Vector quantizer design for memoryless noisy channels

To handle the effect of transmission errors on the performance of vector quantization (VQ) in source coding, a channel index assignment function is proposed that can be incorporated into a source/channel model of VQ. Using this model, conditions for the optimality of a vector quantizer for a given distortion measure are obtained which generalize the familiar centroid and nearest neighbor conditions. The optimal codevectors are linear combinations of those for the noiseless case, weighted by the a posteriori channel transition probabilities. The optimal encoder selects the codevector that minimizes a weighted sum of the distortion between the input and each codevector, where the weights are channel transition probabilities. A derivation of the conditions for a memoryless channel is given, and an iterative design algorithm is described where at each step the average distortion monotonically decreases. Each iteration consists of three steps which separately modify the encoder, decoder, and the channel index assignment.<>