Performance Comparisons of Tcq with Difference Distortion Measures and Short Coding Delays
Min Wang · 2005
The design of trellis coded quantization (TCQ) to minimize the mean-squared error (MSE) has been generalized to minimize E{lz ylv} for positive integer U. Simulation results for memoryless uniform and Gaussian sources with v = 1 and 4 show that TCQ outperforms scalar quantization (SQ) in the same way as for v = 2. Entropy-constrained trellis coded quantization (ECTCQ) has also been studied for difference distortion measure p(z, y) = Iz-y(. Two ECTCQ realizations have been considered. One is to design the TCQ codebook subject to the output entropy of the source encoder. The other is to design the TCQ codebook independent of the output entropy while the followed entropy code is designed based on the probabilities of the (locally) optimized TCQ codewords for the source sequence. The latter is suboptimal but requires less computations. Simulations show that the performance of the TCQ system is generally improved by combining with an entropy encoder. ECTCQ outperforms entropy-constrained scalar quantization (ECSQ) in all cases considered. The performance difference between the two ECTCQ realizations at low output entropyincreases as v gets large, but vanishes as the output entropy increases. TCQ system with short coding delays and squared-error criterion has been studied. Simulations show that, with the same amount of coding delay, the performance of such designed TCQ is comparable to that of vector quantizers (VQ) for the memoryless uniform and Gaussian sources, while slightly inferior to VQ for the memoryless Laplacian source. However, TCQ requires much less computations than VQ, expecially for large vector dimensions or encoding rates. Summary Trellis coded quantization (TCQ) [l] is a low-complexity form of trellis coding [2] in which the trellis branches are labeled with reproduction subsets instead of individual reproduction levels. The idea of designing TCQ to minimize the mean-squared error (MSE) [l] is generalized to minimize the average distortion between the input and the output of the quantizrr, given a distortion measure p(2,y) = )z - yIu for positive integer v. Let the encoding rate be R 2 0. The TCQ codebook contains N = 2RtR codewords partitioned into If = 2'tR subsets (according to the rules in [l]), each subset of L = 2R-R' codewords. 0 5 RI 5 R and 0 5 RI'. The N,-state encoding trellis is defined by a rate-R'/(R' + R) convolutional encoder with 2R' branches entering/leaving each state.