channel capacity per unit cost was introduced by Verdú in 1990 to study the limits of wideband communication. It was shown that an orthogonal coding scheme achieves the channel capacity per unit cost of memoryless stationary channels with a zero-cost input letter. This paper introduces the concept of secrecy capacity per unit cost to study wideband secrecy communications. For degraded memoryless stationary wiretap channels, it is shown that an orthogonal coding scheme achieves the secrecy capacity per unit cost with a zero-cost input letter. For general memoryless stationary wiretap channels, the performance of orthogonal codes is studied and lower and upper bounds on the secrecy capacity per unit cost are provided.

We study the problem of information flow in communication networks with noiseless links in which the dependency relations among the data flowing on the different network edges satisfy matroidal constraints. We present a construction that maps any given matroid to a network that admits vector linear network codes over a certain field if and only if the matroid has a multilinear representation over the same field. This new construction strengthens previous results in the literature and, thus, establishes a deeper connection between network coding and matroid theory. We also explore another, more general, mathematical construct referred to as FD-relation which is more suitable than matroids in capturing the dependency relations in general networks.

In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages X = {x1, …, xk} and a set of receivers R. Each receiver has some side information, known to the server, represented by a subset of X and demands another subset of X. The server uses a noiseless communication channel to broadcast encodings of messages in X to satisfy the receivers’ demands. The goal of the server is to find an encoding scheme that requires the minimum number of transmissions. We show that any instance of the Network Coding problem can be efficiently reduced to an instance of the Index Coding problem. Our reduction shows that several important properties of the Network Coding problem carry over to the Index Coding problem. In particular, we prove that both scalar linear and vector linear codes are insufficient for achieving the minimal number of transmissions.

This paper derives robust minimax estimators for a class of uncertain models. The uncertainty is described by a relative entropy constraint between the unknown joint distribution and a fixed nominal joint distribution. The maximization is addressed using variational methods, while the minimization is addressed using the concept of a sufficient statistic, which is an unnormalized version of the a posteriori density. The theory developed is applied to multipath fading wireless channels, to derive minimax envelope and phase estimates. Related results are also derived when the uncertainty shrinks to zero.

We present algorithms to suppress the asynchronous co-channel interference (CCI) in MIMO OFDM systems. The key challenge is that the cyclic prefix of the interference signal does not line up with that of the intended signal due to the asynchronous transmission in WLAN. Therefore, the orthogonality across the tones of the interference signal is destroyed and the conventional frequency domain minimum mean square error (MMSE) cancelation techniques that employ the interference channel response per tone can not work effectively. To suppress the asynchronous interference, we design an efficient estimator for the spatial covariance matrix of the interference using Cholesky decomposition and low-pass smoothing. Both a MMSE and a maximum a posteriori (MAP) receiver are derived based on the estimated interference statistics. Simulation results demonstrate the effectivity of our solution.

We present algorithms to suppress the asynchronous co-channel interference (CCI) in MIMO OFDM systems, which is becoming the dominant limiting factor in the performance of the emerging high-density WLANs. The key challenge is that the cyclic prefix of the interference signal does not line up with that of the intended signal due to asynchronous transmission in WLAN. Therefore, the orthogonality among the different tones of the interference signal is destroyed and conventional frequency domain minimum mean square error (MMSE) cancelation techniques that measure the interference channel response for each tone can not work effectively. To suppress the asynchronous interference, we design an efficient estimator to measure the interference spatial covariance matrix using Cholesky decomposition and low-pass smoothing. Both a MMSE and a maximum a posteriori (MAP) receiver are derived based on the estimated interference statistics. Simulation results demonstrate the effectiveness of our solution.

Let Aq(n, d) be the maximum order (maximum number of codewords) of a q-ary code of length n and Hamming distance at least d. And let A(n, d, w) that of a binary code of constant weight w. Building on results from algebraic graph theory and Erdos-ko-Rado like theorems in extremal combinatorics, we show how several known bounds on Aq(n,d) and A(n,d, w) can be easily obtained in a single framework. For instance, both the Hamming and Singleton bounds can derived as an application of a property relating the clique number and the independence number of vertex transitive graphs. Using the same techniques, we also derive some new bounds and present some additional applications.

We introduce several low complexity sub-optimal MIMO detection schemes based on the List-BLAST algorithm, which exhausts the constellation points in the first layer of a BLAST scheme to generate multiple candidate solutions from which the maximum likelihood solution is determined. The candidates can also be used as initial points for the space alternating generalized expectation-maximization (SAGE) algorithm to further improve performance. The proposed schemes can achieve close to optimal performance for both hard and soft output detection with lower complexity than that of the sphere detection in our simulation settings

In this paper, we consider a joint source-channel coding problem and minimize the end-to-end mean square error (MSE) distortion of a communication system through power allocation to the transmitted bits. This communication system consists of a quantizer with natural binary mapping and Binary Phase Shift Keying (BPSK) modulator at the transmitter and we consider the cases with and without coding. We show that there is an optimal transmit power allocation to the transmitted bits of the quantized word that minimizes MSE. In the first part of the paper, the case with no channel coding is considered with hard decision decoding at the receiver. The optimum power profile is determined analytically by using the Chernoff bound and through computer-based optimization methods. The optimum power allocation gives a constant MSE gain over the uniform power allocation for high SNRs. In the second part of the paper, (7,4) Hamming code with soft-decision decoding is considered. An upper bound on the MSE expression is derived and nearoptimum power allocation is obtained. It is observed that for lower SNRs, power is allocated only to the information bits showing that coding is not required while for higher SNRs, power is allocated to all the bits in a codeword and it gives a constant gain in MSE over the uniform power allocation.

We study the end-to-end distortion-delay tradeoff for a Gaussian source transmitted over a fading channel. The analog source is quantized and stored in a buffer until it is transmitted. There are two extreme cases as far as buffer delay is concerned: no delay and infinite delay. We observe that there is a significant power gain by introducing a buffer delay. Our goal is to investigate the situation between these two extremes. Using the recently proposed effective capacity concept, we derive a closed-form expression for this tradeoff. In order to characterize the convergence behavior, we derive an asymptotically tight upper bound for our tradeoff curve, which approaches the infinite delay lower bound polynomially. Numerical results demonstrate that introduction of a small amount of delay can save significant transmission power

We investigate the network coding problem in a certain class of minimal multicast networks. In a multicast coding network, a source S needs to deliver h symbols, or packets, to a set of destinations T over an underlying communication network modeled by a graph G. A coding network is said to be h-minimal if it can deliver h symbols from S to the destination nodes, while any proper subnetwork of G can deliver at most h — 1 symbols to the set of destination nodes. This problem is motivated by the requirement to minimize the amount of network resources allocated for a multicast connections. We show that surprisingly, minimal multicast networks have unique properties that distinguish them from the general case of multicast networks. In particular, we show that it is possible to determine whether a 2-minimal network has a routing solution (i.e., a solution without encoding nodes) in polynomial time, while this problem is NP-hard in general. In addition, we show that if a 2-minimal network is planar, then the minimum size of the required field for linear network codes is at most 3. Also, we investigate several structural properties of 2-minimal networks and generalize our results for h > 2.

In frequency-division duplex (FDD) systems, channel-state information (CSI) is estimated by the receiver and then fed back to the transmitter through a feedback link, which inevitably requires additional bandwidth and power. In this letter, we jointly study optimal bandwidth allocation between the data channel, modeled as a flat-fading multiple-input single-output (MISO) channel, and the feedback channel for maximum average throughput in the data channel using a beamforming scheme. We consider two models of the partial CSI at the transmitter (CSIT): the noisy CSIT, modeled as jointly Gaussian with the actual channel state, and the quantized CSIT. In the first model, we use distortion-rate theory to relate the CSIT accuracy to the feedback-link bandwidth. In the second model, we derive a lower bound on the achievable rate of the data channel based on the ensemble of a set of random quantization codebooks. We show that in the MISO flat-fading channel case, beamforming based on feedback CSI can achieve an average rate larger than the capacity without CSIT under a wide range of mobility conditions.

