MMSE-A-MAP Decoder for Block Orthogonal Sparse Superposition Codes in Fading Channels

Block orthogonal sparse superposition (BOSS) codes are a class of sparse superposition codes with orthogonality among sub-codewords. This orthogonal structure allows using a near-optimal maximum a posteriori (MAP) decoder with low complexity. Multi-path fading environments, however, destroy the intrinsic orthogonal property of BOSS codewords and result in a catastrophic loss of decoding performance. In this paper, we suggest a novel decoding algorithm of BOSS codes for multi-path fading channels. The proposed decoder comprises two-stage operations: i) minimum mean square error (MMSE) equalization and ii) approximate element-wise MAP decoding. The MMSE equalization restores the orthogonality in the codewords. Then, the element-wise MAP decoding identifies the non-zero positions of sparse message vectors. It turns out that BOSS codes with the proposed decoder provide a considerable performance improvement in terms of block error rate compared to polar codes in the short blocklength regime, while requiring polynomial time decoding complexity. To verify the performance gains, we provide simulation results. We also study the possibility of covert communications using BOSS codes.