ASYMPTOTIC ANALYSIS OF MULTIPLE DESCRIPTION LATTICE VECTOR QUANTIZATION

Recent results have shown that general K-channel multiple-description-coding (MDC) approaches often have significant advantages over conventional twochannel MDC methods. We provide new asymptotic results to describe the performance of a general K-channel symmetric MDC lattice vector quantizer (MDLVQ). We consider a memoryless L-dimensional source with probability density function f and differential entropy h(f) <∞. We control the redundancy with a parameter a ∈ (0, 1) and consider a symmetric MDC with a K-tuple of {R, R, · · · , R} as side quantizer rates. We show that if κ out of K descriptions are received, then the central distortion D and the side distortions D satisfy lim R→∞ D(K,K)22R[1+a(K−1)] = G(Λ)2, lim R→∞ D(K,κ)22R(1−a) = C(K, κ)G(SKL−L)2, where C(K, κ) = K−κ κ K − K K−1 . G(Λ) is the normalized second moment of a Voronoi cell of the lattice Λ and G(SKL−L) is the normalized second moment of a sphere in KL − L dimensions. We use our results to illustrate some relevant trade-offs that are made in configuring an MDC.