A Slepian-Wolf coding scheme for compressing two uniform memoryless binary sources using a single channel code that can achieve arbitrary rate allocation among encoders was outlined in the work of Pradhan and Ramchandran. Inspired by this work, we address the problem of practical code design for general multiterminal lossless networks where multiple memoryless correlated binary sources are separately compressed and sent; each decoder receives a set of compressed sources and attempts to jointly reconstruct them. First, we propose a near-lossless practical code design for the Slepian-Wolf system with multiple sources. For two uniform sources, if the code approaches the capacity of the channel that models the correlation between the sources, then the system will approach the theoretical limit. Thus, the great advantage of this design method is its possibility to approach the theoretical limits with a single channel code for any rate allocation among the encoders. Based on Slepian-Wolf code constructions, we continue with providing practical designs for the general lossless multiterminal network which consists of an arbitrary number of encoders and decoders. Using irregular repeat-accumulate and turbo codes in our designs, we obtain the best results reported so far and almost reach the theoretical bounds.

We study the ergodic sum-rate capacity of the fading MIMO broadcast channel which is used to model the downlink of a cellular system with N/sub t/ transmit antennas at the,base and K mobile users each having N/sub r/ receive antennas. Assuming perfect channel state information (CSI) for all users is available at the transmitter and the receivers, we evaluate the sum-rate capacity numerically using the duality between uplink and downlink. Assuming Nt K, we also derive both upper and lower bounds on the sum-rate capacity to study its increase rate due to multi-user diversity. Finally, we compare three transmission schemes which use the single-user-MIMO scheme (SU-MIMO), ranked known interference (RKI) and zero-forcing beamforming (ZFB), respectively, to transmit to a selected set of users in order to approach the sum-rate capacity. We show that both ZFB and RKI outperform SU-MIMO in a cellular downlink scenario. when many mobile users are present.

We present the trellis-coded code-division multiple-access (TC-CDMA) system based on a multisequence signaling, called orthogonal plane sequence modulation (OPSM), in correlated Rayleigh fading channels and derive its pairwise error probability with different degrees of channel state information. Numerical results show that the OPSM-based TC-CDMA system outperforms conventional convolutionally coded CDMA or TC-CDMA systems.

We study the constrained capacity of a multiple-input multiple-output (MIMO) fading channel with a phase-shift keying (PSK) input alphabet and show a uniform prior distribution is capacity achieving. An expression for the capacity is derived which requires a single expectation and can be evaluated easily through simulation. The simulations are facilitated by analytical expressions for the eigenvalues and eigenvectors of a required covariance matrix. The derived expression is used to provide good approximations to the capacity at low signal-to-noise ratios (SNRs) as well as to compare the input-constrained MIMO capacity to the unconstrained MIMO capacity.

We present a complex, full-rate quasi-orthogonal space-time block code for four transmit antennas. Using carefully tailored constellation phase rotations, we show that this code achieves full diversity for specialized PSK-based constellations. The optimal receiver for the new code decouples the symbol detection problem into pairs of symbols, thus greatly reducing complexity. Finally, we present and compare performance of the new code with several other codes in the literature. The new code is shown to perform as well as the best known code of its class.

We study optimal transmission strategies in terms of minimum outage probability for a fading channel with multiple transmit antennas and a single receive antenna. We consider two cases of imperfect channel state information (CSI) feedback: mean feedback and covariance feedback. In both cases, the optimum strategy is shown to be transmission of multiple data streams to the same directions as when maximizing the ergodic channel capacity, but with different power allocation strategies which are closely related to the target rate. In the mean feedback case, the optimal power allocation strategy is also related to the accuracy of the feedback CSI, which affects significantly the achievable outage capacity.

It has been proposed recently to replace the cyclic prefix (CP) in OFDM transmission by zero-padding (ZP); this guarantees symbol recovery even when channel nulls are located on a subcarrier. This, though, has the disadvantage that the simple DFT-based receiver does not perform well, but results have shown that if much higher complexity turbo demodulation is used, ZP-OFDM outperforms CP-OFDM. However, by viewing N-carrier OFDM as multicode CDMA with complex spreading codes from the N-PSK alphabet, one can apply to ZP-OFDM the numerous suboptimum multiuser receivers developed for CDMA. The performance of these receivers is dictated by the correlation properties of the IDFT matrix. Therefore, we propose to "modify" the IDFT matrix used to modulate the data in ZP-OFDM so that the resulting matrix possesses better correlation properties, and hence improved performance over multipath channels can be achieved. Simulation results verify the large gains in the uncoded performance of ZP-OFDM with modified IDFT matrix compared to CP-OFDM and ZP-OFDM with the IDFT matrix.

This paper presents a Slepian-Wolf coding of n correlated m-ary sources for LDPC codes. On applying the syndrome concept, multilevel codes with low-density parity-check (LDPC) codes can be used to approach the Slepian-Wolf limit at each level. The advantage of LDPC codes is that they can be designed for different correlation models between source outputs and the side information and approach the Slepian-Wolf limits. Specifically, for Slepian-Wolf coding of three sources, a design rule of rates for coding each source, which facilitates code design and allows multistage decoding was proposed.

A Slepian-Wolf coding scheme that can achieve arbitrary rate allocation among two encoders was outlined in the work of Pradhan and Ramchandran. Inspired by this work, we start with a detailed solution for general (asymmetric or symmetric) Slepian-Wolf coding based on partitioning a single systematic channel code, and continue with practical code designs using advanced channel codes. By using systematic IRA and turbo codes, we devise a powerful scheme that is capable of approaching any point on the Slepian-Wolf bound. We further study an extension of the technique to multiple sources, and show that for a particular correlation model among the sources, a single practical channel code can be designed for coding all the sources in symmetric and asymmetric scenarios. If the code approaches the capacity of the channel that models the correlation between the sources, then the system will approach the Slepian-Wolf limit. Using systematic IRA and punctured turbo codes for coding two binary sources, each being independent identically distributed, with correlation modeled by a binary symmetric channel, we obtain results which are 0.04 bits away from the theoretical limit in both symmetric and asymmetric Slepian-Wolf settings.

We generalize our previous work and present a generic block code design based on a metric-spectrum. That is, based on the communication system and the metric dominating its pairwise error probability, we employ various code search methods to come up with good codes for the corresponding communication problem. Besides generalizing the design methodology, we present also new good complex codes for the AWGN channel as well the coherent Rayleigh fading channel, based on existing and new unitary matrices.

This paper considers a general multiterminal (MT) system, which consists of L encoders and P decoders. Let X/sub 1/,..., X/sub L/ be memoryless, uniform, correlated random binary vectors of length n, and let x/sub 1/,..., x/sub L/ denote their realizations. Let further /spl Sigma/ = {1,...,L}. The i-th encoder compresses X/sub i/ independently from other encoders. The j-th decoder receives the bitstreams from a set of encoders /spl Sigma//sub j//spl sube/ /spl Sigma/ and jointly decodes them. It should reconstruct the received source messages with arbitrarily small probability of error. To construct a practical coding scheme for this network, we exploit the fact that such a network can be split into P subnetworks, each being regarded as a Slepian-Wolf (SW) coding system with multiple sources. This SW subnetwork consists of a decoder which receives encodings of all X/sub k/'s such that k/spl isin//spl Sigma//sub sw//spl sube//spl Sigma/ and attempts to reconstruct them perfectly. Based on (V. Stankovic et al. 2004), we first provide a code design for this setting, and then extend it to the general case.

