Trellis-Based Scalar-Vector Quantization of Sources with Memory

This memo extends the scope of a structured vector quantization scheme, called the trellis-based scalar-vector quantizer (TB-SVQ), which can in principle achieve the rate-distortion bound for memoryless sources, to coding of sources with memory. First, a new quantization scheme, called the predictive TB-SVQ, is considered. It applies the predictive coding operation of the DPCM coders in each survivor paths of the Viterbi codebook search algorithm for the TB-SVQ. Although the predictive TB-SVQ outperforms all other known structured fixed-rate vector quantizers, due to practical reasons, it in general may not approach the rate-distortion limit. A new quantization scheme motivated by the precoding idea of Laroia et al, called the precoded TB-SVQ, is also considered; the granular gain is realized by the underlying trellis code while the combination of the precoder and the SVQ structure provides the boundary gain. This new quantization scheme is asymptotically optimal and can, in principle, approach the rate-distortion bound for Markov sources.