Trellis-based scalar vector quantization of sources with memory

The trellis-based scalar-vector quantizer (TB-SVQ) can achieve the rate-distortion performance bound for memoryless sources. This paper extends the scope of this quantizer to coding of sources with memory. First considered is a simple extension, called the predictive TB-SVQ, which applies a closed-loop predictive coding operation in each survivor path of the Viterbi codebook search algorithm. Although the predictive TB-SVQ outperforms all other known structured fixed-rate vector quantizers, due to practical reasons, it may not approach the rate-distortion limit. A new quantization scheme motivated by the precoding idea of Laroia et al. (1993), 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.