Quantization For Noisy Channels Using Structured Codes

ows. In this sense, randomly chosen index assignments are asymptotically bad for uniform sources. Bounds for the optimal rate allocation between source and channel coding are developed for the cascade of "good" quantizers and channel codes that meet the GilbertVarshamov or Tsfasman-Vladut-Zink bounds. Corresponding high-resolution distortion formulas are also given. High-resolution distortion bounds based on a rate allocation for the cascade of BLVQs and classical linear block channel codes are also obtained. The iii distortion of these practical systems decays to zero exponentially fast as the transmission rate grows, although the exponent is a sublinear function of the transmission rate. As a result, the performance increase per unit rate increase is diminishing for larger transmission rates. Necessary conditions for the optimality of binary lattice vector quantizers with respect to the mean squared error distortion criterion are derived for both noiseless and noisy discrete memor