Universal serially concatenated trellis coded modulation for space-time channels

This paper presents serially concatenated trellis coded modulations (SCTCMs) that perform consistently close to the available mutual information for periodic erasure channel (PEC), periodic fading channel (PFC) and the 2 times 2 compound matrix channel. We use both the maximum-likelihood decoding criteria and iterative decoding criteria to design universal SCTCMs for the PEC and the PFC. For the space-time channel, by demultiplexing the symbols across the antennas, the proposed universal SCTCMs for the period-2 PFC deliver consistent performance over the eigenvalue skew of the matrix channel. Within the family of channels having the same eigenvalue skew, a time-varying linear transformation (TVLT) is used to mitigate the performance variation over different eigenvectors. The proposed space-time SCTCMs of 1.0, 2.0 and 3.0 bits per transmission require excess mutual information in the ranges 0.11-0.15, 0.23- 0.26 and 0.35-0.53 bits per antenna, respectively. Because of their consistent performance over all channels, the proposed codes will have good frame-error-rate (FER) performance over any quasi-static fading distribution. In particular, the codes provide competitive FER performance in quasi-static Rayleigh fading.     

Multiple trellis coded modulation (MTCM)

The authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation (MTCM) wherein more than one channel symbol per trellis branch is transmitted. They have found simple two-state trellis codes for symmetric MPSK multiple phase-shift keying and AM modulations that can achieve 3-dB gain over uncoded modulation at very high signal-to-noise ratios without bandwidth expansion or reduction in information bit rate. The gain of these codes with respect to previously reported two-state trellis codes is between 1 and 2 dB at very high signal-to-noise ratios, depending on the number of bits per Hertz transmitted. These gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram. The authors note that additional computations per branch are needed for the multiple trellis coding scheme. The concept can be extended to a higher number of states and other types of modulations     

High Rate CPFSK Space-Time Trellis Codes

Space-time trellis coding is an established diversity technique that reduces the effects of multipath fading over wireless communication channels. Here, we consider high rate space-time trellis codes (STTC) with continuous phase frequency shift keying (CPFSK). We present optimized rate-2/3 STTC implemented with 3 transmit antennas. These codes provide system throughputs of 4 and 6 bits per channel use with 4-ary and 8-ary CPFSK respectively. Simulated error rate performance of the optimized codes with receive diversity is presented. We show that although the schemes do not achieve full transmit diversity, they provide excellent coding gains compared to full rank schemes that have equivalent throughput, but higher order modulations and greater complexity.     

Space-time codes for high data rate wireless communication:performance criterion and code construction

We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders     

Bootstrap decoding of low-density parity-check codes

An initial bootstrap step for the decoding of low-density parity-check (LDPC) codes is proposed. Decoding is initiated by first erasing a number of less reliable bits. New values and reliabilities are then assigned to erasure bits by passing messages from nonerasure bits through the reliable check equations. The bootstrap step is applied to the weighted bit-flipping algorithm to decode a number of LDPC codes. Large improvements in both performance and complexity are observed.     

Reliable channel regions for good binary codes transmitted over parallel channels

We study the average error probability performance of binary linear code ensembles when each codeword is divided into J subcodewords with each being transmitted over one of J parallel channels. This model is widely accepted for a number of important practical channels and signaling schemes including block-fading channels, incremental redundancy retransmission schemes, and multicarrier communication techniques for frequency-selective channels. Our focus is on ensembles of good codes whose performance in a single channel model is characterized by a threshold behavior, e.g., turbo and low-density parity-check (LDPC) codes. For a given good code ensemble, we investigate reliable channel regions which ensure reliable communications over parallel channels under maximum-likelihood (ML) decoding. To construct reliable regions, we study a modifed 1961 Gallager bound for parallel channels. By allowing codeword bits to be randomly assigned to each component channel, the average parallel-channel Gallager bound is simplified to be a function of code weight enumerators and channel assignment rates. Special cases of this bound, average union-Bhattacharyya (UB), Shulman-Feder (SF), simplified-sphere (SS), and modified Shulman-Feder (MSF) parallel-channel bounds, allow for describing reliable channel regions using simple functions of channel and code spectrum parameters. Parameters describing the channel are the average parallel-channel Bhattacharyya noise parameter, the average channel mutual information, and parallel Gaussian channel signal-to-noise ratios (SNRs). Code parameters include the union-Bhattacharyya noise threshold and the weight spectrum distance to the random binary code ensemble. Reliable channel regions of repeat-accumulate (RA) codes for parallel binary erasure channels (BECs) and of turbo codes for parallel additive white Gaussian noise (AWGN) channels are numerically computed and compared with simulation results based on iterative decoding. In addition, an examp     

