On the joint source-channel decoding of variable-length encoded sources: the additive-Markov case

We propose an optimal joint source-channel maximum a posteriori probability decoder for variable-length encoded sources transmitted over a wireless channel, modeled as an additive-Markov channel. The state space introduced by the authors in a previous paper is used to take care of the unique challenges posed by variable-length codes. Simulations demonstrate, that this decoder performs substantially better than the standard Huffman decoder for a simple test source and is robust to inaccuracies in channel statistics estimates. The proposed algorithm also compares favorably to a standard forward error correction-based system.     

Robust decoding of variable-length encoded Markov sources using a three-dimensional trellis

In this letter, we present an improved index-based a-posteriori probability (APP) decoding approach for the error-resilient transmission of packetized variable-length encoded Markov sources. The proposed algorithm is based on a novel two-dimensional (2D) state representation which leads to a three-dimensional trellis with unique state transitions. APP decoding on this trellis is realized by employing a 2D version of the BCJR algorithm where all available source statistics can be fully exploited in the source decoder. For an additional use of channel codes the proposed approach leads to an increased error-correction performance compared to a one-dimensional state representation.     

Length-constrained MAP decoding of variable-length encoded Markov sequences

In this paper, we consider the problem of length-constrained maximum a posteriori decoding of a Markov sequence that is variable-length encoded and transmitted over a binary symmetric channel. We convert this problem into one of a maximum-weight k-link path in a weighted directed acyclic graph. The induced graph-optimization problem can be solved by a fast parameterized search algorithm that finds either the optimal solution with high probability, or a good approximate solution otherwise. The proposed algorithm has lower complexity and superior performance than the previous approximation algorithms.     

Joint source-channel decoding for variable-length encoded data byexact and approximate MAP sequence estimation

Joint source-channel decoding based on residual source redundancy is an effective paradigm for error-resilient data compression. While previous work only considered fixed-rate systems, the extension of these techniques for variable-length encoded data was independently proposed by the authors and by Demir and Sayood (see Proc. Data Comp. Conf., Snowbird, UT, p.139-48, 1998). We describe and compare the performance of a computationally complex exact maximum a posteriori (MAP) decoder, its efficient approximation, an alternative approximate decoder, and an improved version of this decoder are suggested. Moreover, we evaluate several source and channel coding configurations. The results show that our approximate MAP technique outperforms other approximate methods and provides substantial error protection to variable-length encoded data     

LDPC-based iterative joint source-channel decoding for JPEG2000.

A framework is proposed for iterative joint source-channel decoding of JPEG2000 codestreams. At the encoder, JPEG2000 is used to perform source coding with certain error-resilience (ER) modes, and LDPC codes are used to perform channel coding. During decoding, the source decoder uses the ER modes to identify corrupt sections of the codestream and provides this information to the channel decoder. Decoding is carried out jointly in an iterative fashion. Experimental results indicate that the proposed method requires fewer iterations and improves overall system performance.     

Iterative joint source-channel decoding of variable-length codes using residual source redundancy

We present a novel symbol-based soft-input a posteriori probability (APP) decoder for packetized variable-length encoded source indexes transmitted over wireless channels where the residual redundancy after source encoding is exploited for error protection. In combination with a mean-square or maximum APP estimation of the reconstructed source data, the whole decoding process is close to optimal. Furthermore, solutions for the proposed APP decoder with reduced complexity are discussed and compared to the near-optimal solution. When, in addition, channel codes are employed for protecting the variable-length encoded data, an iterative source-channel decoder can be obtained in the same way as for serially concatenated codes, where the proposed APP source decoder then represents one of the two constituent decoders. The simulation results show that this iterative decoding technique leads to substantial error protection for variable-length encoded correlated source signals, especially, when they are transmitted over highly corrupted channels.     

