We propose four finite-length scaling laws to predict the frame error rate (FER) performance in the waterfall region of spatially-coupled low-density parity-check code ensembles under full belief propagation (BP) decoding with a limit on the number of decoding iterations and a scaling law for sliding window decoding, also with limited iterations. The laws for full BP decoding provide a choice between accuracy and computational complexity; a good balance between them is achieved by the law that models the number of decoded bits after a certain number of BP iterations by a time-integrated Ornstein-Uhlenbeck process. This framework is developed further to model sliding window decoding as a race between the integrated Ornstein-Uhlenbeck process and an absorbing barrier that corresponds to the left boundary of the sliding window. The proposed scaling laws yield accurate FER predictions for the semi-structured code ensembles proposed by Olmos and Urbanke.

The performance of a previously developed analog combining network (ACN) of phase shifters for periodic broadcast vehicle-to-vehicle (V2V) communication is investigated. The original ACN was designed to maximize the sum of signal-to-noise ratios (SNRs) for$K$consecutive cooperative awareness messages (CAMs). The design was based on the assumption of a dominant propagation path with an angle of arrival (AOA) that is constant for$K$messages. In this work, we relax this assumption by allowing the AOA and path-loss (PL) of the dominant path to be time-variant. Assuming a highway scenario with a line of sight (LOS) propagation between vehicles, we use affine approximations to model the time variation of different path quantities, including the PL, the relative distance-dependent phase shift between antennas, and the AOA-dependent far-field function of the antennas. By leveraging these approximations, we analytically derive the ACN sum- SNR as each one of these quantities varies over$K$CAMs. Moreover, we suggest a design rule for a phase slope that is robust against time variation of the dominant path and optimal under time-invariant conditions. Finally, we validate this design rule using numerical computations and an example of vehicular communication antenna elements.

We generalize an existing low-cost analog signal processing concept that takes advantage of the periodicity of vehicle-to-vehicle broadcast service to the transmitter side. In particular, we propose to process multiple antennas using either an analog beamforming network (ABN) of phase shifters, or an antenna switching network (ASN) that periodically alternates between the available antennas, to transmit periodic messages to receivers that have an analog combining network (ACN) of phase shifters, which has been proposed in earlier work. To guarantee robustness, we aim to minimize the burst error probability for the worst receiving vehicular user, in a scenario of bad propagation condition that is modeled by a single dominant path between the communicating vehicles. In absence of any form of channel knowledge, we analytically derive the optimal parameters of both ABN and ASN. The ABN beamforming vector is found to be optimal for all users and not only for the worst receiving user. Further, we demonstrate that Alamouti scheme for the special case of two transmit antennas yields similar performance to ABN and ASN. At last, we show that the derived parameters of the two proposed transmission strategies are also optimal when hybrid ACN-maximal ratio combining is used at the receiver.

A hybrid analog-digital combiner for broadcast vehicular communication is proposed. It has an analog part that does not require any channel state information or feedback from the receiver, and a digital part that uses maximal ratio combining (MRC). We focus on designing the analog part of the combiner to optimize the received signal strength along all azimuth angles for robust periodic vehicle-to-vehicle (V2V) communication, in a scenario of one dominant component between the communicating vehicles (e.g., highway scenario). We show that the parameters of a previously suggested fully analog combiner solves the optimization problem of the analog part of the proposed hybrid combiner. Assuming$L$directional antennas with uniform angular separation together with the special case of a two-port receiver, we show that it is optimal to combine groups of$\lceil {L/2}\rceil $and$\lfloor {L/2}\rfloor $antennas in analog domain and feed the output of each group to one digital port. This is shown to be optimal under a sufficient condition on the sidelobes level of the directional antennas. Moreover, we derive a performance bound for the hybrid combiner to guide the choice of antennas needed to meet the reliability requirements of the V2V communication links.

We consider distributed and dynamic caching of coded content at small base stations (SBSs) in an area served by a macro base station (MBS). Specifically, content is encoded using a maximum distance separable code and cached according to a time-to-live (TTL) cache eviction policy, which allows coded packets to be removed from the caches at periodic times. Mobile users requesting a particular content download coded packets from SBSs within communication range. If additional packets are required to decode the file, these are downloaded from the MBS. We formulate an optimization problem that is efficiently solved numerically, providing TTL caching policies minimizing the overall network load. We demonstrate that distributed coded caching using TTL caching policies can offer significant reductions in terms of network load when request arrivals are bursty. We show how the distributed coded caching problem utilizing TTL caching policies can be analyzed as a specific single cache, convex optimization problem. Our problem encompasses static caching and the single cache as special cases. We prove that, interestingly, static caching is optimal under a Poisson request process, and that for a single cache the optimization problem has a surprisingly simple solution.

