On binary code design for the non-coherent block fading channel

We study the binary code design problem for the fading channel with non-coherent maximum-likelihood detection. The p-spectrum (i.e. all possible pairwise absolute cross-correlations) provides a way to define the optimal codes, based on the union bound on the error probability, as the codes achieving the optimal p-spectrum for some code rate. We introduce some limited search methods based on the p-spectrum, including a nested search, which for some code rates yields optimal codes. With our nested search, good codes were obtained easily up to code rate 12/n, n less than or equal to 4096. The codes developed offer good performance in the fading channel and can be used in place of the Hadamard-Walsh codes in synchronous CDMA systems to increase system capacity.