Guessing Random Additive Noise Decoding (GRAND) is a recently proposed Maximum Likelihood (ML) decoding technique. Irrespective of the structure of the error correcting code, GRAND tries to guess the noise that corrupted the codeword in order to decode any linear error-correcting block code. GRAND Markov Order (GRAND-MO) is a variant of GRAND that is useful to decode error correcting code transmitted over communication channels with memory which are vulnerable to burst noise. Usually, interleavers and de-interleavers are used in communication systems to mitigate the effects of channel memory. Interleaving and de-interleaving introduce undesirable latency, which increases with channel memory. To prevent this added latency penalty, GRAND-MO can be directly used on the hard demodulated channel signals. This work reports the first GRAND-MO hardware architecture which achieves an average throughput of up to 52 Gbps and 64 Gbps for a code length of 128 and 79 respectively. Compared to the GRANDAB, hard-input variant of GRAND, the proposed architecture achieves 3 dB gain in decoding performance for a target FER of 10 −5 . Similarly, comparing the GRAND-MO decoder with a decoder tailored for a (79, 64) BCH code showed that the proposed architecture achieves 33% higher worst case throughput and 2 dB gain in decoding performance.
Polar codes are the first class of error correcting codes that provably achieve the channel capacity at infinite code length. They were selected for use in the fifth generation of cellular mobile communications (5G). In practical scenarios such as 5G, a cyclic redundancy check (CRC) is concatenated with polar codes to improve their finite length performance. This is mostly beneficial for sequential successive-cancellation list decoders. However, for parallel iterative belief propagation (BP) decoders, CRC is only used as an early stopping criterion with incremental error-correction performance improvement. In this paper, we first propose a CRC-polar BP (CPBP) decoder by exchanging the extrinsic information between the factor graph of the polar code and that of the CRC. We then propose a neural CPBP (NCPBP) algorithm which improves the CPBP decoder by introducing trainable normalizing weights on the concatenated factor graph. Our results on a 5G polar code of length 128 show that at the frame error rate of 10 −5 and with a maximum of 30 iterations, the error-correction performance of CPBP and NCPBP are approximately 0.25 dB and 0.5 dB better than that of the conventional CRC-aided BP decoder, respectively, while introducing almost no latency overhead.
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