The Best Binary Linear Block Codes for Scalar Source-Channel Coding

This paper finds the best binary linear block codes to use when an IID uniform source is uniform scalar quantized for transmission over a binary symmetric channel, with performance measured by mean squared error (MSE). The best code is found by optimizing the source-channel rate allocation, the linear code, and the assignment of its codewords to quantization indices. A table shows the maximum attained SNR, together with a code that achieves it, for a range of channel transition probabilities and transmission rates. When optimized, the performance of such systems comes within 1 ~ 2 dB of that of the best nonlinear codes found by an iterative algorithm.