Partial Superposition Reed-Muller Codes

Reed-Muller (RM) codes can be constructed by Plotkin ($u, u \oplus v$) construction. When recursively decoding RM codes based on Plotkin construction, the superposition of component codes u on v acts as interference to the decoding of v, and it has hence been pointed out in the literature that the decoding error is dominated by v. Therefore, in this study we propose a variant of RM codes, leveraging the idea of partial superposition in Plotkin construction. Specifically, only a subset of the bits in u is superposed on v. We call the resulting codes Partial Superposition RM (PS-RM) codes. A superposition pattern design based on row weights of generator matrix is provided. Regarding decoding, we modify Dumer’s recursive list decoding algorithm and Constituent Automorphism Decoding (CAD) algorithm, to render them applicable to PS-RM codes. Simulation results show that the idea of partial superposition leads to evident performance improvements over RM codes, particularly for long code lengths and low/medium Signal-toNoise Ratios (SNRs). We remark that the performance gains of the proposed PS-RM codes are achieved without increasing complexity.