On the analysis and design of variable rate trellis source codes

We extend the fixed slope lossy algorithm derived from the kth order arithmetic codeword length function to the case of trellis structured decoders and, as a result, get a new coding method, namely, the so-called variable rate trellis source encoding which aims to jointly optimize the resulting distortion, compression rate, and selected encoding path. It is shown both theoretically and experimentally that properly designed variable rate trellis source codes are very efficient in low rate regions (below 0.8 bits/sample). 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.