This paper examines different designs for combined channel estimation and decoding for a point to point time varying frequency selective fading channel. The channel state information (CSI) is not known a priori at either the transmitter or the receiver. Channel estimation is performed through a combination of conventional pilots and manufactured pilots from previously decoded data. The paper examines how different interleaver structures affect the tradeoff between achievable rates, delay and complexity. When there is no delay constraint at all, the conventional pilots can be eliminated completely and a proper interleaving scheme can convert half the symbols into manufactured pilots. When there is a delay constraint, the paper explores various interleaver structures that combine the conventional pilots with the manufactured pilots in different ways to get much better achievable rates than conventional pilot-symbol aided channel estimation.

This paper presents analytical upper and lower bounds on the information rate of a multiuser Rayleigh fading channel with no channel state information (CSI) at the transmitters or the receivers. These bounds are shown to converge whenever an individual user's data rate is small compared with the bandwidth, e.g., when users can employ CDMA. The amount of spreading required for a given degree of convergence depends on the number of receive antennas. The number of users can be sufficient for the aggregate spectral density to be large. The paper presents exact analytical expressions for the information rates of both the block fading and the continuous correlated fading channel models in this regime. Finally, the results are extended to more general channel models.

This paper proves that any bandlimited signal within ±0.637V can be represented by a PWM waveform with amplitude V. The number of the pulses in the waveform is equal to the number of the Nyquist samples. This paper also provides a practical iterative procedure to generate the PWM waveform for a given bandlimited signal. The error of this procedure decreases exponentially with the number of iterations.

This paper proposes a new nonlinear equalization approach for the transmission of high-density constellations over nonlinear ISI channels. Multilevel coding is performed at the transmitter, and multistage equalization and decoding at the receiver. Two equalizers are introduced. One uses nonlinear intersymbol interference (ISI) cancellation and has linear complexity in the channel memoryL, and the number of decoding stagesK. The other employs the reduced-state Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, which shows better performance and complexity on the order ofKmiddot2L. Capacity analysis and code simulation results show that these two schemes can achieve significant improvement over the conventional approaches that view nonlinear ISI as additive noise.

This paper proposes a practical successive decoding scheme with finite levels for the finite-state Markov channels (FSMCs) where there is no a priori state information at the transmitter or the receiver. The design employs either a random interleaver or a deterministic interleaver with an irregular pattern and an optional iterative estimation and decoding procedure within each level. The interleaver design criteria may be the achievable rate or the extrinsic information transfer (EXIT) chart, depending on the receiver type. For random interleavers, the optimization problem is solved efficiently using a pilot-utility function, while for deterministic interleavers, a good construction is given using empirical rules. Simulation results demonstrate that the new successive decoding scheme combined with irregular low-density parity-check (LDPC) codes can approach the identically and uniformly distributed (i.u.d.) input capacity on the Markov-fading channel using only a few levels.

This paper studies the performance of bit interleaved coded modulation (BICM) with a single decision feedback. The separation of demodulation and decoding in BICM inevitably reduces the channel's capacity. Altering the conventional bit mapping in BICM and allowing a single decision feedback greatly reduces the capacity loss. The extra complexity introduced by the single decision feedback appears well justified for dense constellations.

This talk presents analytical upper and lower bounds on the information rate of a multiuser Rayleigh fading channel with no channel state information (CSI) at the transmitters or the receivers. These bounds are shown to converge whenever an individual userpsilas data rate is small compared with the bandwidth, e.g., when users can employ CDMA. The amount of spreading required for a given degree of convergence depends on the number of receive antennas; however, the number of users can be sufficient for the aggregate spectral density to be large. The talk presents exact analytical expressions for the information rates of both the block fading and the continuous correlated fading channel models in this regime and presents techniques for extending these to more general channel models.

