Recursive Subproduct Codes with Reed-Muller-like Structure
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arXiv
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| Format: | Preprint |
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2024
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| author | Siddheshwar, Aditya Natarajan, Lakshmi Prasad Krishnan, Prasad |
| author_facet | Siddheshwar, Aditya Natarajan, Lakshmi Prasad Krishnan, Prasad |
| contents | We study a family of subcodes of the $m$-dimensional product code $\mathscr{C}^{\otimes m}$ ('subproduct codes') that have a recursive Plotkin-like structure, and which include Reed-Muller (RM) codes and Dual Berman codes as special cases. We denote the codes in this family as $\mathscr{C}^{\otimes [r,m]}$, where $0 \leq r \leq m$ is the 'order' of the code. These codes allow a 'projection' operation that can be exploited in iterative decoding, viz., the sum of two carefully chosen subvectors of any codeword in $\mathscr{C}^{\otimes [r,m]}$ belongs to $\mathscr{C}^{\otimes [r-1,m-1]}$. Recursive subproduct codes provide a wide range of rates and block lengths compared to RM codes while possessing several of their structural properties, such as the Plotkin-like design, the projection property, and fast ML decoding of first-order codes. Our simulation results for first-order and second-order codes, that are based on a belief propagation decoder and a local graph search algorithm, show instances of subproduct codes that perform either better than or within 0.5 dB of comparable RM codes and CRC-aided Polar codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recursive Subproduct Codes with Reed-Muller-like Structure Siddheshwar, Aditya Natarajan, Lakshmi Prasad Krishnan, Prasad Information Theory We study a family of subcodes of the $m$-dimensional product code $\mathscr{C}^{\otimes m}$ ('subproduct codes') that have a recursive Plotkin-like structure, and which include Reed-Muller (RM) codes and Dual Berman codes as special cases. We denote the codes in this family as $\mathscr{C}^{\otimes [r,m]}$, where $0 \leq r \leq m$ is the 'order' of the code. These codes allow a 'projection' operation that can be exploited in iterative decoding, viz., the sum of two carefully chosen subvectors of any codeword in $\mathscr{C}^{\otimes [r,m]}$ belongs to $\mathscr{C}^{\otimes [r-1,m-1]}$. Recursive subproduct codes provide a wide range of rates and block lengths compared to RM codes while possessing several of their structural properties, such as the Plotkin-like design, the projection property, and fast ML decoding of first-order codes. Our simulation results for first-order and second-order codes, that are based on a belief propagation decoder and a local graph search algorithm, show instances of subproduct codes that perform either better than or within 0.5 dB of comparable RM codes and CRC-aided Polar codes. |
| title | Recursive Subproduct Codes with Reed-Muller-like Structure |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.15678 |