On Decoding First- and Second-Order BiD Codes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914255456960512 |
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| author | Jain, Devansh Natarajan, Lakshmi Prasad |
| author_facet | Jain, Devansh Natarajan, Lakshmi Prasad |
| contents | BiD codes, which are a new family of algebraic codes of length $3^m$, achieve the erasure channel capacity under bit-MAP decoding and offer asymptotically larger minimum distance than Reed-Muller (RM) codes. In this paper we propose fast maximum-likelihood (ML) and max-log-MAP decoders for first-order BiD codes. For second-order codes, we identify their minimum-weight parity checks and ascertain a code property known as 'projection' in the RM coding literature. We use these results to design a belief propagation decoder that performs within 1 dB of ML decoder for block lengths 81 and 243. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Decoding First- and Second-Order BiD Codes Jain, Devansh Natarajan, Lakshmi Prasad Information Theory BiD codes, which are a new family of algebraic codes of length $3^m$, achieve the erasure channel capacity under bit-MAP decoding and offer asymptotically larger minimum distance than Reed-Muller (RM) codes. In this paper we propose fast maximum-likelihood (ML) and max-log-MAP decoders for first-order BiD codes. For second-order codes, we identify their minimum-weight parity checks and ascertain a code property known as 'projection' in the RM coding literature. We use these results to design a belief propagation decoder that performs within 1 dB of ML decoder for block lengths 81 and 243. |
| title | On Decoding First- and Second-Order BiD Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.09390 |