This paper investigates schemes for multihop scheduling and power control for vehicle-to-vehicle (V2V) multicast communication, taking into account the effects of both co-channel interference and adjacent channel interference, such that requirements on latency or age of information (AoI) are satisfied. Optimal performance can be achieved by formulating and solving mixed Boolean linear programming (MBLP) optimization problems for various performance metrics, including network throughput and connectivity. Fairness among network nodes (vehicles) is addressed by considering formulations that maximizes the worst-case network node performance. Solving the optimization problem comes at the cost of significant computational complexity for large networks and requires that (slow) channel state information is gathered at a central point. To address these issues, a clustering method is proposed to partition the optimization problem into a set of smaller problems, which reduces the overall computational complexity, and a decentralized algorithm that does not need channel state information is provided.

This paper proposes scheduling and power control schemes to mitigate the impact of both co-channel interference (CCI) and adjacent channel interference (ACI) on direct vehicle-to-vehicle broadcast communication. The objective is to maximize the number of vehicles that can communicate with the prescribed requirement on latency and reliability. The joint scheduling and power control problem is formulated as a mixed Boolean linear programming (MBLP) problem. A column generation method is proposed to reduce the computational complexity of the joint problem. From the joint problem, we formulate a scheduling-alone problem (given a power allocation) as a Boolean linear programming (BLP) problem and a power control-alone problem (given a schedule) as an MBLP problem. The scheduling problem is numerically sensitive due to the high dynamic range of channel values and adjacent channel interference ratio (ACIR) values. Therefore, a novel sensitivity reduction technique, which can compute a numerically stable optimal solution at the price of increased computational complexity, is proposed. Numerical results show that ACI, just as CCI, is a serious problem in direct vehicle-to-vehicle (V2V) communication due to near-far situations and hence should not be ignored, and its impact can be reduced by proper scheduling and power control.

We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under full belief propagation (BP) decoding. The refined scaling law models the decoding process as two independent Ornstein-Uhlenbeck processes, in correspondence to the two decoding waves that propagate toward the center of the coupled chain for terminated SC-LDPC codes. We then extend the proposed scaling law to predict the performance of (terminated) SC-LDPC code ensembles under the more practical sliding window decoding. Finally, we extend this framework to predict the bit error rate (BER) and block error rate (BLER) of SC-LDPC code ensembles. The proposed scaling law yields very accurate predictions of the FER, BLER, and BER for both full BP and window decoding.

For critical vehicular communication services, such as traffic safety and traffic efficiency, it is advisable to design systems with robustness as the main criteria, possibly at the price of reduced peak performance and efficiency. We describe a simple, low-cost method for combining the output of L directional (i.e., not omnidirectional) antennas to the input of a single-port receiver with the aim to guarantee robustness, i.e., to minimize the probability that K consecutive packets arriving from the worst-case angle-of-arrival are decoded incorrectly. To minimize complexity, the combining network does not estimate or use channel state information. The combining network consists of L - 1 analog phase shifters whose phases are affine functions of time. For a general L ≤ K and when the packet error probability decays exponentially with the received SNR, the optimum slopes of the affine functions can be computed by solving an optimization problem that depends on the antenna far-field functions. We provide analytical solutions for the special case of L = 2 and 3 antennas, which turns out to be independent of the antenna far-field functions and placement on a vehicle. In an experimental setup consisting of two monopole antennas mounted on the roof of a Volvo XC90, the proposed combining method is shown to give significant performance gains, compared to using any one of the antennas.

We propose a refined scaling law to predict the finite-length performance in the waterfall region of spatially coupled low-density parity-check codes over the binary erasure channel. In particular, we introduce some improvements to the scaling law proposed by Olmos and Urbanke that result in a better agreement between the predicted and simulated frame error rate. We also show how the scaling law can be extended to predict the bit error rate performance.