On the joint source-channel decoding of variable-length encodedsources: the BSC case

This paper proposes an optimal maximum a posteriori probability decoder for variable-length encoded sources over binary symmetric channels (BSC) that uses a novel state-space to deal with the problem of variable-length source codes in the decoder. This sequential, finite-delay, joint source-channel decoder delivers substantial improvements over the conventional decoder and also over a system that uses a standard forward error correcting code operating at the same over all bit rates. This decoder is also robust to inaccuracies in the estimation of channel statistics     

A generalized framework for iterative source-channel decoding

Joint source-channel decoding is considered for a transmission system, in which the quantizer indices of several autocorrelated source signals are bit-interleaved, commonly channel encoded, and transmitted in parallel. Since the optimal decoding algorithm is not feasible in most practical situations, iterative source-channel decoding has been introduced. The latter is generalized in the present paper. Furthermore, it is shown in detail, that iterative source-channel decoding can be derived by insertion of appropriate approximations into the optimal joint decoding algorithm. The approximations allow the decomposition of the optimal decoder into two parts, which can be identified as the constituent decoders for the channel-code and the source-code redundancies. Similar as in other concatenated coding systems, the constituent decoders are applied in an iterative decoding scheme. Its performance is analyzed by simulation results.     

Joint source-channel decoding of variable-length codes for convolutional codes and turbo codes

Several recent publications have shown that joint source-channel decoding could be a powerful technique to take advantage of residual source redundancy for fixed- and variable-length source codes. This letter gives an in-depth analysis of a low-complexity method recently proposed by Guivarch et al., where the redundancy left by a Huffman encoder is used at a bit level in the channel decoder to improve its performance. Several simulation results are presented, showing for two first-order Markov sources of different sizes that using a priori knowledge of the source statistics yields a significant improvement, either with a Viterbi channel decoder or with a turbo decoder.     

Joint source-channel decoding of predictively and nonpredictively encoded sources: a two-stage estimation approach

A common joint source-channel (JSC) decoder structure for predictively encoded sources involves first forming a JSC decoding estimate of the prediction residual and then feeding this estimate to a standard predictive decoding (synthesis) filter. In this paper, we demonstrate that in a JSC decoding context, use of this standard filter is suboptimal. In place of the standard filter, we choose the synthesis filter coefficients to give a least-squares (LS) estimate of the original source, based on given training data. For first-order differential pulse-code modulation, this yields as much as 0.65-dB gain in reconstructing first-order Gauss-Markov sources. More gains are achieved with modest additional complexity by increasing the filter order. While performance can also be enhanced by increasing the source's Markov model order and/or the decoder's lookup table memory, complexity grows exponentially in these parameters. For both predictive and nonpredictive coding, our LS approach offers a strategy for increasing the estimation accuracy of JSC decoders while retaining manageable complexity.     

Joint source-channel turbo decoding of entropy-coded sources

We analyze the dependencies between the variables involved in the source and channel coding chain. This analysis is carried out in the framework of Bayesian networks, which provide both an intuitive representation for the global model of the coding chain and a way of deriving joint (soft) decoding algorithms. Three sources of dependencies are involved in the chain: (1) the source model, a Markov chain of symbols; (2) the source coder model, based on a variable length code (VLC), for example a Huffman code; and (3) the channel coder, based on a convolutional error correcting code. Joint decoding relying on the hidden Markov model (HMM) of the global coding chain is intractable, except in trivial cases. We advocate instead an iterative procedure inspired from serial turbo codes, in which the three models of the coding chain are used alternately. This idea of using separately each factor of a big product model inside an iterative procedure usually requires the presence of an interleaver between successive components. We show that only one interleaver is necessary here, placed between the source coder and the channel coder. The decoding scheme we propose can be viewed as a turbo algorithm using alternately the intersymbol correlation due to the Markov source and the redundancy introduced by the channel code. The intermediary element, the source coder model, is used as a translator of soft information from the bit clock to the symbol clock     

Convergence analysis on iterative decoding of variable-length codes

The convergence characteristics of iterative decoding of variable length codes are discussed. It is observed that variable-length codes with greater redundancy perform better. This suggests that inserting more redundant information in the source-coded bits would be helpful in enhancing the overall performance when iterative decoding is employed     

Joint source-channel turbo coding for binary Markov sources

We investigate the construction of joint source-channel (JSC) turbo codes for the reliable communication of binary Markov sources over additive white Gaussian noise and Rayleigh fading channels. To exploit the source Markovian redundancy, the first constituent turbo decoder is designed according to a modified version of Berrou's original decoding algorithm that employs the Gaussian assumption for the extrinsic information. Due to interleaving, the second constituent decoder is unable to adopt the same decoding method; so its extrinsic information is appropriately adjusted via a weighted correction term. The turbo encoder is also optimized according to the Markovian source statistics and by allowing different or asymmetric constituent encoders. Simulation results demonstrate substantial gains over the original (unoptimized) Turbo codes, hence significantly reducing the performance gap to the Shannon limit. Finally, we show that our JSC coding system considerably outperforms tandem coding schemes for bit error rates smaller than 10/sup -4/, while enjoying a lower system complexity.     

