Soft and Joint Source-Channel Decoding of Quasi-Arithmetic Codes
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Soft and Joint Source-Channel Decoding of Quasi-Arithmetic Codes Thomas Guionnet Projet TEMICS, IRISA-INRIA, Campus Universitaire de Beaulieu, 35042 Rennes Cedex, France Email: [email protected]
Christine Guillemot Projet TEMICS, IRISA-INRIA, Campus Universitaire de Beaulieu, 35042 Rennes Cedex, France Email: [email protected] Received 20 November 2002; Revised 7 August 2003; Recommended for Publication by Antonio Ortega The issue of robust and joint source-channel decoding of quasi-arithmetic codes is addressed. Quasi-arithmetic coding is a reduced precision and complexity implementation of arithmetic coding. This amounts to approximating the distribution of the source. The approximation of the source distribution leads to the introduction of redundancy that can be exploited for robust decoding in presence of transmission errors. Hence, this approximation controls both the trade-off between compression efficiency and complexity and at the same time the redundancy (excess rate) introduced by this suboptimality. This paper provides first a state model of a quasi-arithmetic coder and decoder for binary and M-ary sources. The design of an error-resilient soft decoding algorithm follows quite naturally. The compression efficiency of quasi-arithmetic codes allows to add extra redundancy in the form of markers designed specifically to prevent desynchronization. The algorithm is directly amenable for iterative source-channel decoding in the spirit of serial turbo codes. The coding and decoding algorithms have been tested for a wide range of channel signal-tonoise ratios (SNRs). Experimental results reveal improved symbol error rate (SER) and SNR performances against Huffman and optimal arithmetic codes. Keywords and phrases: robust arithmetic and quasi-arithmetic coding, joint source-channel coding, soft decoding, estimation, MAP.
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INTRODUCTION
Entropy coding, producing variable length codewords (VLCs), is a core component of any data compression scheme. However, VLCs are very sensitive to channel noise: when some bits are altered by the channel, synchronization losses can occur at the receiver, the position of symbol boundaries are not properly estimated, leading to dramatic symbol error rates (SERs). This phenomenon has given momentum to extensive work on the design of procedures for soft decoding and joint source-channel decoding of VLCs. Soft VLC decoding ideas, exploiting residual source redundancy (the so-called excess rate), have also been shown to reduce the “desynchronization” effect as well as the residual bit error rate and SER [1, 2, 3]. Models incorporating both VLC-encoded sources and channel codes (CCs) have also been considered [4, 5, 6, 7]. The research effort has first focused on Huffman codes [3, 4, 5, 8] and on reversible VLCs [6, 9, 10]. However, arithmetic codes have gained increased popularity in practi-
cal systems, including JPEG2000, H.264, and MPEG-4 standards. Arithmetic coding allows to decouple the coding process from the source model, hence can be used in conjunction with any p
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