In this paper, we analyze a carrier-sense multiple access system with all-to-all broadcast data traffic to assess the performance gain obtained by using multiple sector antennas and a receiver setup that can decode multiple packets simultaneously when packets arrive in narrow angle of arrivals. In the broadcast mode of IEEE 802.11p-based vehicle-to-vehicle communications, acknowledgment messages are absent and a fixed contention window is used in medium access. As a result, the probability of multiple vehicles simultaneously transmitting a packet increases with the number of vehicles. In the case of a simultaneous transmission, a receiver with omnidirectional antennas receives power from all the transmitting vehicles and the probability of successfully decoding a packet decreases. This problem can be alleviated by using sector antennas when the simultaneously transmitted packets arrive at a receiver in the narrow angle of arrivals. We show through analysis and simulations that the packet success rate (PSR) can be improved significantly by using the sector antennas' setup instead of an omnidirectional antenna. Numerical results show that a several-fold increase in the PSR can be achieved in a setup with four sector antennas compared with an omnidirectional antenna when the density of vehicles is large.

We consider the caching of content in the mobile devices in a dense wireless network using maximum distance separable (MDS) codes. We focus on an area, served by a base station (BS), where mobile devices move around according to a random mobility model. Users requesting a particular file download the coded packets from caching devices within a communication range using device-to-device communication. If additional packets are required to decode the file, these are downloaded from the BS. We analyze the device mobility and derive a good approximation of the distribution of caching devices within the communication range of mobile devices at any given time. We then optimize the MDS codes to minimize the network load under a cache size constraint and show that using optimized MDS codes results in significantly lower network load compared to when caching the most popular files. We further show, numerically, that caching coded packets of each file on all mobile devices, i.e., maximal spreading, is optimal.

We present the construction of a family of erasure correcting codes for distributed storage which achieve low repair bandwidth and complexity at the expense of a lower fault tolerance. The construction is based on two classes of codes, where the primary goal of the first class of codes is to provide fault tolerance, while the second class aims at reducing the repair bandwidth and repair complexity. The repair procedure is a two-step procedure where parts of the failed node are repaired in the first step using the first code. The downloaded symbols during the first step are cached in the memory and used to repair the remaining erased data symbols at minimal additional read cost during the second step. The first class of codes is based on maximum distance separable (MDS) codes modified using piggybacks, while the second class is designed to reduce the number of additional symbols that need to be downloaded to repair the remaining erased symbols. We numerically show that the proposed codes achieve better repair bandwidth compared to MDS codes, codes constructed using piggybacks, and local reconstruction/Pyramid codes, while a better repair complexity is achieved when compared to MDS, Zigzag, Pyramid codes, and codes constructed using piggybacks.

A classical problem in digital communications is to evaluate the symbol error probability (SEP) and bit error probability (BEP) of a multidimensional constellation over an additive white Gaussian noise channel. In this paper, we revisit this problem for nonequally likely symbols and study the behavior of the optimal maximum a posteriori (MAP) detector at asymptotically high signal-to-noise ratios. Exact closed-form asymptotic expressions for SEP and BEP for arbitrary constellations and input distributions are presented. The well-known union bound is proven to be asymptotically tight under general conditions. The performance of the practically relevant maximum likelihood (ML) detector is also analyzed. Although the decision regions with MAP detection converge to the ML regions at high signal-to-noise ratios, the ratio between the MAP and ML detectors in terms of both SEP and BEP approaches a constant, which depends on the constellation and a priori probabilities. Necessary and sufficient conditions for asymptotic equivalence between the MAP and ML detectors are also presented.

We propose an uncoordinated medium access control (MAC) protocol, called all-to-all broadcast coded slotted ALOHA (B-CSA) for reliable all-to-all broadcast with strict latency constraints. In B-CSA, each user acts as both transmitter and receiver in a half-duplex mode. The half-duplex mode gives rise to a double unequal error protection (DUEP) phenomenon: the more a user repeats its packet, the higher the probability that this packet is decoded by other users, but the lower the probability for this user to decode packets from others. We analyze the performance of B-CSA over the packet erasure channel for a finite frame length. In particular, we provide a general analysis of stopping sets for B-CSA and derive an analytical approximation of the performance in the error floor (EF) region, which captures the DUEP feature of B-CSA. Simulation results reveal that the proposed approximation predicts very well the performance of B-CSA in the EF region. Finally, we consider the application of B-CSA to vehicular communications and compare its performance with that of carrier sense multiple access (CSMA), the current MAC protocol in vehicular networks. The results show that B-CSA is able to support a much larger number of users than CSMA with the same reliability.