Interpolation by convolutional codes, overload distortion, and theerasure channel

This paper investigates how closely randomly generated binary source sequences can be matched by convolutional code codewords. What distinguishes it from prior work is that a randomly chosen subsequence with density λ is to be matched as closely as possible. The so-called marked bits of the subsequence could indicate overload quantization points for a source sample generated from the tails of a probability distribution. They might also indicate bits where the initial estimate is considered reliable, as might happen in iterated decoding. The capacity of a convolutional code to interpolate the marked subsequence might be viewed as a measure of its ability to handle overload distortion. We analyze this capacity using a Markov chain whose states are sets of subsets of trellis vertices of the convolutional code. We investigate the effect of memory on the probability of perfect interpolation and calculate the residual rate on the unmarked bits of the binary source sequence. We relate our interpolation methodology to sequence-based methods of quantization and use it to analyze the performance of convolutional codes on the pure erasure channel     

Capacity-achieving ensembles for the binary erasure channel with bounded complexity

We present two sequences of ensembles of nonsystematic irregular repeat-accumulate (IRA) codes which asymptotically (as their block length tends to infinity) achieve capacity on the binary erasure channel (BEC) with bounded complexity per information bit. This is in contrast to all previous constructions of capacity-achieving sequences of ensembles whose complexity grows at least like the log of the inverse of the gap (in rate) to capacity. The new bounded complexity result is achieved by puncturing bits, and allowing in this way a sufficient number of state nodes in the Tanner graph representing the codes. We derive an information-theoretic lower bound on the decoding complexity of randomly punctured codes on graphs. The bound holds for every memoryless binary-input output-symmetric (MBIOS) channel and is refined for the binary erasure channel.     

Results on the Improved Decoding Algorithm for Low-Density Parity-Check Codes Over the Binary Erasure Channel

In this correspondence, we first investigate some analytical aspects of the recently proposed improved decoding algorithm for low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We derive a necessary and sufficient condition for the improved decoding algorithm to successfully complete decoding when the decoder is initialized to guess a predetermined number of guesses after the standard message-passing terminates at a stopping set. Furthermore, we present improved bounds on the number of bits to be guessed for successful completion of the decoding process when a stopping set is encountered. Under suitable conditions, we derive a lower bound on the number of iterations to be performed for complete decoding of the stopping set. We then present a superior, novel improved decoding algorithm for LDPC codes over the binary erasure channel (BEC). The proposed algorithm combines the observation that a considerable fraction of unsatisfied check nodes in the neighborhood of a stopping set are of degree two, and the concept of guessing bits to perform simple and intuitive graph-theoretic manipulations on the Tanner graph. The proposed decoding algorithm has a complexity similar to previous improved decoding algorithms. Finally, we present simulation results of short-length codes over BEC that demonstrate the superiority of our algorithm over previous improved decoding algorithms for a wide range of bit error rates     

Low-complexity iterative joint source-channel decoding for variable-length encoded Markov sources

