
doi: 10.1109/18.796373
Summary: Let a \(q\)-ary linear \((n,k)\)-code \(C\) be used over a memoryless channel. We design a decoding algorithm \(\Psi_N\) that splits the received block into two halves in \(n\) different ways. First, about \(\sqrt N\) error patterns are found on either half. Then the left- and right-hand lists are sorted out and matched to form codewords. Finally, the most probable codeword is chosen among at most \(n\sqrt N\) codewords obtained in all \(n\) trials. The algorithm can be applied to any linear code \(C\) and has complexity order of \(n^2 \sqrt N\). For any \(N\geq q^{n-k}\), the decoding error probability \(P_N\) exceeds at most \(1+q^{n-k}/N\) times the probability \(P_\Psi(C)\) of maximum-likelihood decoding. For code rates \(R\geq 1/2\), the complexity order \(q^{(n-k) /2}\) grows as square root of general trellis complexity \(q^{\min \{n-k,k\}}\). When used on quantized additive white Gaussian noise (AWGN) channels, algorithm \(\Psi_N\) can provide maximum-likelihood decoding for most binary linear codes even when \(N\) has exponential order of \(q^{n-k}\).
quantized additive white Gaussian noise channels, splitting, Decoding, trellis, decoding error probability, maximum-likelihood decoding, syndromes, complexity, decoding algorithm, sorting, Linear codes (general theory)
quantized additive white Gaussian noise channels, splitting, Decoding, trellis, decoding error probability, maximum-likelihood decoding, syndromes, complexity, decoding algorithm, sorting, Linear codes (general theory)
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