Optimizing binary decision systems by manipulating transmission intervals

We study the optimization of a binary decision system where quantized (soft) decisions are transmitted across an additive white Gaussian noise channel. We adjust the bit transmission intervals to maximize the Chemoff distance at the output of the channel. At low channel signal-to-noise ratios (when the probability of a bit error is higher), we find unequal transmission intervals yield significant gains in terms of Chernoff distance and the information transfer ratio over the equal transmission case. This paper is a companion paper to [Johnson, D.H. and Rodriguez-Diaz, H., 2003] wherein the gains of unequal bit transmissions are studied in terms of minimum squared error.