M-ary phase coding for the noncoherent AWGN channel

This work considers coded M-ary phase-shift keying (MPSK) schemes with noncoherent detection. A class of block codes called module-phase codes is described. The algebraic framework used for describing these codes relies on elements from module theory which are discussed along with a method for constructing such codes for noncoherent detection. It is shown that differential encoding may be viewed as a specific code from a particular class of module-phase codes. Two classes of codes that achieve significant coding gain with respect to coherent detection of uncoded MPSK are presented. In the first class of module-phase codes, the coding gain is achieved at the expense of bandwidth expansion. In the second class, however, the coding gain is achieved at the expense of signal constellation expansion without expanding bandwidth. Finally, an integrated demodulation/decoding technique based on a modification of information set decoding is presented. It Is shown that this reduced-complexity, suboptimal decoding strategy performs nearly as well as maximum-likelihood decoding