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Due to complexity considerations, synchronous multiple-access schemes, such as TDMA, CDMA, and OFDM, have been mainly based on orthogonal (unitary) transformations of the multiuser signal, which makes the receiver less complex, at the cost of bandwidth efficiency. In future systems, however, it seems that the limiting factor will not be processing power, but rather bandwidth. Therefore there is a need for redesigning multiple-access schemes, or rather unifying their design, in a multiple-access scheme that is bandwidth efficient. The efficiency in the bandwidth can he achieved by applying non-unitary transformations to the multiuser signal such that the multiuser interference can he handled by a reasonably complex receiver. In this paper we attempt to unify the design of the aforementioned multiple-access schemes to a scheme that efficiently utilities the bandwidth, given that receivers of reasonable complexity can be deployed.

For the additive white Gaussian noise channel, we consider the problem of frame synchronization for coded systems. We present an algorithm that takes advantage of soft information provided by a soft decoder to produce an enhanced estimate of the frame boundary. To reduce complexity, a companion algorithm is introduced that is a hybrid of the optimal uncoded frame synchronizer introduced by Massey and the list synchronizer introduced by Robertson. The high-complexity coded maximum-likelihood frame synchronizer used by Robertson will accordingly be replaced by our algorithm, which operates on decoder-provided soft decisions. The algorithm begins by obtaining a list of high-probability starting positions via the log-likelihood function of the optimal uncoded frame synchronizer. Then, a test /spl delta/ is used to decide if the decision of the optimal uncoded frame synchronizer is sufficient, or whether list synchronization is required. If the test chooses in favor of using the optimal uncoded synchronizer, the estimate is obtained with relative ease. Otherwise, list synchronization is performed, and statistics provided by the decoder are used to resolve the frame boundary. Monte Carlo simulations demonstrate that the frame-synchronization-error rate (the probability of the synchronizer making an error) achieves the lower bound for signal-to-noise ratio values exceeding 1 dB.

We consider joint channel estimation and data detection in uplink asynchronous code-division multiple-access systems employing aperiodic (long) spreading sequences in the presence of unknown multipath fading. Since maximum-likelihood (ML) sequence estimation is too complex to perform, multiuser receivers are proposed based on the sequential expectation-maximization (EM) algorithm. With the prior knowledge of only the signature waveforms, the delays and the second-order statistics of the fading channel, the receivers sequentially estimate the channel using the sequential EM algorithm. Moreover, the snapshot estimates of each path are tracked by linear minimum mean-squared error filters. The user data are detected by a ML sequence detector, given the channel estimates. The proposed receivers that use the exact expressions have a computational complexity O(2/sup K/) per bit, where K is the number of users. Using the EM algorithm, we derive low-complexity approximations which have a computational complexity of O(K/sup 2/) per bit. Simulation results demonstrate that the proposed receivers offer substantial performance gains over conventional pilot-symbol-assisted techniques and achieve a performance close to the known channel bounds. Furthermore, the proposed receivers even outperform the single-user RAKE receiver with Nyquist pilot-insertion rate in a single-user environment.

We present an efficient algorithm to compute the distance spectrum of a general finite intersymbol interference (ISI) channel, whose complexity is lower than those of existing methods. Closed-form expressions are derived for both input-output Euclidean distance enumerators and asymptotic distance spectrum shapes for 2-tap and 3-tap ISI channels. Coded and/or precoded ISI channels are also discussed.

We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's (1999) simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2.

We analyze the performance of space-time trellis codes over shadowed Rician fading channels. The shadowed Rician channel is a generalization of the Rician model, where the line-of-sight path is subjected to a lognormal transformation due to foliage attenuation, also referred to as shadowing. Using the moment generating function method, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis coded systems operating over this channel. The asymptotic analysis of PEP shows that the design criteria of space-time trellis codes proposed for Rayleigh fading still hold when used over shadowed Rician channels. We also present simulation results for bit-error rate performance under various degrees of shadowing.

We present analytical performance results for space-time trellis codes over spatially correlated Rayleigh fading channels. Bit-error-probability estimates are obtained based on the derivation of an exact pairwise error probability expression using a residue technique combined with a characteristic function approach. We investigate both quasi-static and interleaved channels and demonstrate how the spatial fading correlation affects the performance of space-time codes over these two different channel models. Simulation results are also included to confirm the accuracy of analytical estimates.

It is shown how conventional parallel (turbo) and serial concatenated convolutional codes can be used to compress close to the Slepian-Wolf limit for the correlated binary sources. Conventional refers to codes already used in channel coding. Focusing on the asymmetric case of compression of an equipolarable memoryless binary source with side information at the decoder, the approach is based on modeling the correlation as a channel and using syndromes. The encoding and decoding procedures are explained in detail. The performance achieved is seen to be better than the recently published results using nonconventional turbo codes and close to the Slepian-Wolf limit.

We study the effects of quantization at the output of a binary-input additive white Gaussian noise (BIAWGN) channel on the performance of low-density parity-check (LDPC) codes. The LDPC decoder works with unlimited precision. The quantizer design is based on either optimizing the equivalent channel capacity, cutoff-rate, mean-squared error (MSE) or the LDPC code convergence. All the approaches are compared in search of the most appropriate design criterion.

In this paper, we study the binary code design problem for the fading channel with noncoherent maximum-likelihood detection. The /spl rho/-spectrum (i.e. all possible pairwise absolute cross-correlations) provides a way to define the optimal codes, based on the union bound on the error probability, as the codes achieving the optimal /spl rho/-spectrum for some code rate. We introduce some limited search methods based on the /spl rho/-spectrum, including a nested search, which for some code rates yields optimal codes. With our nested search, good codes were obtained easily up to code rate 12/n, n/spl les/4096. The codes developed offer good performance in the fading channel and can be used in place of the Hadamard-Walsh codes in synchronous CDMA systems to increase system capacity.

An optimal transmission strategies in terms of minimum outage probability for a fading channel with multiple transmit antennas and a single receive antenna is studied. We consider two cases of imperfect channel state information (CSI) feedback, mean feedback and covariance feedback. In both cases the optimum strategies are shown to be transmission of multiple data streams to the same directions as when maximizing the ergodic channel capacity, but with different power allocation strategies related to the target rate. Moreover, the accuracy of the feedback CSI affects significantly the achievable outage capacity in the case of mean feedback; the outage capacity achieved in the case of covariance feedback is much lower than that in the case of mean feedback. Therefore, accurate tracking of the instantaneous CSI is essential in maximizing outage capacity.

We show how concatenated (convolutional) codes can be used to compress close to the Wyner-Ziv limit for binary sources. Focusing on the case of lossy compression of an equiprobable memoryless binary source with side information at the decoder, the approach is based on nested binary linear codes, which is the extension of Wyner's lossless compression scheme to the lossy case proposed by Shamai, Verdu and Zamir. Based on our previous work on lossless compression with concatenated codes, we are able to combine the only two previously suggested nested schemes into a novel turbo scheme with improved performance. Our scheme can come within 0.09 bits from the theoretical limit, which to our knowledge is the first result ever reported for the binary Wyner-Ziv problem.

The wireless industry's demand for higher data rates from cellular CDMA systems, makes the use of higher order modulation (e.g. 16-QAM) a necessity. Unfortunately, the high data rate schemes of the current 3G cellular standards don't work well in wireless channels due to the poor equalization of the highly dense constellations. In this work we look at the performance of a fully-loaded CDMA system when we remove the spreading, if not the scrambling.

