The design of scalar quantizers for communication systems that use diversity to overcome channel impairments is considered. The design problem is posed as an optimization problem and necessary conditions for optimality are derived. A design algorithm, a generalization of Lloyd's algorithm for quantizer design, is developed. Unlike a single channel scalar quantizer, the performance of a multiple description scalar quantizer is dependent on the index assignment. The problem of index assignment is addressed. Good index assignments, performance results, and sample quantizer designs are presented for a memoryless Gaussian source. Furthermore, comparisons are made against rate distortion bounds for the multiple descriptions problem.

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The problem of designing a multiple description vector quantizer with lattice codebook Λ is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A 2 and Z i , i = 1, 2, 4, 8, that make use of this labeling algorithm.The high-rate squared-error distortions for this family of L-dimensional vector quantizers are then analyzed for a memoryless source with probability density function p and differential entropy h(p) < ∞. For any a ∈ (0, 1) and rate pair (R, R), it is shown that the two-channel distortiond 0 and the channel 1 (or channel 2) distortiond s satisfy lim R→∞d 0 2 2R(1+a) = 1 4 G(Λ)2 2h(p) and lim R→∞d s 2 2R(1−a) = G(S L )2 2h(p) ,where G(Λ) is the normalized second moment of a Voronoi cell of the lattice Λ and G(S L ) is the normalized second moment of a sphere in L dimensions.

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We consider the problem of predicting packet loss visibility in MPEG-2 video. We use two modeling approaches: CART and GLM. The former classifies each packet loss as visible or not; the latter predicts the probability that a packet loss is visible. For each modeling approach, we develop three methods, which differ in the amount of information available to them. A reduced reference method has access to limited information based on the video at the encoder's side and has access to the video at the decoder's side. A no-reference pixel-based method has access to the video at the decoder's side but lacks access to information at the encoder's side. A no-reference bitstream-based method does not have access to the decoded video either; it has access only to the compressed video bitstream, potentially affected by packet losses. We design our models using the results of a subjective test based on 1080 packet losses in 72 minutes of video.