We consider a frame asynchronous coded slotted ALOHA (FA-CSA) system for uncoordinated multiple access, where users join the system on a slot-by-slot basis according to a Poisson random process, and in contrast to standard frame synchronous CSA (FS-CSA), users are not frame-synchronized. We analyze the performance of FA-CSA in terms of packet loss rate and delay. In particular, we derive the (approximate) density evolution that characterizes the asymptotic performance of FA-CSA when the frame length goes to infinity. We show that, if the receiver can monitor the system before anyone starts transmitting, a boundary effect similar to that of spatially coupled codes occurs, which greatly improves the iterative decoding threshold. Furthermore, we derive tight approximations of the error floor (EF) for the finite frame length regime, based on the probability of occurrence of the most frequent stopping sets. We show that, in general, FA-CSA provides better performance in both the EF and waterfall regions as compared to FS-CSA. Moreover, FA-CSA exhibits better delay properties than FS-CSA.

This paper studies the synchronization problem for mobile cellular device-to-device (D2D) networks. Depending on the number of devices that are in coverage of the base station, the D2D environment can be divided into three categories where the partial-coverage and out-of-coverage are challenging scenarios and thus are the focus of this paper. First, we discuss five main challenges imposed on the synchronization problem in mobile D2D networks. More specifically, there are different challenges in the two coverage scenarios, since they do not have exactly the same synchronization objectives. Second, we propose a low-complexity Adaptive distRibuted nEtwork Synchronization (ARES) algorithm to address the five challenges. The design principles and the theories behind the ARES scheme are also analyzed in detail. Finally, we provide comprehensive simulations to evaluate different synchronization schemes, where the proposed ARES mechanism shows very promising performance.

Generalized product codes (GPCs) are extensions of product codes (PCs), where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed to randomized code ensembles) and analyze the asymptotic performance over the binary erasure channel under iterative decoding. Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, blockwise braided codes, and staircase codes. It is assumed that the component codes can correct a fixed number of erasures and that the length of each component code tends to infinity. We show that this setup is equivalent to studying the behavior of a peeling algorithm applied to a sparse inhomogeneous random graph. Using a convergence result for these graphs, we derive the density evolution equations that characterize the asymptotic decoding performance. As an application, we discuss the design of irregular GPCs, employing a mixture of component codes with different erasure-correcting capabilities.

This paper investigates the power control problem for broadcast vehicular communications in the presence of adjacent carrier interference (ACI). First, we study the impact of ACI on vehicle-to-vehicle (V2V) communications and conclude that the ACI indeed significantly affects the reliability of V2V links. Second, we formulate a power control optimization problem for vehicles to reduce the negative influence of ACI, which is shown to be NP-hard. Furthermore, we propose two power control schemes where the first one solves the formulated problem by a branch and bound method and the second one considers a heuristic algorithm with much reduced complexity. Finally, simulations are presented which illustrate the necessity of power control when ACI exists and also show promising performance of the proposed algorithms.

Several authors have proposed spatially-coupled (or convolutional-like) variants of product codes (PCs). In this paper, we focus on a parametrized family of generalized PCs that recovers some of these codes (e.g., staircase and block-wise braided codes) as special cases and study the iterative decoding performance over the binary erasure channel. Even though our code construction is deterministic (and not based on a randomized ensemble), we show that it is still possible to rigorously derive the density evolution (DE) equations that govern the asymptotic performance. The obtained DE equations are then compared to those for a related spatially-coupled PC ensemble. In particular, we show that there exists a family of (deterministic) braided codes that follows the same DE equation as the ensemble, for any spatial length and coupling width.

We consider the use of distributed storage (DS) to reduce the communication cost of content delivery in wireless networks. Content is stored (cached) in a number of mobile devices using an erasure correcting code. Users retrieve content from other devices using device-to-device communication or from the base station (BS), at the expense of higher communication cost. We address the repair problem when a device storing data leaves the cell. We introduce a repair scheduling where repair is performed periodically and derive analytical expressions for the overall communication cost of content download and data repair as a function of the repair interval. The derived expressions are then used to evaluate the communication cost entailed by DS using several erasure correcting codes. Our results show that DS can reduce the communication cost with respect to the case where content is downloaded only from the BS, provided that the repairs are performed frequently enough. If devices storing content arrive to the cell, the communication cost using DS is further reduced and, for a large enough arrival rate, it is always beneficial. Interestingly, we show that maximum distance separable codes, which do not perform well for classical DS, can yield a low overall communication cost in wireless DS.