Turbo decodulation: iterative combined demodulation and source-channel decoding

We propose the combination of iterative demodulation and iterative source-channel decoding as a multiple turbo process. The receiver structures of bit-interleaved coded modulation with iterative decoding (BICM-ID), iterative source-channel decoding (ISCD), and iterative source coded modulation (ISCM) are merged to one novel turbo system, in which in two iterative loops reliability information is exchanged between the three single components, demodulator, channel decoder and (softbit) source decoder. Simulations show quality improvements compared to the different previously known systems, which use iterative processing only for two components of the receiver.     

基于HMM的信源—信道迭代联合译码

提出一种在接收端利用Turbo译码软输出,结合HMM（隐马尔可夫模型）中的Baum-Welch重估算法获取信源模型参数并进行信源-信道迭代联合译码的算法.通过含噪接收序列信道译码后的软输出对信源模型参数进行估计,并将迭代估计获得的信源精确概率结构和信道译码结合进行信源-信道联合迭代译码.同时从信息论角度提出用鉴别信息来度量估计获得的信源模型参数的精度,以及确定迭代估计终止的条件.     

LDPC-based channel coding of correlated sources with iterative joint decoding

This letter considers low-density parity-check (LDPC) coding of correlated binary sources and a novel iterative joint channel decoding without communication of any side information. We demonstrate that depending on the extent of the source correlation, additional coding gains can be obtained. Two stages of iterative decoding are employed. During global iterations, updated estimates of the source correlation are obtained and passed on to the sum-product decoder that performs local iterations with a predefined stopping criterion and/or a maximum number of local decoding iterations. Simulation results indicate that very few global iterations (2-5) are sufficient to reap significant benefits from implicit knowledge of source correlation. Finally, we provide analytical performance bounds for our iterative joint decoder and comparisons with sample simulation results.     

Low-complexity iterative decoding with decision-aided equalizationfor magnetic recording channels

Turbo codes are applied to magnetic recoding channels by treating the channel as a rate-one convolutional code that requires a soft a posteriori probability (APP) detector for channel inputs. The complexity of conventional APP detectors, such as the BCJR algorithm or the soft-output Viterbi algorithm (SOVA), grows exponentially with the channel memory length. This paper derives a new APP module for binary intersymbol interference (ISI) channels based on minimum mean squared error (MMSE) decision-aided equalization (DAE), whose complexity grows linearly with the channel memory length, and it shows that the MMSE DAE is also optimal by the maximum a posteriori probability (MAP) criterion. The performance of the DAE is analyzed, and an implementable turbo-DAE structure is proposed. The reduction of channel APP detection complexity reaches 95% for a five-tap ISI channel when the DAE is applied. Simulations performed on partial response channels show close to optimum performance for this turbo-DAE structure. Error propagation of the DAE is also studied, and two fixed-delay solutions are proposed based on combining the DAE with the BCJR algorithm     

Joint source-channel coding using combined TCQ/CPM: iterative decoding

An iterative decoding approach to joint source and channel coding (JSCC) using combined trellis-coded quantization (TCQ) and continuous phase modulation (CPM) is proposed. The channel is assumed to be the additive white Gaussian noise channel. This iterative procedure exploits the structure of the TCQ encoder and the continuous phase modulator. The performance in terms of the signal-to-distortion ratio (SDR) is compared with that of a combined TCQ/trellis-coded modulation (TCM) system. It is shown that the combined TCQ/CPM systems are both power- and bandwidth-efficient, compared with the combined TCQ/TCM system. For source encoding rate R=2 b/sample, it is observed that the combined TCQ/CPM systems with iterative decoding working at symbol level converge faster than the systems working at bit level. The novelty of this work is the use of a soft decoder and an iterative decoding algorithm for TCQ-based JSCC systems. The combined TCQ/CPM with iterative decoding is considered for the first time.