Decoding Reed-Muller and polar codes by successive factor graph permutations

S.A. Hashemi, N. Doan, M. Mondelli, W. Gross, in:, 2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing, IEEE, 2018, pp. 1–5.


Conference Paper | Published | English
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Abstract
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and polar codes. Using the symmetric group of RM and polar codes, the specific decoding algorithm can be carried out on multiple permutations of the factor graph to boost the error-correction performance. However, this approach results in high decoding complexity. In this paper, we first derive the total number of factor graph permutations on which the decoding can be performed. We further propose a successive permutation (SP) scheme which finds the permutations on the fly, thus the decoding always progresses on a single factor graph permutation. We show that SP can be used to improve the error-correction performance of RM and polar codes under successive-cancellation (SC) and SC list (SCL) decoding, while keeping the memory requirements of the decoders unaltered. Our results for RM and polar codes of length 128 and rate 0.5 show that when SP is used and at a target frame error rate of 10 -4 , up to 0.5 dB and 0.1 dB improvement can be achieved for RM and polar codes respectively.
Publishing Year
Date Published
2018-12-01
Proceedings Title
2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing
Page
1-5
Conference
ISTC: Symposium on Turbo Codes & Iterative Information Processing
Conference Location
Hong Kong, China
Conference Date
2018-12-03 – 2018-12-07
IST-REx-ID

Cite this

Hashemi SA, Doan N, Mondelli M, Gross W. Decoding Reed-Muller and polar codes by successive factor graph permutations. In: 2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing. IEEE; 2018:1-5. doi:10.1109/istc.2018.8625281
Hashemi, S. A., Doan, N., Mondelli, M., & Gross, W. (2018). Decoding Reed-Muller and polar codes by successive factor graph permutations. In 2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing (pp. 1–5). Hong Kong, China: IEEE. https://doi.org/10.1109/istc.2018.8625281
Hashemi, Seyyed Ali, Nghia Doan, Marco Mondelli, and Warren Gross. “Decoding Reed-Muller and Polar Codes by Successive Factor Graph Permutations.” In 2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing, 1–5. IEEE, 2018. https://doi.org/10.1109/istc.2018.8625281.
S. A. Hashemi, N. Doan, M. Mondelli, and W. Gross, “Decoding Reed-Muller and polar codes by successive factor graph permutations,” in 2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing, Hong Kong, China, 2018, pp. 1–5.
Hashemi SA, Doan N, Mondelli M, Gross W. 2018. Decoding Reed-Muller and polar codes by successive factor graph permutations. 2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing. ISTC: Symposium on Turbo Codes & Iterative Information Processing 1–5.
Hashemi, Seyyed Ali, et al. “Decoding Reed-Muller and Polar Codes by Successive Factor Graph Permutations.” 2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing, IEEE, 2018, pp. 1–5, doi:10.1109/istc.2018.8625281.

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