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.     

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.     

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.     

Iterative Source-Channel Decoding With Markov Random Field Source Models

We propose a joint source-channel decoding approach for multidimensional correlated source signals. A Markov random field (MRF) source model is used which exemplarily considers the residual spatial correlations in an image signal after source encoding. Furthermore, the MRF parameters are selected via an analysis based on extrinsic information transfer charts. Due to the link between MRFs and the Gibbs distribution, the resulting soft-input soft-output (SISO) source decoder can be implemented with very low complexity. We prove that the inclusion of a high-rate block code after the quantization stage allows the MRF-based decoder to yield the maximum average extrinsic information. When channel codes are used for additional error protection the MRF-based SISO source decoder can be used as the outer constituent decoder in an iterative source-channel decoding scheme. Considering an example of a simple image transmission system we show that iterative decoding can be successfully employed for recovering the image data, especially when the channel is heavily corrupted.     

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     

基于隐马尔科夫模型的多元LDPC联合译码

采用隐马尔科夫模型对信源估计,对基于多进制LDPC码的联合信源信道译码算法展开研究。该算法通过对传统的多进制LDPC译码算法的改进,在迭代过程中加入通过估计算法得到的信源冗余,校正了迭代软信息,提高译码性能。仿真结果表明,在AWGN信道中,改进算法相比传统译码算法性能优越。     

Hybrid symbol- and bit-based source-controlled channel decoding for MELP speech parameters

A joint source channel coding (JSCC) scheme which exploits bit-level correlation as well as symbol-level correlation efficiently in a source-controlled channel decoding (SCCD) process is proposed and applied to the mixed-excitation linear prediction (MELP) parameters of speech. A modified BCJR algorithm is also proposed for use in the SCCD algorithm. Simulation results show that our proposed scheme performs better than other redundancy-based JSCC schemes such as bit-based SCCD, soft-bit speech decoding (SBSD) and iterative source-channel decoding.     

Sequence MAP decoding of trellis codes for Gaussian and Rayleighchannels

This paper considers the use of sequence maximum a posteriori (MAP) decoding of trellis codes. A MAP receiver can exploit any “residual redundancy” that may exist in the channel encoded signal in the form of memory and/or a nonuniform distribution, thereby providing enhanced performance over very noisy channels, relative to maximum likelihood (ML) decoding. The paper begins with a first-order two-state Markov model for the channel encoder input. A variety of different systems with different source parameters, different modulation schemes, and different encoder complexities are simulated. Sequence MAP decoding is shown to substantially improve performance under very noisy channel conditions for systems with low-to-moderate redundancy, with relative gain increasing as the rate increases. As a result, coding schemes with multidimensional constellations are shown to have higher MAP gains than comparable schemes with two-dimensional (2-D) constellations. The second part of the paper considers trellis encoding of the code-excited linear predictive (CELP) speech coder's line spectral parameters (LSPs) with four-dimensional (4-D) QPSK modulation. Two source LSP models are used. One assumes only intraframe correlation of LSPs while the second one models both intraframe and interframe correlation. MAP decoding gains (over ML decoding) as much as 4 dB are achieved. Also, a comparison between the conventionally designed codes and an I-Q QPSK scheme shows that the I-Q scheme achieves better performance even though the first (sampler) LSP model is used     

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     

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.     

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.     

Relation between encoder and syndrome former variables and symbol reliability estimation using a syndrome trellis

We derive a linear correspondence between the variables of an encoder and those of a corresponding syndrome former. Using the derived correspondence, we show that the log-likelihood ratio of an information bit conditioned on a received sequence can be equally calculated using the syndrome trellis. It is shown that the proposed method also applies to recursive systematic convolutional codes which are typical constituent codes for turbo codes. Moreover, we show that soft-in syndrome decoding considering a priori probabilities of information bits is possible in the same way as for Viterbi decoding based on the code trellis. Hence, the proposed method can be applied to iterative decoding such as turbo decoding. We also show that the proposed method is effective for high-rate codes by making use of trellis modification.     

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.     

Joint turbo decoding and estimation of hidden Markov sources

We describe a joint source-channel scheme for modifying a turbo decoder in order to exploit the statistical characteristics of hidden Markov sources. The basic idea is to treat the trellis describing the hidden Markov source as another constituent decoder which exchanges information with the other constituent decoder blocks. The source block uses as extrinsic information the probability of the input bits that is provided by the constituent decoder blocks. On the other hand, it produces a new estimation of such a probability which will be used as extrinsic information by the constituent turbo decoders. The proposed joint source-channel decoding technique leads to significantly improved performance relative to systems in which source statistics are not exploited and avoids the need to perform any explicit source coding prior to transmission. Lack of a priori knowledge of the source parameters does not degrade the performance of the system, since these parameters can be jointly estimated with turbo decoding     

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.     

On the iterative approximation of optimal joint source-channeldecoding

Joint source-channel decoding is formulated as an estimation problem. The optimal solution is stated and it is shown that it is not feasible in many practical systems due to its complexity. Therefore, a novel iterative procedure for the approximation of the optimal solution is introduced, which is based on the principle of iterative decoding of turbo codes. New analytical expressions for different types of information in the optimal algorithm are used to derive the iterative approximation. A direct comparison of the performance of the optimal algorithm and its iterative approximation is given for a simple transmission system with “short” channel codewords. Furthermore, the performance of iterative joint source-channel decoding is investigated for a more realistic system     

Joint Source and Space Time Decoding over Fading Channels

For high data rate communications, variable length codes (VLC) and multiple input multiple output (MIMO) techniques are required in the application layer and the physical layer, respectively. In this paper, we study the joint decoding for systems that consist of reversible VLC (RVLC) as the source codes and recursive space time trellis codes (STTC) as the coded modulation. The maximum a posteriori probability (MAP) decoding algorithm is modified to accommodate issues including the inseparable systematic information, the unsymmetric trellis structure, and information in both bit and symbol domains. Further, by converting extrinsic information based on the modulation mode and the mapping method, iterative information exchange can be performed so as to fully utilize the redundancy in both RVLC and recursive STTC. The performance of the proposed joint decoding is evaluated over both rapid fading and quasi- static flat fading channels, which shows significant improvement in coding gain in comparison with the non-iterative receiver.     

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     

An error resilient scheme for image transmission over noisychannels with memory

This article addresses the use of a joint source-channel coding strategy for enhancing the error resilience of images transmitted over a binary channel with additive Markov noise. In this scheme, inherent or residual (after source coding) image redundancy is exploited at the receiver via a maximum a posteriori (MAP) channel detector. This detector, which is optimal in terms of minimizing the probability of error, also exploits the larger capacity of the channel with memory as opposed to the interleaved (memoryless) channel. We first consider MAP channel decoding of uncompressed two-tone and bit-plane encoded grey-level images. Next, we propose a scheme relying on unequal error protection and MAP detection for transmitting grey-level images compressed using the discrete cosine transform (DCT), zonal coding, and quantization. Experimental results demonstrate that for various overall (source and channel) operational rates, significant performance improvements can be achieved over interleaved systems that do not incorporate image redundancy.     

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.