A novel representation, using soft-bit messages, of the belief propagation (BP) decoding algorithm for low-density parity-check codes is derived as an alternative to the log-likelihood-ratio (LLR)-based BP and min-sum...
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A novel representation, using soft-bit messages, of the belief propagation (BP) decoding algorithm for low-density parity-check codes is derived as an alternative to the log-likelihood-ratio (LLR)-based BP and min-sum decodingalgorithms. A simple approximation is also presented. Simulation results demonstrate the functionality of the soft-bit decoding algorithm. Floating-point soft-bit and LLR BP decoding show equivalent performance;the approximation incurs 0.5-dB loss, comparable to min-sum performance loss over BE Fixed-point results show similar performance to LLR BP decoding;the approximation converges to floating-point results with one less bit of precision.
In this paper, we construct parity-concatenated trellis codes in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. From the Tanner-Wiberg-Loeliger (TWL) graph rep...
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In this paper, we construct parity-concatenated trellis codes in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. From the Tanner-Wiberg-Loeliger (TWL) graph representation, several iterative decoding algorithms can be derived. However, since the graph of the parity-concatenated code contains many short cycles, the conventional min-sum and sum-product algorithms cannot achieve near-optimal decoding. After some simple modifications, we obtain near-optimal iterative decoders. The modifications include either a) introducing a normalization operation in the min-sum and sum-product algorithms or b) cutting the short cycles which arise in the iterative Viterbi algorithm (IVA), After modification, all three algorithms can achieve near-optimal performance, but the IVA has the least average complexity. We also show that asymptotically maximum-likelihood (ML) decoding and a posteriori probability (APP) decoding can be achieved using iterative decoders with only two iterations, Unfortunately, this asymptotic behavior is only exhibited when the bit-energy-to-noise ratio is above the cutoff rate. Simulation results show that with trellis shaping, iterativedecoding can perform within 1.2 dB of the Shannon limit at a bit error rate (BER) of 4 x 10(-5) for a block size of 20 000 symbols. For a block size of 200 symbols, iterativedecoding can perform within 2.1 dB of the Shannon limit.
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