This paper first presents an optimal receiver and coding scheme for a multi-user, multi-receiver, non-coherent Rayleigh flat fading channel which achieves the channel's constrained capacity (i.e., the capacity for a fixed input distribution). The paper then goes on to analyze the optimal receiver and uses it to generate tight upper and lower bounds on the constrained capacity. Knowing this constrained capacity is essential to judge the efficiency of coding schemes for the channel; it performs the same function as BPSK capacity for the AWGN channel in judging LDPC codes. The paper then goes on to present a practicable correlation based receiver that uses a novel iterative channel estimation technique. The performance of this receiver remains close to the constrained capacity as long as the per-user SNR is low; there is no requirement on the aggregate SNR. With 50 users, 50 receivers and a brickwall fading channel with a coherence length of 200 symbols, for example, the correlation based receiver achieves a sum rate of 36 bits/sec/Hz, significantly greater than any current cellular standards.

This work studies the performance of Bit Interleaved Coded Modulation with a single decision feedback. The separation of demodulation and decoding in BICM inevitably reduces the channelpsilas capacity. Altering the conventional bit-mapping in BICM and allowing a single decision feedback greatly reduces the capacity loss. The extra complexity due to the single decision feedback appears well justified for dense constellations.

This paper proposes a multilevel coding system with linear mapping for fading channels. The receiver performs multi-stage decoding. Each stage employs the decision-aided successive estimation and decoding method that decouples the channel estimation and decoding without loss of information. As a result, existing codes designed for memoryless channels can be applied directly. The overall system can achieve the constrained capacity of the fading channel with a given input distribution, provided that the memoryless channel codes are capacity achieving and the channel estimator is lossless. This paper uses the block fading channel as example, and derives a low complexity channel estimator. For i.i.d. Gaussian inputs, the estimator is lossless and so the multilevel coding system achieves the mutual information of the channel. For QAM inputs, the same estimator is shown numerically to have good performance.

This paper presents a practicable scheme for building a high-frequency, direct digital-to-RF transmitter. The transmitter uses a simple look-up table to generate a binary output stream which then is filtered to produce a radiated signal, so that there is no need for precise digital-to-analog converters. The look-up table entries are produced by a new constrained list decoding algorithm operating over the real alphabet. This all-digital transmitter can be a modulator only, or a combined encoder and modulator and supports the direct generation of RF signals using currently available high-speed CMOS. The paper concludes with spectra having carrier frequencies over 10 GHz and data rates up to 1200 Mbps.

This paper proposes a multilevel coding scheme with linear mapping for intersymbol interference (ISI) channels and derives a low-complexity receiver structure that can achieve the ISI channel capacity. The transmitter superimposes many layers of independent binary antipodal streams to generate a quadrature amplitude modulation (QAM) or Gaussian-like channel input. The receiver performs multistage decoding with decision feedback and interference cancellation. Within each stage is a linear minimum mean-square-error (MMSE) equalizer followed by an error-correcting decoder. The complexity scales linearly with the channel length and the number of layers, and the process is shown to be asymptotically information lossless if a fixed input power is properly distributed over a sufficiently large number of layers. This framework is then extended to achieve the capacity of the ISI channel using a transmitter-side spectral shaping filter that converts a Gaussian input sequence with a white spectrum to one with a water-filling spectrum.

This paper presents a new technique for communication over channels with memory where the channel state is unknown at the transmitter and receiver. A deep interleaver combined with successive decoding decomposes a channel with memory into an array of parallel memoryless channels on which a conventional coding system can operate individually. The problems of joint channel estimation and decoding thus are separated without loss of capacity. This technique achieves channel capacity and so may be used to evaluate the capacities of different channels. A general information-theoretic framework is developed and applied to intersymbol interference (ISI), finite-state Markov, and Rayleigh-fading channels. A full system implementation, which performs within 1.1 dB of the channel capacity upper bound, is presented for the Rayleigh-fading channel

A receiver structure that uses decision feedback and successive decoding is proposed for a noncoherent channel with independent block fading. The transceiver employs a block interleaver to decompose the channel into a set of independent fading sub-channels. LDPC codes are used on each sub-channel, and the decoded data are fed back to help in channel estimation. Simulation results indicate that the performance of the proposed system is within 0.7 dB of the Shannon capacity of the binary-input block fading channel.