We present a comprehensive study of the information rate loss of the max-log approximation for M-ary pulse-amplitude modulation (PAM) in a bit-interleaved coded modulation (BICM) system. It is widely assumed that the calculation of L-values using the max-log approximation leads to an information loss. We prove that this assumption is correct for all M-PAM constellations and labelings with the exception of a symmetric 4-PAM constellation labeled with a Gray code. We also show that for max-log L-values, the BICM generalized mutual information (GMI), which is an achievable rate for a standard BICM decoder, is too pessimistic. In particular, it is proved that the so-called harmonized GMI, which can be seen as the sum of bit-level GMIs, is achievable without any modifications to the decoder. We then study how bit-level channel symmetrization and mixing affect the MI and the GMI for max-log L-values. Our results show that these operations, which are often used when analyzing BICM systems, preserve the GMI. However, this is not necessarily the case when the MI is considered. Necessary and sufficient conditions under which these operations preserve the MI are provided.

Deploying direct device-to-device (D2D) links is a promising technology for vehicle-to-X (V2X) applications. However, intracell interference, along with stringent requirements on latency and reliability, are challenging issues. In this paper, we study the radio resource management problem for D2D-based safety-critical V2X communications. We first transform the V2X requirements into the constraints that are computable using slowly varying channel state information only. Secondly, we formulate an optimization problem, taking into account the requirements of both vehicular users (V-UEs) and cellular users (C-UEs), where resource sharing can take place not only between a V-UE and a C-UE but also among different V-UEs. The NP-hardness of the problem is rigorously proved. Moreover, a heuristic algorithm, called Cluster-based Resource block sharing and pOWer allocatioN (CROWN), is proposed to solve this problem. Finally, simulation results indicate promising performance of the CROWN scheme.

We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the first class of symbols is to provide good fault tolerance, while the second class facilitates node repair, reducing the repair bandwidth and the repair complexity. We compare the proposed codes with other codes proposed in the literature.

Clock synchronization is a crucial issue for mobile ad hoc networks due to the dynamic and distributed nature of these networks. In this paper, employing affine models for local clocks, a random broadcast based distributed consensus clock synchronization algorithm is proposed. In the absence of transmission delays, we theoretically prove the convergence of the proposed scheme, which is further illustrated by numerical results. In addition, it is concluded from simulations that the proposed scheme is scalable and robust to transmission delays as well as different accuracy requirements.

In many practical communication systems, one binary encoder/decoder pair is used to communicate over a set of parallel channels. Examples of this setup include multi-carrier transmission, rate-compatible puncturing of turbo-like codes, and bit-interleaved coded modulation (BICM). A bit mapper is commonly employed to determine how the coded bits are allocated to the channels. In this paper, we study spatially coupled low-density parity check codes over parallel channels and optimize the bit mapper using BICM as the driving example. For simplicity, the parallel bit channels that arise in BICM are replaced by independent binary erasure channels (BECs). For two parallel BECs modeled according to a 4-PAM constellation labeled by the binary reflected Gray code, the optimization results show that the decoding threshold can be improved over a uniform random bit mapper, or, alternatively, the spatial chain length of the code can be reduced for a given gap to capacity. It is also shown that for rate-loss free, circular (tail-biting) ensembles, a decoding wave effect can be initiated using only an optimized bit mapper.

Vehicular wireless channels are highly time-varying and the pilot pattern in the 802.11p orthogonal frequency-division multiplexing frame has been shown to be ill suited for long data packets. The high frame error rate in off-the-shelf chipsets with noniterative receiver configurations is mostly due to the use of outdated channel estimates for equalization. This paper deals with improving the channel estimation in 802.11p systems using a cross layered approach, where known data bits are inserted in the higher layers and a modified receiver makes use of these bits as training data for improved channel estimation. We also describe a noniterative receiver configuration for utilizing the additional training bits and show through simulations that frame error rates close to the case with perfect channel knowledge can be achieved.

Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.

Two decoder structures for coded modulation over the Gaussian channel are studied: 1) the maximum likelihood symbol-wise decoder and 2) the (suboptimal) bit-wise decoder based on the bit-interleaved coded modulation paradigm. We consider a 16-ary quadrature amplitude constellation labeled with a Gray labeling. It is shown that the asymptotic loss in terms of pairwise error probability, for any two codewords caused by the bit-wise decoder, is bounded by 1.25 dB. The analysis also shows that the asymptotic loss is zero for a wide range of linear codes, including all rate-1/2 convolutional codes.

This paper investigates the problem of clock synchronization of nodes in a wireless sensor network based on the two-way timing message exchange mechanism with an unknown deterministic transmission delay and random exponential transmission delays. Without knowing the fixed delay, a novel synchronization scheme is proposed for the linear clock model, which works well in both symmetric and asymmetric links. In the proposed algorithm, the clock skew and offset are estimated by directly utilizing mean square error as the metric to be optimized. This consideration results in significant performance improvements compared to the existing synchronization methods, especially for a small number of observations and large standard deviation of the random delays.

