On the block size of trellis quantizers

Summary form only given. In this paper, we examine the effect of block size on the performance of trellis based quantization. In particular, the Viterbi and tailbiting BCJR algorithms are compared. It is shown that for short blocks of data, the T-BCJR algorithm achieves a superior performance over the Viterbi algorithm (VA). One approach is to use the maximum a posteriori probability (MAP) heuristic and the T-BCJR algorithm. If the MAP-encoder does not produce a tailbiting state sequence, the path is modified for a number of stages at the beginning and end of the block such that it tailbites. The enclosed figure shows MSE as a function of block size and sample position, respectively, for a rate R=1 bit per sample, 32-state trellis quantizer and an IID Gaussian source. The effects of start-up are clearly visible. For the T-BCJR algorithm, the distortion is evenly distributed across the whole block. The performance decrease for short blocks stems from the increase in the number of tailbiting violations for short blocks and the suboptimal modification to ensure tailbiting. The results presented here hold for a large class of trellis constructions, such as TCQ.