Optimizing Secrecy Codes Using Gradient Descent
<|reference_start|>Optimizing Secrecy Codes Using Gradient Descent: 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.<|reference_end|>
@article{hunn2024optimizing,
    title={Optimizing Secrecy Codes Using Gradient Descent},
    author={David Hunn and Willie K. Harrison},
    journal={arXiv preprint arXiv:2405.15935},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.15935},
    primaryClass={cs.IT math.IT}
}