The asymptotic behavior of the mutual information (MI) at high signal-to-noise ratio (SNR) for discrete constellations over the scalar additive white Gaussian noise channel is studied. Exact asymptotic expressions for the MI for arbitrary one-dimensional constellations and input distributions are presented in the limit as the SNR tends to infinity. Asymptotics of the minimum mean-square error (MMSE) are also developed. It is shown that for any input distribution, the MI and the MMSE have an asymptotic behavior proportional to a Gaussian Q-function, whose argument depends on the minimum Euclidean distance of the constellation and the SNR. Closed-form expressions for the coefficients of these Q-functions are calculated.

An asymptotically optimal trellis-coded modulation (TCM) encoder requires the joint design of the encoder and the binary labeling of the constellation. Since analytical approaches are unknown, the only available solution is to perform an exhaustive search over the encoder and the labeling. For large constellation sizes and/or many encoder states, however, an exhaustive search is unfeasible. Traditional TCM designs overcome this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. In this paper we study binary labelings for TCM and show how they can be grouped into classes, which considerably reduces the search space in a joint design. For 8-ary constellations, the number of different binary labelings that must be tested is reduced from 8!=40320 to 240. For the particular case of an 8-ary pulse amplitude modulation constellation, this number is further reduced to 120 and for 8-ary phase shift keying to only 30. An algorithm to generate one labeling in each class is also introduced. Asymptotically optimal TCM encoders are tabulated which are up to 0.3 dB better than the previously best known encoders.

The optimal bit-wise demodulator for M-ary pulse amplitude modulation (PAM) over the additive white Gaussian noise channel is analyzed in terms of uncoded bit-error rate (BER). The BER analysis is based on studying the bit patterns that form a labeling. New closed-form BER expressions for 4-PAM with any labeling are developed. Moreover, closed-form BER expressions for 11 out of 23 possible bit patterns for 8-PAM are presented, which enable us to obtain the BER for 8-PAM with some of the most popular labelings, including the binary reflected Gray code and the natural binary code. Numerical results show that, regardless of the labeling, there is no difference between the optimal demodulator and the symbol-wise demodulator for any BER of practical interest (below 0.1).

A novel general ready-to-use bit-error rate (BER) expression for one-dimensional constellations is developed. The BER analysis is performed for bit patterns that form a labeling. The number of patterns for equally spaced M-PAM constellations with different BER is analyzed.

Clock synchronization is a crucial issue in the operation of wireless sensor networks. Although the existing synchronization algorithms under linear clock model assumptions perform well for short periods, they will become problematic for applications with long-term requirements. In this paper, we consider a more realistic and flexible relationship model for two clocks and exploit a Taylor expansion to approximate the relationship. Based on this model and a two-way time message exchange procedure, an estimation algorithm is proposed to recover the relationship and then achieve the synchronization. Finally, simulation results demonstrate that the proposed algorithm improves the accuracy of synchronization as compared to existing algorithms in many scenarios, and is also robust to different distributions of random delays.

Optimal trellis-coded modulation (TCM) schemes are obtained by jointly designing the convolutional encoder and the binary labeling of the constellation. Unfortunately this approach is infeasible for large encoder memories or constellation sizes. Traditional TCM designs circumvent this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. Therefore, traditional TCM schemes are not necessarily optimal. In this paper, we study binary labelings for TCM and show how they can be grouped into classes, which considerably reduces the search space in a joint design. For the particular case of 8-ary modulation the search space for the labelings is reduced from 8! to 240. Using this classification, we formally prove that for any channel it is always possible to design a TCM system based on the binary-reflected Gray code with identical performance to the one proposed by Ungerboeck in 1982. Moreover, the classification is used to tabulate asymptotically optimal TCM schemes.

In this paper, different aspects of the bit-interleaved coded modulation (BICM) capacity for the Gaussian channel are analyzed. Analytical bounds for the BICM capacity are developed. These bounds suggest that the BICM capacity at high signal-to-noise ration (SNR) is determined by the multiplicity of the minimum Euclidean distance over all the subconstellations generated by the mapper. Based on this observation, we conjecture that for any constellation, the highest BICM capacity at high SNR is always obtained by a Gray code, if one exists. Ready-to-use expressions based on Gauss - Hermite quadratures to compute the coded modulation and BICM capacities for any SNR are also presented. Using these expressions, it is shown that the BICM capacity is in general a nonconvex, nonconcave function of the input bit distribution. For 8PAM and 8PSK, there exist 12 and 7 classes of mappings, respectively, with equivalent high-SNR behavior, of which the best class comprises all Gray codes.

