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Register a new userSuccessive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding
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Mustafa Cemil Coskun
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within $0.7$ dB from the random coding union bound are provided.
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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.
The interest in polar codes has been increasing significantly since their adoption for use in the 5$^{rm th}$ generation wireless systems standard. Successive cancellation (SC) decoding algorithm has low implementation complexity, but yields mediocre error-correction performance at the code lengths of interest. SC-Flip algorithm improves the error-correction performance of SC by identifying possibly erroneous decisions made by SC and re-iterates after flipping one bit. It was recently shown that only a portion of bit-channels are most likely to be in error. In this work, we investigate the average log-likelihood ratio (LLR) values and their distribution related to the erroneous bit-channels, and develop the Thresholded SC-Flip (TSCF) decoding algorithm. We also replace the LLR selection and sorting of SC-Flip with a comparator to reduce the implementation complexity. Simulation results demonstrate that for practical code lengths and a wide range of rates, TSCF shows negligible loss compared to the error-correction performance obtained when all single-errors are corrected. At matching maximum iterations, TSCF has an error-correction performance gain of up to $0.45$ dB compared with SC-Flip decoding. At matching error-correction performance, the computational complexity of TSCF is reduced by up to $40%$ on average, and requires up to $5times$ lower maximum number of iterations.
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 $10^{-3}$.
Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar codes has mediocre error-correction performance on short to moderate codeword lengths: the SC-Flip decoding algorithm is one of the solutions that have been proposed to overcome this issue. On the other hand, SC-Flip has a higher implementation complexity compared to SC due to the required log-likelihood ratio (LLR) selection and sorting process. Moreover, it requires a high number of iterations to reach good error-correction performance. In this work, we propose two techniques to improve the SC-Flip decoding algorithm for low-rate codes, based on the observation of channel-induced error distributions. The first one is a fixed index selection (FIS) scheme to avoid the substantial implementation cost of LLR selection and sorting with no cost on error-correction performance. The second is an enhanced index selection (EIS) criterion to improve the error-correction performance of SC-Flip decoding. A reduction of $24.6%$ in the implementation cost of logic elements is estimated with the FIS approach, while simulation results show that EIS leads to an improvement on error-correction performance improvement up to $0.42$ dB at a target FER of $10^{-4}$.
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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