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Soft-decision decoding of linear block codes using efficient iterative G-space encodings

This paper proposes a sub-optimal maximum-likelihood decoding algorithm for linear block codes. Given reliability information about each bit in the received word, our approach initially finds the set of most reliable "basis" information bits; it then searches for the most likely codeword by iteratively flipping bits in this basis set, constructing the corresponding codeword and determining its likelihood. The search of "test error patterns" on the set of basis information bits is conducted so that at each iteration the new set of basis information bits differs from a previously studied (and stored) one in a single bit position. Thus, the new codeword can be obtained from a stored codeword by modifying only the redundant bits that depend on the modified bit. The space complexity of the proposed decoding scheme is polynomial in the code length. We also describe an heuristic criterion to approximate the optimal set of test error patterns subject to a limit on the maximum computational effort. Simulation results with codes of relatively large length show that the proposed approach is very efficient, especially under low SNR.