We introduce a scheme that achieves a diversity gain for coded systems under static fading conditions by using multiple antennas and random signal mapping. In a two-antenna system, the bit-error rate performance of the proposed scheme approaches that of Alamouti's scheme when the channel is perfectly known. In the presence of channel mismatch, the proposed scheme outperforms Alamouti's scheme significantly. It is shown that, as the number of transmit antennas N goes to infinity, the effective channel for the introduced scheme behaves as if it were perfectly interleaved (i.e., as if the fading was independent). When N is small, further performance gain can be achieved by expanding the original signal constellation.

Faster-than-Nyquist signaling introduces intersymbol interference, but increases the bit rate while preserving the signaling bandwidth. For sinc pulses, it has been established that with a small increase in the signaling rate beyond the Nyquist rate, there is no reduction in the minimum Euclidean distance for binary signaling. We generalize these observations to the family of raised-cosine pulses. The structure of the error events that reduce the minimum distance is examined, and constrained coding ideas are suggested that theoretically allow even faster signaling. Then we propose ways of achieving these gains practically by designing appropriate constrained codes and through equalization and iterative joint equalization and decoding (turbo equalization).

We investigate maximum-likelihood (ML) sequence estimation for space-time block coded systems without assuming channel knowledge. The quadratic form of the ML receiver in this case does not readily lend itself to efficient implementation. However, under quasi-static channel conditions, the likelihood function reduces to a simple form similar to the classical correlation receiver in matrix notation. It also allows the development of a recursive expression that can be easily implemented by a Viterbi-type algorithm with a reasonable complexity. Although the receiver is suboptimum for the nonstatic case, its performance is close to the optimum for a range of signal-to-noise ratios.

We study channel estimation for orthogonal frequency-division multiplexing (OFDM) systems utilizing transmitter diversity and operating over multipath fading channels. Two expectation-maximization (EM)-type algorithms are introduced and compared with each other in terms of convergence rate. At each iteration and for every OFDM link, the EM-type algorithms partition the problem of estimating a multi-input channel into independent channel estimations for each transmit-receive antenna pair, therefore avoiding the matrix inversion encountered in the joint least-square estimation. The EM-type algorithms can also be used to efficiently implement a recently proposed algorithm, termed the significant-tap-catching estimator, so that the system performance is more robust to different multipath channel delay profiles.

It is shown how low-density parity-check (LDPC) codes can be used as an application of the Slepian-Wolf (1973) theorem for correlated binary sources. We focus on the asymmetric case of compression with side information. The approach is based on viewing the correlation as a channel and applying the syndrome concept. The encoding and decoding procedures, i.e. the compression and decompression, are explained in detail. The simulated performance results are better than most of the existing turbo code results available in the literature and very close to the Slepian-Wolf limit.

According to the Slepian-Wolf theorem [1], the output of two correlated sources can be compressed to the same extent without loss, no matter if they communicate with each other or not, provided that the decompression takes place at a common decoder having both compressed outputs available. In this paper, as an application of the Slepian-Wolf theorem, an advanced distributed source coding scheme for correlated images is presented. Assuming that the correlated image is a noisy version of the original, the scheme involves modulo encoding of the pixel values and encoding (compression) of the resulting symbols with binary and nonbinary turbo-codes, so that rate savings are achieved practically without loss.

Combining Orthogonal Frequency Division Multiplexing (OFDM) with transmitter diversity can be used for capacity improvement in high-rate wireless data communication systems. For coherent detection in such systems, channel state information (CSI) is required. In this paper we investigate a Space-Alternating Generalized Expectation-Maximization (SAGE) algorithm to iteratively estimate the channel impulse responses associated with multiple transmitters and the receiver. The performance of the estimator is compared with a previously proposed Expectation-Maximization (EM) based algorithm in terms of convergence rate.

We introduce a space-time block-coded orthogonal frequency-division multiplexing (MC-OFDM) scheme for frequency-selective fading channels which does not require channel knowledge either at the transmitter or at the receiver. The decoding algorithm is based on generalized maximum-likelihood sequence estimation. Due to the assumed orthogonality structure of STBC, the decoding rule reduces to a single step. Its form also allows the derivation of a recursive expression, which can be easily implemented by a Viterbi-type algorithm. We investigate the performance of the proposed scheme over two-tap Rayleigh fading channels. Simulation results show the performance of the proposed recursive-type receiver to be near optimum.

In this paper, analytical performance results for space-time trellis codes over Rayleigh fading channels are presented. Bit error probability estimates are obtained, based on the derivation of an exact pairwise error probability expression through a residue technique combined with characteristic function approach. We investigate both quasi-static and interleaved channels as well as the effect of spatial fading correlation on the performance of space-time codes in both channels. Simulation results are also included to confirm the accuracy of analytical estimates.

We introduce a novel signal set defined over a signal space that consists of L (L/spl ges/2) orthogonal planes, and a quasi-synchronous trellis-coded code-division multiple-access (TC-CDMA) system based on it. The proposed scheme makes efficient use of the available processing gain to improve power and/or bandwidth efficiency for practical multiuser interference environments. Having a multiplanar signal constellation structure, the proposed scheme provides several options for a given required data rate, which makes it better adapted to dynamic channel conditions. Analytical bounds and simulation results indicate that at practical error rates and 2 b/s/Hz the proposed scheme is approximately 1.2 dB better than a TC-CDMA system based on 8-PSK, and 3 dB better at 3 b/s/Hz compared to TC-CDMA using 16-QAM. Additionally, the proposed system is approximately 1 dB better than a multicoded system using two signature sequences per user.

Much of the work on turbo decoding assumes that the decoder has access to infinitely soft (unquantized) channel data. In practice, however, a quantizer is used at the receiver and the turbo decoder must operate on finite precision, quantized data. Hence, the maximum a posteriori (MAP) component decoder which was designed assuming infinitely soft data is not necessarily optimum when operating on quantized data. We modify the well-known normalized MAP algorithm taking into account the presence of the quantizer. This algorithm is optimum given any quantizer and is no more complex than quantized implementations of the MAP algorithm derived based on unquantized data. Simulation results on an additive white Gaussian noise channel show that, even with four bits of quantization, the new algorithm based on quantized data achieves a performance practically equal to the MAP algorithm operating on infinite precision data.

This paper evaluates two-dimensional turbo product codes based on single-parity check codes (TPC/SPC) and low-density parity check (LDPC) codes for use in digital magnetic recording systems. It is first shown that the combination of a TPC/SPC code and a precoded partial response (PR) channel results in a good distance spectrum due to the interleaving gain. Then, density evolution is used to compute the thresholds for TPC/SPC codes and LDPC codes over PR channels. Analysis shows that TPC/SPC codes have a performance close to that of LDPC codes for large codeword lengths. Simulation results for practical block lengths show that TPC/SPC codes perform as well as LDPC codes in terms of bit error rate, but possess better burst error statistics which is important in the presence of an outer Reed-Solomon code. Further, the encoding complexity of TPC/SPC codes is only linear in the codeword length and the generator matrix does not have to be stored explicitly. Based on. the results in the paper and these advantages, TPC/SPC codes seem like a viable alternative to LDPC codes.

We introduce an adaptive band-selection (ABS) scheme for Multi Carrier-Code Division Multiple Access (MC-CDMA) systems to improve system capacity. Instead of using all subcarriers, mobile stations transmit message data only through the selected frequency bands based on band-selection coefficients from the base station. By using the adaptive band-selection scheme, ABS MC-CDMA systems accommodate more users than MC-CDMA systems that use all frequency bands for message data transmission. Due to the time-varying wireless channel conditions and dynamic power allocations, band-selection coefficients should be adaptively determined at the base station every update period. In our ABS MC-CDMA systems, the processing gain, the transmitted power and the data rate depend on the number of selected bands. Under the assumption that the total transmission power and the total amount of transmission data are the same for both MC-CDMA systems and ABS MC-CDMA systems, SNR behaviors are investigated and BER performances are presented in terms of the number of users and the normalized Doppler frequencies.

