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variable-rate trellis source encoding

IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第2期45卷 586-608页

作者： Yang, EH Zhang, Z Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada Univ So Calif Dept Elect Engn Syst Inst Commun Sci Los Angeles CA 90089 USA

The fixed slope lossy algorithm derived from the kth-order adaptive arithmetic codeword length function is extended to the case of finite-state decoders or trellis-structured decoders. It is shown that when this algorithm is used to encode a stationary, ergodic source with a continuous alphabet, the Lagrangian performance (i.e., the resulting compression rate plus lambda times the resulting distortion) converges with probability one to a quantity computable as the infimum of an information-theoretic functional over a set of auxiliary random variables and reproduction levels, where lambda > 0 and -lambda is designated to be the slope of the rate-distortion function R(D) of the source at some D;the quantity is close to R(D) + lambda D when the order k used in the arithmetic coding or the number of states in the decoders is large enough, An alternating minimization algorithm for computing the quantity is presented;this algorithm is based on a training sequence and in turn gives rise to a design algorithm for variable-rate trellis source codes, The resulting variable-rate trellis source codes are very efficient in low-rate regions (below 0.8 bits/sample), With k = 8, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Gaussian sources is comparable to that afforded by trellis-coded quantizers;with k = 8 and the number of states in the decoder = 32, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Laplacian sources is about 1 dB better than that afforded by the trellis-coded quantizers with 256 states, With k = 8 and the number of states in the decoder = 256, the mean-squared error encoding performance at the rates of a fraction of 1 bit/sample for highly dependent Gauss-Markov sources with correlation coefficient 0.9 is within about 0.6 dB of the distortion-rate function. Note that at such low rates, predictive coders usually perform poorly.

关键词： arithmetic coding data compression quantization rate-distortion function stationary and ergodic sources variable-rate trellis source encoding

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