Entropy constrained multiple description lattice vector quantization

Recently, lattice vector quantizers (LVQ) capable of performing close to known information theoretic bounds were introduced in the area of multiple description coding (MDC). We derive analytical expressions for the central and side quantizers which minimize the expected distortion of an LVQ subject to entropy constraints on the side descriptions for given packet loss probabilities. We show that for certain packet loss probabilities, an optimal LVQ for single descriptions might not be optimal for multiple descriptions. Specifically, we show that the Z² lattice performs better than the A₂ lattice in some cases. Moreover, our results suggest a practical way of determining which lattice quantizers are optimal for given packet loss probabilities.