An improved concatenated code structure, which generalizes parallel and serially concatenated convolutional codes is presented and investigated. The structure is ideal for designing low-complexity rate-compatible code families with good performance in both the waterfall and error floor regions. As an additional feature, the structure provides a unified analysis and design framework, which includes both parallel and serially concatenated codes as particular cases. We derive design criteria for the generalized class of concatenated convolutional codes based on union bounds for the error probability and extrinsic information transfer (EXIT) charts for the decoding threshold.

The performance of bit-interleaved coded modulation (BICM) with (or without) iterative decoding (ID) is significantly influenced by the mapping of bits to the symbol constellation. Our main objective in this paper is to develop a systematic design approach for BICM-ID schemes, ensuring the best possible performance with iterative decoding. Although useful mappings for BICM-ID have been found based on various search strategies, no attempt has been made to systematically enumerate and classify all unique mappers for a given constellation. As the basis for a systematic enumeration and classification, we define the average bit-wise distance spectrum for a mapping from bits to symbols. Different bit-wise distance spectra are derived assuming no prior information or full prior information, respectively. The bit-wise distance spectra determine corresponding bit-wise error probability and bit-wise mutual information. The latter allows us to use the classification of mappings with unique bit-wise distance spectra to also classify mappings with unique extremal points in the corresponding extrinsic information transfer (EXIT) curves. As an example of our approach, we classify 8PSK mappings into 86 classes of unique mappings according to bit-wise distance spectra. The classification can be used to significantly reduce the complexity of the search for suitable mappers for BICM-ID. For 8PSK and a given encoder, only 86 different mappings need to be investigated. As examples of the systematic design approach, the best 8PSK mappings for minimizing the convergence threshold are found for concatenation with the rate 1/2 (5,7)8 and (133,171)8 convolutional codes, and the rate 1/2 UMTS turbo code with identical constituent convolutional codes (15/13)8.

We propose a systematic design framework for optimal, low-complexity punctured multiple parallel concatenated codes (MPCCs), based on minimizing the convergence threshold using extrinsic information transfer (EXIT) charts. As the convergence threshold is related to the area between the two EXIT curves, the corresponding optimization problem is equivalent to a curve-fitting problem. The EXIT curves are determined by the respective EXIT functions of the constituents, which can be conveniently shaped through the use of random puncturing and unequal energy allocations across parallel coding streams. The design task is therefore to find the optimal combination of constituents, puncturing ratios, and energy allocation for matching the EXIT curves. A search over all rate-one convolutional codes of memory length four or less is performed, identifying 98 classes of codes with unique EXIT functions out of a total of 310 codes. Low-complexity MPCCs with up to four constituents are found, where the convergence thresholds are observed to be within 0.1 dB or less of the fundamental minimum signal-to-noise ratio (SNR) corresponding to the binary phase-shift keying (BPSK) capacity for code rates1/3lesRles 7/8. Further allowing for unequal energy allocation, the convergence thresholds for lower code rates are similarly improved.

Extrinsic information transfer (EXIT) charts are utilized to optimize the iterative multiuser detector receiver in a multiuser turbo-coded CDMA system. The (receive) power levels are optimized for the system load using a constrained nonlinear optimization approach. The optimal decoding schedule is derived dynamically using the power optimized EXIT chart and a Viterbi search algorithm. Dynamic scheduling is shown to be a more flexible approach which results in a more stable QoS for a typical system configuration than one-shot scheduling, and large complexity savings over a receiver without scheduling. We verify through simulations that complexity savings of over 50% and power savings of over 8dB can be achieved. We show that the optimized power levels combined with adaptive scheduling allows for efficient utilization of receiver resources for heavily loaded systems.

The performance of bit-interleaved coded modulation with iterative decoding is significantly influenced by the mapping of bits to the symbol constellation. A range of mappers have been suggested in the literature, however, no attempt has been made to systematically enumerate all unique mappers for a given signal constellation. In this paper, we classify 8PSK mappers based on bit-wise distance spectra for no prior information, and full prior information, respectively.

In this paper we show how to find optimal energy distribution together with optimal puncturing ratios for parallel concatenated codes with two or more constituent codes. The energy distribution and the puncturing ratios are optimal in terms of minimizing the average signal-to-noise ratio convergence threshold. The extrinsic information transfer functions of the constituent codes are used for the optimization. Using this technique we obtain additional degrees of freedom for constructing codes with low convergence thresholds over a large range of code rates.