An optimal equalizer for the transmission of densely modulated signals on nonlinear ISI channels requires the use of full-branched BCJR algorithm, which has an extremely high complexity. This paper proposes a new nonlinear equalization approach that significantly lowers the complexity and yields good performance at the same time. Multilevel coding is performed at the transmitter, and multistage equalization and decoding at the receiver. A linear complexity equalization scheme using nonlinear ISI cancellation is presented, as well as an equalization scheme based on the reduced-state BCJR algorithm for improved performance at a slightly higher complexity. Capacity analysis and code simulation results show that these two schemes substantially outperform the conventional approach, which views the nonlinear ISI as additive noise

This paper calculates both an upper bound and a constructive lower bound on the capacity of an N transmitter, K receiver MIMO fading network. The channel between the transmitters and the receivers is Rayleigh flat fading with fading coefficients unknown to both transmitters and receivers. The lower bound is derived from a practicable successive decoding scheme, and when N is significantly larger than K, it approaches the upper bound with increasing coherence length of the fading process. Obviously, in the limit of large coherence lengths, the system becomes coherent and so is trivial. However, the lower and upper bounds of this paper are close to the MIMO capacity even when the system is highly non-coherent. For example, with N = 50, K = 15 and a coherence length of 200, the achievable rate of the successive decoding scheme diverges from the upper bound by just 6%, even when it is only 40% of coherent capacity. At this design point, the scheme achieves a rate of 13 bits/sec/Hz, significantly greater than any current cellular standards

This paper proposes novel successive decoding paradigm for fading channels, K independent codewords of different rates and lengths are interleaved at the transmitter according to a pattern, and successively decoded at the receiver. This enables progressively better channel estimates for the receiver, at a minimal cost of pilot symbols. At each decoding stage, channel estimation and decoding are performed separately. or iteratively if the residual channel correlation within a codeword can be exploited. The flexible interleaver pattern, after some level of optimization, achieves near-capacity system performance with only a small number of codewords K, as demonstrated numerically by a finite state Markov modelled flat fading channel

This paper proves that low density parity check (LDPC) codes are universal codes on correlated fading channels if a successive decoding receiver is used. A universal LDPC code is defined as a code with the same performance over a class of channels, in which the performance is measured by the threshold of the code in terms of mutual information (in bits/sec/Hz). The receiver proposed in this paper decomposes the fading channel into a bank of memoryless sub-channels. Each sub-channel is encoded with a LDPC code. An MMSE estimator followed by a LDPC decoder is used to successively decodes the channel code. With this scheme, we show that LDPC codes have the universal performance on fading channels with variant fading rates. We also prove that the LDPC code design is unified. Hence, the optimal LDPC codes for the perfect CSI receiver is also optimal for correlated fading channels without CSI.

This paper introduces a new trellis pruning method which uses nonlinear convolutional coding for peak-to-average power ratio (PAPR) reduction of filtered QPSK and 16-QAM modulations. The Nyquist filter is viewed as a convolutional encoder that controls the analog waveforms of the filter output directly. Pruning some edges of the encoder trellis can effectively reduce the PAPR. The only tradeoff is a slightly lower channel capacity and increased complexity. The paper presents simulation results of the pruning action and the resulting PAPR, and also discusses the decoding algorithm and the capacity of the filtered and pruned QPSK and 16-QAM modulations on the AWGN channel. Simulation results show that the pruning method reduces the PAPR significantly without much damage to capacity.

This paper presents both an information lossless coding scheme and a method to evaluate constrained capacity for channels with memory and unknown state. The fundamental idea is to decompose the original channel into a bank of memoryless sub-channels with partially known states, then successively decode these sub-channels. The receiver of each sub-channel consists of an optimal estimator followed by a memoryless channel decoder. The coding scheme translates the codes and decoders designed for memoryless channels with near capacity performance to channels with memory. The results are applied to both finite state Markov channels and correlated flat fading channels

