Alphabet-constrained vector quantization

Alphabet-constrained rate-distortion theory is extended to coding of sources with memory. Two different cases are considered: when only the size of the codebook is constrained and when the codevector values are also held fixed. For both cases, nth-order constrained-alphabet rate-distortion functions are defined and a convergent algorithm for their evaluation is presented. Specific simulations using AR(1) sources show that performance near the rate-distortion bound is possible using a reproduction alphabet consisting of a small number of codevectors. It is also shown that the additional constraint of holding the codevector values fixed does not degrade performance of the coder in relation to the size-only constrained case. This observation motivates the development of a fixed-codebook vector quantizer, called the alphabet- and entropy-constrained vector quantizer, the performance of which is comparable to the entropy-constrained vector quantizer. A number of examples using an AR(1) and a speech source are presented to corroborate the theory