Following the trend of turbo codes and low density parity check (LDPC) codes, single-parity turbo product codes (TPC/SPC) are being seriously considered for application in future high-density recording systems. Recent work on TPC/SPC codes has focused on ideal partial response channels with additive white Gaussian noise. This work extends the investigation to a more realistic equalized Lorentzian channel model where imperfect channel shaping, colored noise and recording density effect are taken into consideration. The effect of precoding is discussed and the interleaving gain is quantified. Simulation results of the turbo decoding system with both channel models are presented. A comprehensive evaluation is conducted, including BER performance, code rate selection, equalization targets and error statistics, which demonstrate TPC/SPC codes to be a promising candidate for future high-density recording systems.

Product accumulate (PA) codes were proposed and shown by Li, Narayanan and Georghiades (see Proc. Intl.. Symp. Inform. Theory, Washington DC, p.122-22, June 2001, and IEEE Tran. Info. Theory) to be a class of simple and provably good codes for rate R/spl ges/1/2. This work investigates the generalized product accumulate (GPA) codes which have rates over the entire range and which are also "good" both in the maximum likelihood (ML) sense and under the iterative approach. Analysis concentrates on the weight distribution over the code ensemble, the ML bounds, and the existence and computation of threshold phenomenon in the iterative decoding. A tight upper bound due to Divsalar (see Proc. 1998 Allerton Conf. Commun. and Control, Sept. 1998, p.201-10) and the thresholds computed using density evolution are examined. Simulations are presented and evaluated, especially for rate R/spl les/1/2.

This paper proposes an efficient graph-based sum-product algorithm for decoding 1/(1+D/sup n/) code, whose Tanner (1981) graph is cycle-free. A rigorous proof is given which shows the proposed algorithm is equivalent to the MAP decoding implementing the BCJR algorithm, but with a lower complexity magnitude. The paper presents an explicit example which confirms the claim that the sum-product algorithm is optimal on cycle-free graphs. A parallel realization is then discussed and shown to resemble low density parity check (LDPC) decoding. The paper further proposes a min-sum algorithm which is equivalent to the max-log-MAP algorithm. Prospective applications which can take advantage of the proposed decoding algorithms are discussed and simulations are provided.

Most current space-time block codes are designed based on an orthogonality principle. By relaxing the orthogonality requirement, it is possible to construct new codes with higher throughput efficiency. In this paper, new non-orthogonal space-time block codes for three transmit antennas are proposed, achieving throughput rates larger than those of currently known orthogonal designs. The proposed codes are found through a code search based on the rank criterion, determinant criterion and rank distribution. Performance results through Monte Carlo simulations demonstrate that there is a trade-off between the error-rate, diversity order and throughput rate.

We study channel estimation for OFDM systems utilizing transmitter diversity and operating over multipath fading channels. An expectation-maximization (EM) based estimation algorithm is introduced and compared to least-squares based estimation algorithms. At each iteration and for every OFDM link, the EM algorithm partitions the problem of estimating a multi-input channel into independent channel estimations for each transmit-receive antenna pair. It is shown that the EM algorithm is more robust to multipath channel delay profile variations and can be implemented more efficiently compared to a previously proposed algorithm.

We investigate the performance of low density parity check (LDPC) codes, single-parity turbo product codes (TPC/SPC) and multi-parity turbo product codes (TPC/MPC) over various partial response channels (PR) encountered in magnetic and magneto-optical (MO) recording systems, like PR4/EPR4 and PR1/PR2 channels. The codes have similarity in structures and can be decoded using simple message-passing algorithms. We show that the combination of a TPC/SPC code and a precoded PR channel results in good distance spectrum due to interleaving gain. Density evolution is then used to compute the thresholds for TPC/SPC and LDPC codes over PR channels. Through analysis and through simulations, we show the three types of codes yield comparable bit error rate performance with similar complexity, but they exhibit quite different error statistics, which in turn may result in sharp differences in block failure rate after the Reed-Solomon error correction code (RS-ECC).

A new class of codes, named product accumulate codes, which are the concatenation of an outer product code and an inner rate-1 differential encoder (or accumulator) is proposed. We show that these codes can perform within a few tenths of a dB from the Shannon limit for rates/spl ges/1/2. For practical block lengths, these codes provide similar performance to turbo codes but with significantly lower decoding complexity.

We present results on multipath channel estimation and detection for space-time coded systems used in conjunction with orthogonal frequency-division multiplexing (OFDM). An expectation-maximization (EM) based algorithm is introduced and is shown to be more robust to multipath channel delay profile variations and can be implemented more efficiently compared to a recently proposed alternative algorithm at similar or better performance.

Three space-time block-coding schemes with two transmit antennas for frequency-selective fading channels are described and compared. The three schemes implement the symbol-level Alamouti scheme (see Alamouti, S., IEEE Journal on Selected Areas in Communications, p.1451-8, 1998) developed for flat-fading channels at a block level either in the time or frequency domains. Receiver structures that aim at exploiting the spatial diversity offered by the two transmit antennas and the temporal diversity offered by the channel frequency selectivity are presented. The three schemes are applied to the EDGE TDMA system and their performance compared on a typical urban channel under both perfect and estimated channel conditions at the receiver.

In previous work on decoding space-time codes, it is either assumed that perfect channel state information (CSI) is present, or a channel estimate is obtained using pilot symbols and then used as if it were perfect to extract symbol estimates. In the latter case, a loss in performance is incurred, since the resulting overall receiver is not optimal. We look at maximum-likelihood (ML) sequence estimation for space-time coded systems without assuming CSI. The log-likelihood function is presented for both-quasi-static and nonstatic fading channels, and an expectation-maximization (EM)-based algorithm is introduced for producing ML data estimates, whose complexity is much smaller than a direct evaluation of the log-likelihood function. Simulation results indicate the EM-based algorithm achieves a performance close to that of a receiver which knows the channel perfectly.

A new approach to sequence estimation is proposed and its performance is analyzed for a number of channels of practical interest. The proposed approach, termed the slowest descent method, comprises as a special case the zero-forcing equalizer for intersymbol interference channels and the decorrelator for the multiuser detection problem. The latter two methods quantize the unconstrained sequence that maximizes the likelihood function. The proposed method can be viewed as a generalization of these two methods in two ways. First, the unconstrained maximization is extended to nonquadratic log-likelihood functions; second, the decorrelator estimate can be "refined" by comparing its likelihood to a set of discrete-valued sequences along mutually orthogonal lines of the least decrease in the likelihood function. The gradient descent method for iterative computation of the line of least likelihood decrease (i.e., slowest likelihood descent) and its relationship to the expectation-maximization (EM) algorithm for unconstrained likelihood maximization is discussed. The slowest descent method is shown to provide a performance comparable to maximum-likelihood for a number of channels. These problems can be described by either quadratic or nonquadratic log-likelihood functions.

A merit factor based on the sequence autocorrelation function, whose minimization leads to the reduction in the Cramer-Rao lower bound (CRLB) for the variance of "two-sided" intersymbol interference (ISI) channel estimation is introduced. Pairs of binary pilot symbol sequences (a preamble and a postamble) for channel estimation are jointly designed to minimize this merit factor. Given that the number of channel taps is L and the length of a pilot symbol sequence is (N+L-1), where N/spl ges/L, we distinguish between the case when N is even and the case when it is odd. For even N, we show that complementary sequences not only minimize the merit factor, but also the CRLB. For a subset of odd N we construct almost-complementary periodic sequence pairs that minimize the merit factor. The optimal pilot symbol block signaling requires alternating between two (in most cases) different binary sequences that form the merit-minimizing pair.