This paper presents a new coding scheme with capacity approaching performance for correlated fading channels with unknown state. The transceiver employs a deep interleaver to decompose the original channel into a bank of independent fading sub-channels. Sub-channels are successively decoded and decisions are fed back as new training symbols. The unknown state of each sub-channel can be estimated from past channel observations and future channel outputs. We show that the sub-channel has the same capacity as the original channel, given a sufficiently large estimation window. Therefore, the correlated fading channel capacity can be approached if each sub-channel uses an optimized capacity achieving code. Simulations show a universal performance within 1 dB of capacity upper bound regardless of fading rate. The scheme is also robust against decision feedback errors when the sub-channels use a long LDPC code

This paper calculates the capacity of continuous phase modulation (CPM) schemes, modeling CPM as a finite state machine. The novel capacity-calculation algorithm gives a reliable estimate of the capacity using minimal computer time. This algorithm allows the production of a more generalized class of modulation schemes called generalized CPM, which have a higher capacity than traditional CPM schemes of comparable bandwidth

This paper presents a practicable scheme for building high frequency direct digitizing transmitters. The transmitter uses a simple look up table approach to generate a binary stream which is then merely filtered to produce the radiated signal. Thus, there is no need for precise digital to analog converters. A new constrained list decoding algorithm operating over the real alphabet produces the data in the look up table. The transmitter can be a modulator only or a combined encoder and modulator. The paper concludes with spectra and error vector magnitude measurements for GMSK with frequencies over 10 Ghz

This paper presents a state generated training symbol (SGTS) algorithm as a novel channel estimation scheme for sequence detector under time-varying flat-fading channels. The key idea of SGTS is that data-aided unknown parameters estimation can be embedded into the Viterbi decoding structure. By using a systematic convolutional code, the SGTS scheme uses a `future' training sequence manufactured by the current decoding state to estimate the channel parameter. This is distinct from the conventional per-survivor processing (PSP) algorithm which uses `past' survivor data to do the estimation. Simulation results are provided to show that the novel SGTS-based sequence detector has similar performance with lower computation load compared with the PSP-based one. Furthermore, SGTS can coordinate with PSP. The resulting sequence detector achieves significant performance improvements with better channel estimation, especially under fast fading channels

This paper proves that CDMA with beam forming single user detection (SUD-CDMA) is asymptotically optimum, even if it is done on a user by user basis (naive CDMA), for many large wireless networks in the presence of unknown fading. The paper models the transmitters and receivers as uniformly distributed over a grid in a 3-D, 2-D or 1-D universe and allows every transmitter to broadcast to all receivers with a power inversely proportional to the second, third or the fourth power of its distance from the receiver. The channel between the transmitters and the receivers is a fading channel where the receivers do not have any knowledge of the fading realizations. The introduction of unknown fading (even if very slow) and interference from all the transmitters make the model and hence the result of this paper fundamentally different from previous results. The paper proves that, when the number of users increases while keeping the network expanse constant SUD-CDMA is optimal irrespective of the geometry of the network or the path loss exponent. When the number of users increases while keeping the network density constant SUD-CDMA is optimal for most geometries when the path loss exponent is low.

The paper presents a. practical scheme for building high frequency direct digitizing transmitters. The transmitter uses a. simple lookup table approach to generate a binary stream which is then merely filtered to produce the radiated signal. Thus, there is no need for precise digital to analog converters. A new constrained list decoding algorithm operating over the real alphabet produces the data in the lookup table. The transmitter can be a modulator only or a combined encoder and modulator. The paper concludes with spectra and error vector magnitude measurements for GMSK with frequencies over 10 GHz.

This paper proves that the optimum algorithm for waveform synthesis of an analog waveform such that the quantisation noise over a band in frequency is minimised, is Viterbi decoding the analog waveform over the convolutional code generated by a band pass filter with the same passband. A novel application of waveform synthesis to design of efficient modulation systems is proposed, resulting in a completely digital transmitter with no analog stages required for modulation and upconversion. High speed applications of the proposed scheme require list decoder compatible filters of low constraint lengths. The paper proposes a design methodology for designing short list-decoder compatible filters by optimising their equivalent performance profiles (EPP) and analyses the performance of these encoders with varying list lengths. The paper also explains the transition phenomena observed in the performance of the encoders and derives a theoretical upper bound on the minimum number of list survivors to be retained to ensure negligible drop in the performance of the encoders.

