Optimal Linear MAP Decoding for Non-Binary Convolutional Codes
Published in GLOBECOM 2025 - 2025 IEEE Global Communications Conference, 2025
Non-binary convolutional codes (NBCCs) offer significant performance advantages in modern communication systems, but their optimal decoding using classical maximum a posteriori probability (MAP) algorithms is computationally intensive. This paper proposes a low-complexity linear MAP (LMAP) decoding method for rate-1/2 NBCCs. By representing the MAP forward and backward decoding processes as shift register structures operating on probability mass functions (PMFs) of signal estimates, the method supports single direction (forward and backward) SISO decoding, and can achieve the optimal bidirectional MAP decoding performance. The decoder structure is determined offline, and the decoding process only involves simple shift register operations, finite field convolutions, and permutations. Simulation results demonstrate that the proposed LMAP decoder achieves identical error performance to the conventional BCJR MAP decoder, while significantly reducing decoding latency and hardware complexity.