We introduce a novel modulation signal set defined over a signal space that consists of L Euclidean signal planes, and the synchronous trellis-coded CDMA system based on it. Whereas conventional schemes utilize a limited number of orthogonal sequences due to delay and power control error, this scheme fully and efficiently utilizes the N orthogonal signature sequences (i.e. the processing gain N) such that power and/or bandwidth efficiency is improved. The proposed scheme could be highly adaptable to the dynamic channel conditions, because for a single data rate we can choose the best signal constellation from a multi-planar signal space.

We apply a simple transmit diversity technique to downlink multicarrier CDMA (MC-CDMA) systems. The resulting diversity on each subcarrier improves orthogonality among users which is distorted by the subcarriers' multipath fading. Accordingly, the diversity suppresses multiuser interference. For equal-gain-combining (EGC) receivers, both theoretical analysis and simulation results show that interference is approximately reduced by half compared to MC-CDMA without space diversity. For the orthogonality-restoring combining (ORC) receiver, simulation results show that it suppresses noise amplification while rejecting multiuser interference.

Turbo coding is one of the most powerful techniques for enhancing the performance of next-generation wideband systems. In time-variant wireless fading channels, pilot symbol assisted modulation (PSAM) is a useful method that enables coherent demodulation. In this paper, we develop an iterative joint channel-data estimation receiver structure for coded PSAM systems in a fading environment, which exploits the power of both techniques. The key innovation in the proposed receiver is a low-complexity soft channel estimator, which divides a processing block into overlapped cells and performs maximum a posteriori (MAP) sequence estimation and MMSE filtering based on the received signal and extrinsic information delivered by the soft channel decoder. Moreover, the refined channel extrinsic information obtained in one cell is passed to subsequent cells to enhance estimation of the fading process. During iterations, code extrinsic information is sent to channel estimator by soft channel decoder and updated channel estimation is sent back to soft channel decoder to achieve successively refined estimate of the users' signal. The soft channel estimator has a complexity of O(2/sup W//W) per bit, where W is the cell size. Simulation results demonstrate that for turbo-coded PSAM systems under time-variant fading, the proposed receiver, at a low complexity, i.e. W/spl les/7, offers significant performance gains over the non-iterative receiver and two other estimation schemes.

In this paper, a computationally efficient algorithm is presented for joint maximum likelihood (ML) timing and carrier phase estimation of OFDM systems employing M-PSK modulation scheme with additive Gaussian noise, based on the expectation-maximization (EM) algorithm. A nondata-aided (NDA) scheme is considered for the joint timing and phase synchronizer which maximizes the low SNR limit of the likelihood function averaged over the M-PSK signal constellation. For this, an EM algorithm is derived which estimates the timing offset and the phase rotations of each subcarrier iteratively and which converges to the true ML estimation of the unknown timing and phase. It is shown that the algorithm becomes independent of the signal-to-noise ratio for both low and high SNR cases. The algorithm is applied to the QPSK modulated OFDM systems and it is concluded that for SNR values greater than 10 dB the convergence is achieved in first iteration and for SNR values less than 10 dB, at most in three iterations. It is also concluded that the convergence is independent of the initial starting points.

Channel coding is an integral part of most data communication systems. However, most existing carrier synchronization algorithms do not take advantage of the redundancy introduced in the data stream by the code and operate at an uncoded SNR which can be significantly lower than the coded SNR. Thus, whereas it used to be the case that if detection could be achieved reliably, so could synchronization, this may not be true any more for heavily coded systems. We introduce an approximate maximum likelihood estimator that incorporates the code structure in obtaining phase estimates. Simulation results show the performance of the introduced algorithm is significantly better than those which do not make use of the code structure.

We introduce a new scheme that achieves a diversity gain for coded systems under static fading conditions by using multiple antennas and random signal mapping. It is shown that as the number of transmit antennas N goes to infinity, the effective channel behaves as if it were perfectly interleaved (i.e. as if the fading was independent). When N is small, a further performance gain can be achieved by expanding the original signal constellation. Simulation results show that N/spl ap/8 is enough to achieve close to the performance of a perfectly interleaved system.

Multiuser detection and turbo coding are two of the most powerful techniques for enhancing the performance of next-generation wideband CDMA systems. In this paper, we develop an iterative multiuser receiver structure for turbo-coded CDMA systems with aperiodic spreading sequences in a multipath fading environment, which exploits the power of both techniques. The key innovation in the proposed receiver is a low-complexity soft multiuser detector which uses the same decision statistic as the conventional RAKE receiver and performs soft-interference cancellation and instantaneous MMSE filtering. During iterations, extrinsic information is computed and exchanged by the soft multiuser detector and a bank of modified turbo decoders, to achieve successively refined estimate of the users' signal. The soft multiuser detector has a complexity of O(K/sup 2/) per bit per user, where K is the number of users. A single-user receiver which employs a soft RAKE detector followed by a turbo decoder is also considered. Simulation results demonstrate that under various channel impairment, such as multiple-access interference, multipath dispersion and time-variant fading, the proposed multiuser receiver offers significant performance gain over the single-user RAKE receiver. Moreover, it is seen that the turbo multiuser receiver in a multiuser environment even outperforms the single-user RAKE receiver in a single-user environment, because the RAKE receiver neglects intersymbol interference.

Frequency offset due to Doppler shift and/or oscillator instabilities degrade the receiver performance. A family of frequency detectors for frequency offset estimation and compensation in digital receivers is introduced. The proposed detectors are best suited for frequency offset compensation of a subclass of binary continuous phase modulation with h=1/2 that includes modulation schemes with nonnegative frequency pulses. For the considered modulation schemes, the modulation-induced self-noise term is absent from the variance of the frequency estimate. The estimator is nondata- and nontiming-aided and its estimation range is either half or a quarter of the bit rate (R). With larger frequency offsets, the estimators that have a /spl plusmn/R/2 estimation range introduce a frequency ambiguity of R that is of no relevance to the performance of a differential detection based receiver.

We consider a geometric view of multiuser detection and present results on the problem of efficient computation of the optimal decision regions (Voronoi diagram) for synchronous direct-sequence code division multiple access (DS/CDMA). Among other results, it is shown that Verdu's (1986) algebraic notion of "indecomposable error sequences" relates directly to the geometric construction of the Voronoi diagram for multiuser detection. Based on the presented geometric results we introduce two multiuser detectors whose performance compares favorably to some popular existing detectors.

A maximum likelihood (ML) estimation algorithm is derived for carrier synchronization in OFDM systems with MPSK modulation. The algorithm derived is nondecision-aided (NDA) and maximizes the low SNR limit of the likelihood function averaged over the MPSK signal constellation. It is also shown that for sufficient small SNR the ML phase estimator obtained reduces to the familiar Mth order power synchronizer which belongs to the class of NDA feedforward carrier synchronizers introduced earlier in the literature. Its mean-squared performance is obtained analytically and compared with simulation results. We observe that the resulting algorithm generates very accurate estimation even when the phase offset is high, that the self noise is absent and the performance of the NDA algorithm is basically the same as the Cramer-Rao bound for moderate to high SNR. Finally we note that the error variance derived for the mean-squared performance of this NDA ML synchronizer is an extension of the approximate variance formula of Moeneclaey and de Jonghe (1994) for M-PSK constellations.