This paper presents a method for calculating arbitrarily tight upper and lower bounds on the capacity of a flat fading channel with M-ary inputs, where the fading process is modelled as a Gaussian random process with any spectral density. Neither the transmitter nor the receiver knows the channel state. The paper also presents a practicable method for adapting any family of codes designed for i.i.d. channels to work on correlated fading channels. Thus, the near-capacity performance of existing codes with iterative decoders can be translated directly to fading channels.

This talk introduces the concept of coding for variable channel coherence. The need for this type of coding arises naturally in the multiuser broadcast channel since the more mobile a terminal, the harder it is to maintain coherence. The talk shows that noncoherent users can be accommodated without loss to the overall capacity, as long as there are not too many of them. This derivation leads naturally to an efficient (capacity lossless) method of using codes designed for memoryless channels on channels with memory.

This talk extends the theory of list-decoders to derive bounds on the maximum number of survivor paths required for waveform synthesis using noisy codeword decoding of convolutional codes over the real alphabet. This technique gives a noise shaping far superior to that of the conventional /spl Sigma//spl Delta/. The talk also proposes an algorithm for designing short list-decoder friendly encoders/filters.

Turbo codes with long frame lengths are usually constructed using a randomly chosen interleaver. Statistically, this guarantees excellent bit-error rate (BER) performance but also generates a certain number of low weight codewords, resulting in the appearance of an error floor in the BER curve. Several methods, including using an outer code, have been proposed to improve the error floor region of the BER curve. We study the effect of an outer BCH code on the frame-error rate (FER) of turbo codes. We show that additional coding gain is possible not only in the error floor region but also in the waterfall region. Also, the outer code improves the iterative APP decoder by providing a stopping criterion and alleviating convergence problems. With this method, we obtain codes whose performance is within 0.6 dB of the sphere packing bound at an FER of 10/sup -6/.

This article demonstrates that increasing the number of measurements made on a system beyond the minimum (i.e., the number of degrees of freedom in the system) can reduce the effect of measurement errors. The article shows, for three broad classes of measurement problems, that, as the measurement redundancy increases, the residual error falls to a small constant value. Twice the number of degrees of freedom will allow performance very close to the ultimate limits. The article presents one example within each class; however, a vast number of other measurement problems have a formulation identical to one of these three. The first example is the calibration of a resistive voltage divider consisting of a number of nominally equal resistors in series. The second is the determination of the complex response of a filter whose output can be observed only through a power detector. The third is the calibration of a resistive current combiner or current mode digital-to-analog converter (DAC). The basic ideas in the article are general and extensions to other measurement problems outside of the three categories should be straightforward, although the details of the solution will be problem dependent.

This paper calculates new bounds on the size of the performance gap between random codes and the best possible codes. The first result shows that, for large block sizes, the ratio of the error probability of a random code to the sphere-packing lower bound on the error probability of every code on the binary symmetric channel (BSC) is small for a wide range of useful crossover probabilities. Thus even far from capacity, random codes have nearly the same error performance as the best possible long codes. The paper also demonstrates that a small reduction k-k/spl tilde/ in the number of information bits conveyed by a codeword will make the error performance of an (n,k/spl tilde/) random code better than the sphere-packing lower bound for an (n,k) code as long as the channel crossover probability is somewhat greater than a critical probability. For example, the sphere-packing lower bound for a long (n,k), rate 1/2, code will exceed the error probability of an (n,k/spl tilde/) random code if k-k/spl tilde/>10 and the crossover probability is between 0.035 and 0.11=H/sup -1/(1/2). Analogous results are presented for the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) channel. The paper also presents substantial numerical evaluation of the performance of random codes and existing standard lower bounds for the BEC, BSC, and the AWGN channel. These last results provide a useful standard against which to measure many popular codes including turbo codes, e.g., there exist turbo codes that perform within 0.6 dB of the bounds over a wide range of block lengths.

