A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912342780936192 |
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| author | Ma, Xiao |
| author_facet | Ma, Xiao |
| contents | In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a short proof that RM codes are entropy-achieving as source coding for Bernoulli sources and capacity-achieving as channel coding for binary memoryless symmetric (BMS) channels, also known as memoryless binary-input output-symmetric (BIOS) channels, in terms of bit error rate (BER) under maximum-likelihood (ML) decoding. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption Ma, Xiao Information Theory In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a short proof that RM codes are entropy-achieving as source coding for Bernoulli sources and capacity-achieving as channel coding for binary memoryless symmetric (BMS) channels, also known as memoryless binary-input output-symmetric (BIOS) channels, in terms of bit error rate (BER) under maximum-likelihood (ML) decoding. |
| title | A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.14842 |