An iterative pilot symbol aided procedure for detection in multipath fading channels that does not neglect intersymbol interference (ISI) and achieves diversity combining with unresolved signal path components is introduced. The algorithm resolves the received signal into components corresponding to each path. The estimated components are combined for obtaining the next sequence estimate, and, thus, no signal energy is lost. The proposed approach attempts iterative unconstrained maximization of the likelihood function using the expectation-maximization (EM) algorithm. The EM solution is based on the approach to parameter estimation for superimposed signals introduced by Feder and Weinstein (1988). It allows for symbol-by-symbol maximization in the M-step for orthogonal signaling pulses.

Maximum-likelihood estimation of phase and frequency offset involves the maximization of a nonlinear likelihood function. We develop an estimator for carrier acquisition by linearizing the likelihood-function, and show that its performance is close to the Cramer-Rao bound (CRB). The estimator is then extended to blind frequency acquisition and combined with testing to eliminate unlikely hypotheses. With proper modeling of the likelihood resulting from the blind search, simulations show that the algorithm quickly rejects all but the correct frequency hypothesis.

We investigate the synchronization properties of slot-synchronized multipulse pulse position modulation (MPPM) sequences. We derive a bound on the probability of MPPM symbol synchronization and identify synchronizable MPPM symbols, which, when periodically inserted in the data stream, can remove an observed performance floor.

We look at multiple-track detection for magnetic recording systems that use array heads to write and read over multiple tracks simultaneously. The recording channel is modeled as having intersymbol interference (ISI) in the axial direction, and intertrack interference (ITI) in the radial direction. Optimum multihead and single-head detectors are derived and analyzed in terms of error-probability performance for various levels of intertrack interference. Among other results, it is seen that for a range of ITI levels, codes designed to increase distance in single-head systems can provide the same coding gains for multihead systems.

A constant need for ever-increasing throughputs through fixed bandwidths, fueled by several high-speed applications (such as digital TV), has pushed system designers toward more throughput-efficient modulation schemes. Because of their relatively good performance, large quadrature amplitude modulation (QAM) constellations are being used in many of these applications. One of the problems associated with the use of large QAM constellations is that of carrier acquisition, which, for efficiency reasons, must often be done without the use of a preamble. The problem is further complicated for cross constellations, for which the high signal-to-noise ratio (SNR) corner points used by some simple carrier phase estimators are not available. We derive simple algorithms for carrier phase acquisition that can be used for both square and cross constellations, and compare their performance to those of the maximum-likelihood (ML), the fourth-power estimator, and a modified fourth-power estimator, obtained by considering a reduced constellation. The introduced algorithms convert the problem of carrier phase estimation into one of estimating the mode of an underlying distribution. An expression for this underlying distribution is also obtained. The results obtained indicate that the introduced algorithms significantly outperform the fourth-power estimator for moderate to high SNRs, especially when cross constellations are used.

The expectation-maximization (EM) algorithm was first introduced in the statistics literature as an iterative procedure that under some conditions produces maximum-likelihood (hit) parameter estimates. In this paper we investigate the application of the EM algorithm to sequence estimation in the presence of random disturbances and additive white Gaussian noise. As examples of the use of the EM algorithm, we look at the random-phase and fading channels, and show that a formulation of the sequence estimation problem based on the EM algorithm can provide a means of obtaining ML sequence estimates, a task that has been previously too complex to perform.

We investigate frame synchronization algorithms for direct detection multi-pulse pulse position modulation (MPPM) optical communication systems. The optimal rules (in a maximum likelihood sense) are derived, approximations to them that are computationally easier to implement are identified, and upper bounds on the synchronization probability are obtained. It is seen that the high SNR rules have a performance nearly equal to that of the ML rules, but provide a significant performance improvement over the simple correlation rules and are virtually as simple to implement for a wide range of signal energies. We also address the problem of designing periodic MPPM synchronization sequences with good autocorrelation properties, based on a maximum, worst case, peak-to-sidelobe distance criterion. Upper bounds on the peak-to-sidelobe distance for such sequences are derived, and a few sequences, generated by computer simulations, for different synchronization sequence lengths are given.>

A reduction in the track width in disc-recording systems results in a desirable increase in areal density, but also in the undesirable appearance of inter-track interference (ITI) and loss of signal-to-noise ratio (SNR). One way the effects of ITI may be alleviated is through the use of multiple-head systems simultaneously writing and reading a number of adjacent tracks. In this paper we investigate the performance of two-track detectors, and design codes that combat two-dimensional interference patterns, ISI in the axial dimension, and ITI in the radial dimension, and recover the loss in SNR due to track-narrowing. Sliding-block decoders and reduced-complexity Viterbi detectors are also designed for these codes, which are seen to more than compensate for the performance loss for a large range of ITI levels.>

For an optical Poisson channel, we consider the problem of symbol synchronization and detection of chipsynchronized, random overlapping pulse-position modulation (OPPM) sequences. Maximum-likelihood algorithms are derived for both synchronization and detection and for soft and hard data, and their performances are evaluated through simulations and an upper bound on the symbol detection and symbol synchronization probabilities. As for the case of pulse-position modulation previously studied, it is seen that a performance ceiling exists when only chip synchronization is present, which can be removed through the periodic insertion of synchronizable symbols in the random data stream.

Random overlapping pulse-position modulation (OPPM) sequences result in an unrecoverable error floor on both the probability of erroneous synchronization and the probability of symbol error when only chip synchronization is present. It is known, however, that for a given sequence length M, a subset of the set of all possible sequences is synchronizable in the sense that in the absence of noise, the receiver can correctly symbol synchronize by observing M or more symbol intervals. The authors design finite-state machines and codes over a J-ary alphabet, which produce sequences with the property that every subsequence of length L is synchronizable. Some of the codes, in addition to being synchronizable, produce a coding gain. For an optical Poisson channel the authors introduce joint synchronization and detection algorithms that utilize the memory in the encoded sequences to produce joint estimates of timing and sequences. Their performance is analyzed through simulations and analytical results.>

Optical direct-detection systems are currently being considered for some high-speed intersatellite links, where data rates of a few hundred megabits per second are envisioned under power and pulsewidth constraints. The authors investigate the capacity, cutoff rate, and error-probability performance of uncoded and trellis-coded systems for various modulation schemes and under throughput and power constraints. Modulation schemes considered are on-off keying, pulse-position modulation (PPM), overlapping PPM, and multipulse (combinatorial) PPM.>

The maximum-likelihood rules for locating data frames in direct-detection optical communication systems utilizing overlapping pulse-position modulation (OPPM) are derived under two distinct assumptions of symbol and chip synchronization, respectively. Various approximations to the optimal rules are identified, as well as upper and lower bounds on the probability of correct synchronization. Further, the problem of sequence design based on a maximum peak-to-sidelobe distance criterion is studied, and upper bounds on peak-to-sidelobe distance for sequences of OPPM symbols are derived. Some good sequences are obtained through a computer search.>

The expectation-maximization (EM) algorithm for maximizing likelihood functions, combined with the Viterbi algorithm, is applied to the problem of sequence detection when symbol timing information is not present. Although the EM algorithm is noncausal, results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations, making it both of theoretical and of practical interest. A practical algorithm based on the EM algorithm is introduced. It reduces the computational burden and improves performance by making use of timing estimates in previous observation windows.>

The authors study the problem of maximum-likelihood sequence estimation and synchronization from samples of the output of a matched filter taken at integer multiples of the symbol rate, which is assumed perfectly known by the receiver. A general analysis is presented of sampled receivers that handle arbitrary baseband pulse shapes and arbitrary sampling rates. It is observed that the optimal processing of the matched-filter samples consists of digital interpolation, followed by symbol-by-symbol decoding when sampling is at (or above) the Nyquist rate or Viterbi decoding when sampling is below the Nyquist rate. Performance is studied through the Cramer-Rao bound on mean-square estimation error and a lower-bound on error-probability.>

