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Register a new userSuccessive-Cancellation Decoding of Reed-Muller Codes with Fast Hadamard Transform
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Nghia Doan Mr.
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this paper we propose efficient decoding techniques to significantly improve the error-correction performance of fast successive-cancellation (FSC) and FSC list (FSCL) decoding algorithms for short low-order Reed-Muller (RM) codes. In particular, we first integrate Fast Hadamard Transform (FHT) into FSC (FHT-FSC) and FSCL (FHT-FSCL) decoding algorithms to optimally decode the first-order RM subcodes. We then utilize the rich permutation group of RM codes by independently running the FHT-FSC and the FHT-FSCL decoders on a list of random bit-index permutations of the codes. The simulation results show that the error-correction performance of the FHT-FSC decoders on a list of $L$ random code permutations outperforms that of the FSCL decoder with list size $L$, while requiring lower memory requirement and computational complexity for various configurations of the RM codes. In addition, when compared with the state-of-the-art recursive projection-aggregation (RPA) decoding, the permuted FHT-FSCL decoder can obtain a similar error probability for the RM codes of lengths $128$, $256$, and $512$ at various code rates, while requiring several orders of magnitude lower computational complexity.
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This paper presents a novel successive factor-graph permutation (SFP) scheme that significantly improves the error-correction performance of Reed-Muller (RM) codes under successive-cancellation list (SCL) decoding. In particular, we perform maximum-likelihood decoding on the symmetry group of RM codes to carefully select a good factor-graph permutation on the fly. We further propose an SFP-aided fast SCL decoding that significantly reduces the decoding latency while preserving the error-correction performance of the code. The simulation results show that for the third and fourth order RM codes of length $256$, the proposed decoder reduces up to $85%$ of the memory consumption, $78%$ of the decoding latency, and more than $99%$ of the computational complexity of the state-of-the-art recursive projection-aggregation decoder at the frame error rate of $10^{-3}$.
Fast SC decoding overcomes the latency caused by the serial nature of the SC decoding by identifying new nodes in the upper levels of the SC decoding tree and implementing their fast parallel decoders. In this work, we first present a novel sequence repetition node corresponding to a particular class of bit sequences. Most existing special node types are special cases of the proposed sequence repetition node. Then, a fast parallel decoder is proposed for this class of node. To further speed up the decoding process of general nodes outside this class, a threshold-based hard-decision-aided scheme is introduced. The threshold value that guarantees a given error-correction performance in the proposed scheme is derived theoretically. Analysis and hardware implementation results on a polar code of length $1024$ with code rates $1/4$, $1/2$, and $3/4$ show that our proposed algorithm reduces the required clock cycles by up to $8%$, and leads to a $10%$ improvement in the maximum operating frequency compared to state-of-the-art decoders without tangibly altering the error-correction performance. In addition, using the proposed threshold-based hard-decision-aided scheme, the decoding latency can be further reduced by $57%$ at $mathrm{E_b}/mathrm{N_0} = 5.0$~dB.
Polar codes are a class of channel capacity achieving codes that has been selected for the next generation of wireless communication standards. Successive-cancellation (SC) is the first proposed decoding algorithm, suffering from mediocre error-correction performance at moderate code length. In order to improve the error-correction performance of SC, two approaches are available: (i) SC-List decoding which keeps a list of candidates by running a number of SC decoders in parallel, thus increasing the implementation complexity, and (ii) SC-Flip decoding that relies on a single SC module, and keeps the computational complexity close to SC. In this work, we propose the partitioned SC-Flip (PSCF) decoding algorithm, which outperforms SC-Flip in terms of error-correction performance and average computational complexity, leading to higher throughput and reduced energy consumption per codeword. We also introduce a partitioning scheme that best suits our PSCF decoder. Simulation results show that at equivalent frame error rate, PSCF has up to $5 times$ less computational complexity than the SC-Flip decoder. At equivalent average number of iterations, the error-correction performance of PSCF outperforms SC-Flip by up to $0.15$ dB at frame error rate of $10^{-3}$.
A deep-learning-aided successive-cancellation list (DL-SCL) decoding algorithm for polar codes is introduced with deep-learning-aided successive-cancellation (DL-SC) decoding being a specific case of it. The DL-SCL decoder works by allowing additional rounds of SCL decoding when the first SCL decoding attempt fails, using a novel bit-flipping metric. The proposed bit-flipping metric exploits the inherent relations between the information bits in polar codes that are represented by a correlation matrix. The correlation matrix is then optimized using emerging deep-learning techniques. Performance results on a polar code of length 128 with 64 information bits concatenated with a 24-bit cyclic redundancy check show that the proposed bit-flipping metric in the proposed DL-SCL decoder requires up to 66% fewer multiplications and up to 36% fewer additions, without any need to perform transcendental functions, and by providing almost the same error-correction performance in comparison with the state of the art.
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Mustafa Cemil Coc{s}kun
, Gianluigi Liva
, Alexandre Graell i Amat andn Michael Lentmaier
2017
We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias decoding.
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