In this paper, we present a novel packetized bit-level decoding algorithm for variable-length encoded Markov sources, which calculates reliability information for the decoded bits in the form of a posteriori probabilities (APPs). An interesting feature of the proposed approach is that symbol-based source statistics in the form of the transition probabilities of the Markov source are exploited as a priori information on a bit-level trellis. This method is especially well-suited for long input blocks, since in contrast to other symbol-based APP decoding approaches, the number of trellis states does not depend on the packet length. When additionally the variable-length encoded source data is protected by channel codes, an iterative source-channel decoding scheme can be obtained in the same way as for serially concatenated codes. Furthermore, based on an analysis of the iterative decoder via extrinsic information transfer charts, it can be shown that by using reversible variable-length codes with a free distance of two, in combination with rate-1 channel codes and residual source redundancy, a reliable transmission is possible even for highly corrupted channels. This justifies a new source-channel encoding technique where explicit redundancy for error protection is only added in the source encoder.     

Rateless Coding for Arbitrary Channel Mixtures With Decoder Channel State Information

Rateless coding has recently been the focus of much practical as well as theoretical research. In this paper, rateless codes are shown to find a natural application in channels where the channel law varies unpredictably. Such unpredictability means that to ensure reliable communication block codes are limited by worst case channel variations. However, the dynamic decoding nature of rateless codes allows them to adapt opportunistically to channel variations. If the channel state selector is not malicious, but also not predictable, decoding can occur earlier, producing a rate of communication that can be much higher than the worst case. The application of rateless or “fountain” codes to the binary erasure channel (BEC) can be understood as an application of these ideas. Further, this sort of decoding can be usefully understood as an incremental form of erasure decoding. The use of ideas of erasure decoding result in a significant increase in reliability.      

Trellis-coded direct-sequence spread-spectrum communications

This paper considers the application of trellis coding techniques to direct-sequence spread-spectrum multiple-access (DS/SSMA) communication. The unique feature of the trellis codes considered is that they are constructed over the set of possible signature sequences rather than over some standard 2-D signal constellation. The resulting codes have a small number of signals per dimension. We present several examples of these trellis codes, and suggest possible methods of implementation. We also present a detailed error analysis for this system, which employs techniques developed by Lehnert and Pursley (1987, 1989)) to accurately model the multiple access interference. We generate numerical results for several examples and conclude that the proposed trellis coded systems yield significant performance improvements over binary antipodal DS/SSMA systems. In addition, the new trellis codes perform better than standard error control techniques with the same complexity and code rate. Analytic results are verified with simulations     

Universal space-time codes from demultiplexed trellis codes

In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents two-dimensional trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes, found by exhaustive search, guarantee consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or, in some cases, superior, frame-error rate and bit-error rate performance under quasi-static Rayleigh fading, as compared with trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh-fading scenario.     

Convolutionally interleaved PSK and DPSK trellis codes forshadowed, fast fading mobile satellite communication channels

Using a model from the literature, the performance of convolutionally interleaved phase-shift-keying (PSK) and differential phase-shift-keying (DPSK) trellis codes for digital speech transmission over shadowed mobile satellite communication channels is determined by computer simulation. First the characteristics of fading channels are examined and analyzed in terms of the probability distributions of amplitude, phase, and burst errors. A statistical method, using a histogram approach, is utilized along with the simulations of fading channels to generate these probability distributions. A test for channel burst error behavior is presented. A periodic convolutional interleaver/deinterleaver to be used with trellis coding to combat slow fading in digital, shadowed mobile satellite channels is designed. This interleaver ha less than half the time delay for the same bit error performance than a block interleaver. The results show that the periodic convolutional interleaver provides considerable improvement in the error and time delay performance of mobile satellite communication channels for up to average shadowing conditions as compared to other techniques     