This paper analyzes the performance of concatenated coding systems operating over the binary-symmetric channel (BSC) by examining the loss of capacity resulting from each of the processing steps. The techniques described in this paper allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. They are, moreover, very useful for the overall design of a communications system, e.g., for evaluating the benefits of inner decoders that produce side information. The first two sections of this paper provide a general technique (based on the coset weight distribution of a binary linear code) for calculating the composite capacity of the code and a BSC in isolation. The later sections examine the composite capacities of binary linear codes, the BSC, and various decoders. The composite capacities of the (8,4) extended Hamming, (24, 12) extended Golay, and (48, 24) quadratic residue codes appear as examples throughout the paper. The calculations in these examples show that, in a concatenated coding system, having an inner decoder provide more information than the maximum-likelihood (ML) estimate to an outer decoder is not a computationally efficient technique, unless generalized minimum-distance decoding of an outer code is extremely easy. Specifically, for the (8,4) extended Hamming and (24, 12) extended Golay inner codes, the gains from using any inner decoder providing side information, instead of a strictly ML inner decoder, are shown to be no greater than 0.77 and 0.34 dB, respectively, for a BSC crossover probability of 0.1 or less, However, if computationally efficient generalized minimum distance decoders for powerful outer codes, e.g., Reed-Solomon codes, become available, they will allow the use of simple inner codes, since both simple and complex inner codes have very similar capacity losses.

This correspondence analyzes the performance of concatenated coding systems and modulation schemes operating over the additive white Gaussian noise (AWGN) channel by examining the loss of capacity resulting from each of the processing steps. The techniques described in this correspondence allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. Knowledge of this capacity loss is very useful for the overall design of a communications system, e.g., for evaluating the benefits of inner decoders that produce information beyond the maximum-likelihood (ML) estimate. The first two sections of this correspondence provide a general technique for calculating the composite capacity of an orthogonal or a bi-orthogonal code and the AWGN channel in isolation. The later sections examine the composite capacities of an orthogonal or a bi-orthogonal code, the AWGN channel, and various inner decoders including the decoder estimating the bit-by-bit probability of a one, as is used in turbo codes. The calculations in these examples show that the ML decoder introduces a large loss in capacity. Much of this capacity loss can be regained by using only slightly more complex inner decoders, e.g., a detector for M-ary frequency-shift keying (MFSK) that puts out the two most likely frequencies and the probability the ML estimate is correct produces significantly less degradation than one that puts out only the most likely frequency.

Coding performance is limited not only by Shannon's (1950) bounds but also by the complexity of decoders. Decoder complexity is in turn governed by the need for the different pieces of the machine to communicate with one another. This paper calculates lower limits on the intra-system information flow for the Viterbi decoding of shift-register-based codes, e.g., convolutional codes. These limits provide practical guidance for the construction of decoders for the current generation of convolutional and trellis codes. In particular, these bounds prove that a very specialized decoder family, called graph partition decoders, have an asymptotically optimum communications growth rate. The techniques used in this paper can, moreover, be applied to the design of new (non-shift-register-based) codes which may possibly circumvent the limits derived in the paper and to the design of parallel processors.>

A determinate state convolutional code is formed from a conventional convolutional code by pruning away some of the possible state transitions in the decoding trellis. This staged power transfer proves to be an extremely efficient way of enhancing the performance of a concatenated coding system. The authors analyze the decoding complexity and free distances of these new codes, determine some important statistical properties of the decoder output, and provide simulation results for performance at the low signal-to-noise ratios where a real communications system would operate. Several concise, practical examples are presented.>

A series of algorithms, circuit designs, and analytical techniques as well as a few tricks are presented. Each is essential to the design, which created a constraint-length-15, 1-Mb/s Viterbi decoder. The focus is the maximum-likelihood decoding of very-long-constraint-length convolutional codes, but many of the concepts will find other applications ranging from extremely fast constraint-length-7 decoders to software simulations of codes with constraint lengths even longer than 15. The constraint-length-15 decoder is now working and will form the basis for the coding system used in the next generation of deep space probes.>