Non-data-aided (NDA) parameter estimation is considered for binary-phase-shift-keying transmission in an additive white Gaussian noise channel. Cramer-Rao lower bounds (CRLBs) for signal amplitude, noise standard deviation, channel reliability constant and bit-error rate are derived and it is shown how these parameters relate to the signal-to-noise ratio (SNR). An alternative derivation of the iterative maximum likelihood (ML) SNR estimator is presented together with a novel, low complexity NDA SNR estimator. The performance of the proposed estimator is compared to previously suggested estimators and the CRLB. The results show that the proposed estimator performs close to the iterative ML estimator at significantly lower computational complexity

An interesting practical consideration for decoding of serial or parallel concatenated codes with more than two components is the determination of the lowest complexity component decoder schedule which results in convergence. This correspondence presents an algorithm that finds such an optimal decoder schedule. A technique is also given for combining and projecting a series of three-dimensional extrinsic information transfer (EXIT) functions onto a single two-dimensional EXIT chart. This is a useful technique for visualizing the convergence threshold for multiple concatenated codes and provides a design tool for concatenated codes with more than two components.

Optimal puncturing ratios for parallel concatenated codes with two or more constituent codes are found using extrinsic information transfer functions. These ratios minimize the signal-to-noise ratio convergence threshold and provide additional degrees of freedom for constructing codes with low thresholds over a wide range of code rates.

Convergence analysis of iterative detectors for narrow-band multiple access is performed using extrinsic information transfer charts. The system has no bandwidth expansion, so K users use the same bandwidth as a single user. The load (the number of bits used per channel) of the system is therefore higher than the load in, for example, conventional CDMA systems. The analysis provides useful guidelines on how to combine outer codes with the chosen mapper for different loads of the system. Both memoryless mappers and differential mappers are evaluated. We present the limitations of the system measured with the maximum number of users and the required SNR for different scenarios.

Trellis-code multiple-access (TCMA) is a narrow-band multiple-access scheme based on trellis-coded modulation. There is no bandwidth expansion, so K users occupy the same bandwidth as one single user. The load of the system, in number of bits per channel use, is therefore much higher than the load in, for example, conventional code-division multiple-access systems. Interleavers are introduced as a new feature to separate the users. This implies that the maximum-likelihood sequence detector (MLSD) is now too complex to implement. Iterative detectors are therefore suggested as an alternative to the joint MLSD. The conventional interference cancellation (IC), detector has lower complexity than the MLSD, but its performance is shown to be far from acceptable. Even after a novel improvement of the IC detector, the performance is unsatisfactory. Instead of using IC, another iterative detector is suggested. This detector updates the branch metric for every iteration, and avoids the standard Gaussian approximation. Simulations show that the performance of this detector can be close to single-user performance, even when the interleaver and the phase offset are the only user-specific features in the TCMA system.

Trellis code multiple access (TCMA) is a narrowband multiple access scheme. There is no bandwidth expansion, so K users are using the same bandwidth as one single user. The load (the number of bits per channel use) of the system is therefore much higher than the load in, for example, conventional CDMA systems. It is shown here that the maximum number of users in a TCMA system is usually modest. This fact is based on constellation-constrained capacity, ie, the maximum capacity of a system with a specific constellation of the transmitted symbols. The minimum required signal-to-noise ratio for reliable transmission is also given for different code rates.

Iterative detectors for trellis code multiple access (TCMA) are suggested as an alternative to the joint maximum likelihood sequence detector (MLSD). Interleavers are introduced in the TCMA system as a new feature to separate the users. This implies that MLSD is now too complex to implement. The conventional interference cancellation (IC) detector has lower complexity, but its performance is shown to be far from acceptable. Another iterative detector having close to single user performance is therefore suggested. Instead of using IC, this detector updates the branch metric for every iteration and avoids the standard Gaussian approximation. It is also shown that the users can be detected when the interleaver is the only user specific feature in the TCMA system.

Trellis code multiple access (TCMA) is a narrow-band multiple access scheme. There is no bandwidth expansion, so K users are using the same bandwidth as one single user. The load (the number of bits per channel use) of the system is therefore much higher than the load in, for example, conventional CDMA systems. It is shown here that the maximum number of users in a TCMA system is usually modest. This fact is based on constellation-constrained capacity, i.e., the maximum capacity of a system with a specific constellation of the transmitted symbols. The minimum required signal-to-noise ratio for reliable transmission is also given for different code rates.