Adaptive Generator Sequence Selection in Multilevel Space–Time Trellis Codes

It has been shown that multilevel space–time trellis codes (MLSTTCs) designed by combining multilevel coding (MLC) with space–time trellis codes (STTCs) can provide improvement in diversity gain and coding gain of the STTCs. MLSTTCs assume perfect channel state information (CSI) at receiver and no knowledge of CSI at transmitter. Weighted multilevel space–time trellis codes (WMLSTTCs), designed by combining MLSTTCs and perfect CSI at transmitter are capable of providing improvement in coding gain of MLSTTCs. In this paper, we present improvement in performance of MLSTTCs by using channel feedback information from the receiver for adaptive selection of generator sequences. The selected generator sequences are used for encoding the component STTCs. The receiver compares current channel profile at receiver with a set of predetermined channel profiles, and sends an index of a predefined channel profile closest to the current channel profile to the transmitter. The transmitter selects a code set that matches best with the current channel profile at receiver using the index. The selected code set having different sets of generator sequences is used by STTC encoders to generate dynamic space–time trellis codes (DSTTCs). The DSTTCs act as component codes in multilevel coding for generating new codes henceforth referred to as multilevel dynamic space–time trellis codes (MLDSTTCs). Analysis and simulation results show that MLDSTTCs provide improvement in performance over MLSTTCs.     

半双工译码转发中继信道下的空间耦合RA码设计

针对半双工译码转发中继信道,提出了一种可逼近三节点中继信道容量限的空间耦合RA码的设计方法。针对二进制删除信道,源节点分别向中继节点和目的节点发送空间耦合RA码,中继节点先正确恢复出源节点发送的空间耦合RA,然后再次编码产生额外的校验比特并转发给目的节点;目的节点结合中继节点发送的额外校验比特和源节点发送的空间耦合RA码进行译码,正确恢复出源节点的信息。为了评估所设计的空间耦合RA码在三节点中继信道下的渐近性能,推导了密度进化算法用于计算阈值。阈值分析结果表明,所提出的空间耦合RA码能够同时逼近源到中继链路和源到目的链路的容量限。同时,基于半双工二进制删除中继信道,仿真了所设计的空间耦合RA码的误码性能,结果表明,其误码性能与所推导的密度进化算法计算的阈值结果一致,呈现出逼近于容量限的优异性能,且优于采用空间耦合低密度奇偶校验(Low Density Parity Check,LDPC)码的性能。     

Universal Space–Time Codes From Demultiplexed Trellis Codes

In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents 2-D trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes are found by an exhaustive search that guarantees consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or in some cases, superior frame-error rate and bit-error rate performance under quasi-static Rayleigh fading to trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh fading scenario.     

New results on unequal error protection using LDPC codes

In this letter, we propose a new scheme to construct low-density parity-check (LDPC) codes that are suitable for unequal error protection (UEP). We derive UEP density evolution (UDE) formulas for the proposed ensemble over the binary erasure channel (BEC). Using the UDE formulas, high performance UEP codes can be found. Simulation results depict an improvement in the bit error rate of more important bits in comparison with previous results on UEP-LDPC codes.     

LT码的性能分析及参数优化规则

As a new class of forward error correcting encoding algorithm, Luby Transform codes are suitable for the erasure channel environment based on the packet communication. The encoding, decoding algorithms and the implementation of LT codes are summarized in the paper. Meanwhile simulations of the ideal soliton distribution and robust soliton distribution are conducted to evaluate the performance of LT codes in terms of successful decoding probability, mean degree and decoding time over the erasure channel. The parameter optimization rules of LT codes are deeply discussed and proposed in the paper. The research results are of great practical importance for improving the real time performance in the erasure correction applications.     

Discrete multiple tone modulation with coset coding for thespectrally shaped channel

A discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference (ISI) and additive Gaussian noise. Multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete Fourier transform (DFT) code vectors, and high gain coset or trellis codes. Symbol blocks from an inverse DFT (IDFT) are cyclically extended to generate ISI-free channel-output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels. Asymptotic performance of this system is derived, and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample. This discrete multiple tone technique is linear in both the modulation and the demodulation, and is free from the effects of error propagation that often afflict systems employing bandwidth-optimized decision feedback plus coset codes