OPTIMAL BINARY INDEX ASSIGNMENTS FOR A CLASS OF EQUIPROBABLE SCALAR AND VECTOR QUANTIZERS

The problem of scalar and vector quantization in conjunction with a no isy binary symmetric channel is considered. The issue is the assignmen t of the shortest possible distinct binary sequences to quantization l evels or vectors so as to minimize the mean-squared error caused by ch annel errors. By formulating the assignment as a matrix (or vector in the scalar case) and showing that the mean-squared error due to channe l errors is determined by the projections of its columns onto the eige nspaces of the multidimensional channel transition matrix, a class of source/quantizer pairs Is identified for which the optimal index assig nment has a simple and natural form. Among other things, this provides a simpler and more accessible proof of the result of Crimmins et al., that the natural binary code is an optimal index assignment for the u niform scalar quantizer and uniform source. It also provides a potenti ally useful approach to further developments in source-channel coding.