Optimizing Secrecy Codes Using Gradient Descent
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916259687301120 |
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| author | Hunn, David Harrison, Willie K. |
| author_facet | Hunn, David Harrison, Willie K. |
| contents | Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for incorporating these functions, along with a complex set of constraints, into a gradient descent optimization algorithm. This algorithm employs a movement cost function and trigonometric update step to ensure that the continuous-valued code definition vector ultimately reaches a value which yields a realizable coset code. This algorithm is used to produce coset codes with blocklength up to a few thousand. These codes were compared against published codes, including both short-blocklength and capacity-achieving constructions. For most code sizes, codes generated using gradient descent outperformed all others, especially capacity-achieving constructions, which performed significantly worse than randomly-generated codes at short blocklength. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimizing Secrecy Codes Using Gradient Descent Hunn, David Harrison, Willie K. Information Theory Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for incorporating these functions, along with a complex set of constraints, into a gradient descent optimization algorithm. This algorithm employs a movement cost function and trigonometric update step to ensure that the continuous-valued code definition vector ultimately reaches a value which yields a realizable coset code. This algorithm is used to produce coset codes with blocklength up to a few thousand. These codes were compared against published codes, including both short-blocklength and capacity-achieving constructions. For most code sizes, codes generated using gradient descent outperformed all others, especially capacity-achieving constructions, which performed significantly worse than randomly-generated codes at short blocklength. |
| title | Optimizing Secrecy Codes Using Gradient Descent |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.15935 |