Sparse Superposition Codes with Binomial Dictionary are Capacity-Achieving with Maximum Likelihood Decoding
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908328221736960 |
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| author | Takeishi, Yoshinari Takeuchi, Jun'ichi |
| author_facet | Takeishi, Yoshinari Takeuchi, Jun'ichi |
| contents | It is known that sparse superposition codes asymptotically achieve the channel capacity over the additive white Gaussian noise channel with both maximum likelihood decoding and efficient decoding (Joseph and Barron in 2012, 2014). Takeishi et al. (in 2014, 2019) demonstrated that these codes can also asymptotically achieve the channel capacity with maximum likelihood decoding when the dictionary is drawn from a Bernoulli distribution. In this paper, we extend these results by showing that the dictionary distribution can be naturally generalized to the binomial distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse Superposition Codes with Binomial Dictionary are Capacity-Achieving with Maximum Likelihood Decoding Takeishi, Yoshinari Takeuchi, Jun'ichi Information Theory It is known that sparse superposition codes asymptotically achieve the channel capacity over the additive white Gaussian noise channel with both maximum likelihood decoding and efficient decoding (Joseph and Barron in 2012, 2014). Takeishi et al. (in 2014, 2019) demonstrated that these codes can also asymptotically achieve the channel capacity with maximum likelihood decoding when the dictionary is drawn from a Bernoulli distribution. In this paper, we extend these results by showing that the dictionary distribution can be naturally generalized to the binomial distribution. |
| title | Sparse Superposition Codes with Binomial Dictionary are Capacity-Achieving with Maximum Likelihood Decoding |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.14262 |