Optimizing Secrecy Codes Using Gradient Descent

TL;DR

This paper introduces a gradient descent-based method to optimize coset secrecy codes, improving their performance at various blocklengths by incorporating theoretical functions and constraints into the design process.

Contribution

It develops a novel gradient descent algorithm that effectively incorporates theoretical secrecy functions and constraints to optimize coset codes for enhanced secrecy performance.

Findings

Codes optimized with the method outperform published codes at most sizes.

The approach yields better results than capacity-achieving codes at short blocklengths.

The algorithm can produce codes with blocklengths up to a few thousand.

Abstract

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.