Robust transmission of variable-length encoded sources

Digital communications systems commonly use compression (source coding) and error control (channel coding) to allow efficient and robust transmission of data over noisy channels. When compression is imperfect, some residual redundancy remains in the transmitted data and can be exploited at the decoder to improve the decoder’s probability-of-error performance. A new approach to joint source-channel maximum a posteriori probability (MAP) decoding applicable to systems employing variable-length source codes (VLCs) was recently developed by the authors – the resulting joint decoder’s structure is similar to that of the conventional Viterbi decoder. This paper extends the authors’ previous work to address the problem of error propagation, an inherent problem with using VLCs. Options considered include list decoding, trellis-pruning, and composite schemes. Simulation results presented show that the proposed techniques can result in significant improvement in decoding performance. Introduction Communications systems for data transmission commonly use compression (source coding) followed by error control (channel coding) using a convolutional or trellis code. At the receiver, the noisy received data is decoded using a channel decoder (frequently a maximum-likelihood (ML) Viterbi decoder) in tandem with a source decoder. In most cases, the ideal source encoder would be prohibitively complex to implement, therefore in practical systems some redundancy inevitably remains in the compressed data. The redundancy in the compressed transmitted data may be of two types: due to non-uniform distribution of the transmitted data, or due to memory. In this paper we present a method of exploiting this inevitable residual redundancy to improve decoding through the use of maximum a posteriori probability (MAP) decoding. The problem of MAP decoding for systems employing fixed-length source codes has been studied by several researchers [1–4]; the resulting decoder is identical to a ML Viterbi decoder with path metrics augmented by a priori information. However, until recently [5–8], little work was done on MAP decoding for systems employing variablelength source codes. In [5], a novel method was proposed that uses specialized convolutional codes over the source alphabet and a source-symbol synchronized Viterbi decoder. In [6], an alternate method was proposed for MAP decoding of data transmitted over a binary symmetric channel. In [8], the problem was formulated and solved in a recursive manner, with the resulting solution similar to that in [6]. Variable-length coded systems present some difficulty for MAP decoding since different paths in the channel decoder trellis correspond to different numbers of source symbols. Computation of MAP path metrics requires knowledge of both the source and channel decoder states, and the strategy of selecting a single survivor from several paths merging at each state is no longer optimal. In [7], the authors proposed a new technique for joint source-channel optimal MAP decoding of variable-length encoded sources. This technique has wide applicability; it applies to systems in which the source, the source decoder, and the channel decoder can all be modeled as finite-state machines (FSMs). This includes finite-alphabet memoryless, and finite-alphabet, finite-state Markov sources; Huffman and other tree-structured source codes; and both convolutional and trellis channel codes. The construction of the joint source-channel decoder and some simulation results comparing its performance to the conventional tandem decoding scheme are presented in section 2. Systems employing variable-length codes are especially prone to error propagation. A single error may cause a symbol to be transformed into another of different length causing catastrophic failure due to a large fraction of the subsequent symbols being decoded erroneously. Frequently, the data are divided into blocks to limit error propagation to the end of the block. In section 3, we propose methods which try to further alleviate this problem by providing additional side-information to the decoder – the length of the block in bits and symbols – to assist recovery. One method considered is list decoding (see [9]) where at each state, the joint source-channel decoder maintains a list of L survivor paths rather than a single path as in the conventional decoder. Another method considered is trellis pruning where paths that do not have valid extensions (in terms of bit-length and symbol-length) are eliminated from the joint decoder trellis. A composite scheme combining the two approaches is also proposed, and shown to yield the best performance. Joint Source-Channel Decoder The basis for construction of the joint source-channel decoder is the recognition that all three principle components † Supported in part by COMSAT Laboratories. ‡ Supported in part by NSF grant NCR-9623318.