Jointly optimal receivers that make decisions in the absence of symbol synchronization are derived and analyzed for a pulse-position modulation, optical direct-detection channel. Both receivers that observe the complete sample-path (count record data) and receivers that observe histogram data are studied, and approximations to them are derived. It is seen that jointly optimal receivers are superior to conventional receivers that have separately designed synchronization and decision subsystems. However, their performance advantage is significant only at very low signal levels. Perhaps more significant is that an approximation to the jointly optimal receivers that is much easier to implement than an optimal, separately synchronized receiver achieves nearly the same performance as the latter. Simulation results indicate that the much less complicated receivers that observe histogram data perform as well as receivers that observe the complete sample path at a rather small number of bins per slot.>

An easily implementable dynamic programming algorithm that estimates sequences and timing delay jointly from the contaminated decision statistics available to the receiver is introduced. Although the algorithm is optimal in a joint maximum-likelihood sense, given the observed data, it is not globally optimal, since the observed data do not constitute a sufficient statistic in the absence of synchronization. On the other hand, the observed data are simple to collect, the receiver is simple to implement, and the performance obtained is robust to timing errors. Moreover, the simplicity of the observed data makes the receiver easily implementable digitally, and the need for a separate synchronizer is obviated.>

Two optimal receivers, along with their approximations derived for the optical on-off keying channel, are briefly described. These receivers make symbol decisions in the absence of synchronization. The various approximations to the optimal rules are derived. Computer simulations are presented that compare the performance of suboptimal receivers to that of jointly optimal receivers, as well as to receivers utilizing a separate synchronizer. It is observed that one of the approximations, which is rather simple to implement, performs as well as the significantly more complicated receiver that utilizes a separate, optimal, synchronizer. Further computer simulations show that the suboptimal receivers are quite robust to nonperfect knowledge of the received signal power.>

Consideration is given to the optical direct-detection channel, and it is shown how simple trellis-coded modulation (TCM) can be used to improve performance or increase throughput (in bits per second) without bandwidth expansion or performance loss. In fact, a modest performance gain can be achieved. Although the approach can be used with other signal constellations, the authors concentrate on signals derived from the pulse-position modulation (PPM) format by allowing overlap. Theoretical motivation for using this signal set, known as overlapping PPM (OPPM), was recently given by I. Bar David and G. Kaplan (1984), who showed a capacity gain when overlap is introduced.>

The problem of synchronization and detection of random pulse-position modulation (PPM) sequences is investigated under the assumption of perfect slot synchronization. Maximum-likelihood PPM symbol synchronization and receiver algorithms are derived that make decisions based on both soft and hard data; these algorithms are seen to be easily implementable. The author derives bounds on the symbol error probability and the probability of false synchronization that indicate the existence of a severe performance floor, which can be the limiting factor in the overall system performance. The performance floor is inherent in the PPM format and random data and becomes more serious as the PPM alphabet size Q is increased. A way to eliminate the performance floor is suggested by inserting 'special' PPM symbols in the random data stream.>

The author derives receivers that make optimal sequence decisions from observations of modulated data in the absence of symbol synchronization for the direct-detection optical channel. He shows that, for soft-decision sequence estimation, the average number of likelihoods that must be evaluated need increase only linearly with the sequence length, with the average number of likelihood evaluations actually needed being smaller than the sequence length. Finally, the author presents computer simulations that compare the performance of two of the receivers to the performance of a receiver utilizing a separate synchronizer and to that of a receiver that is perfectly synchronized.>

The problem of designing sequences of Q-ary pulse-position-modulation (PPM) symbols that have good periodic autocorrelation properties is investigated. Two cases are considered. In the first it is assumed that only slot synchronization is present and thus cyclic shifts are one slot at a time; in the second PPM symbol synchronization is present, in which case cyclic shifts are by one symbol (Q slots) at a time. In both cases, upper bounds are derived on the maximum peak-to-sidelobe distance, which are shown through a computer search to be nearly tight. When symbol synchronization is present, the bound reduces to the Plotkin bound, but it is slightly tighter in general.>

The maximum-likelihood symbol synchronization statistic is derived from noisy observations of randomly modulated on-off-keying data for the direct-detection optical channel. A similar statistic for the case when the transmitter sends a special pattern of alternating O's and 1's for synchronization purposes only is also derived. Various approximations to the optimal statistic are introduced and their performance compared to the optimal one under a new criterion, believed to be more appropriate for the Poisson channel than the mean-square error criterion routinely used with other channels. It is shown that although the variable associated with symbol transitions is continuous, the possible values of it that maximize the maximum-likelihood (ML) statistic belong to a discrete set with relatively few elements.

A maximum-likelihood statistic for pulse-position-modulation (PPM) symbol synchronization in the absence of slot synchronization is derived for the direct-direction optical channel from noisy observations of randomly modulated data, observed through a windowMsymbols wide. Two approximations to the optimal rule that are easier to implement are also derived and their performance analyzed by computer simulations. It is seen that the performance of one approximation, which is quite easy to implement, is almost identical to the more complex approximation.

An incoherent receiver is derived for the heterodyne optical channel under the assumption of Phase coherence at the start of each transmitted sequence. The receiver is optimal in the limit of small bit intervals with respect to the coherence time of the laser oscillators, and reduces to that proposed by Jeromin and Chan [1] when no initial phase coherence is present. Computer simulations indicate that the small amount of performance improvement obtained by resolving an initial phase uncertainty may not justify the extra complexity needed, for the data rates currently considered.

A model for the heterodyne optical channel that is consistent with experimental observations is introduced, and a general maximum-likelihood sequence estimation receiver that accounts for laser phase instabilities is proposed using the generalized log-likelihood functional. The performance of various suboptimal "estimator-correlator" receivers, obtained from optimal, nonimplementable receiver equations, is studied by simulation and compared to that of an incoherent receiver for practical parameter values. It is observed that, for hard decisions, the proposed receiver performs significantly better than an incoherent receiver for bit intervals larger than about half the coherence time of the laser oscillators, with larger gains to be expected when soft decisions on long sequences are made. A way of reducing the complexity of the soft-decisions receiver for long sequences is discussed.

The maximum-likelihood frame synchronizer was recently derived for direct-detection optical communications assuming baud synchronization. In this paper we present an extension to those results when pulse-position modulation is used and jointly derive baud and frame synchronization from slot synchronization. The optimum rule is seen to consist of a simple correlation term and a nonlinear correction term. Simulation results for the optimum rule compared to analytical and simulation results for the simple correlation rule show that equivalent performance for the simple correlation rule requires a substantial increase in signal power. To design good synchronization patterns, we use a divergence measure derived from the optimum rule. A simple algorithm is derived to test whether a given sequence is good or not.

Coherent heterodyne detection in optical communication is degraded by phase instabilities present when a semiconductor laser is used as a local oscillator. Postdetection processing that accounts for these instabilities is suggested, based on a diffusion-process model for oscillator instabilities and a maximum-likelihood sequence-estimator of information symbols modulating the received light.

The maximum-likelihood rule for locating a frame-synchronization pattern in a direct-detection optical communication system employing eitherQ-ary pulse-position modulation or on-off keying is identified. We show that equivalent performance for the simple correlation and postdctection-correlation rules used in practice can require substantially more than a 3 dB increase in signal power over that required using the maximum-likelihood rule.

We show thatQ-ary pulse-position modulation with raised cosine pulses minimizes the average power (photons/s) required to communicate at a specified throughput rate (nats/s) over a band-limited, noisy optical channel. The best choice ofQis identified, as are other encoder parameters.