Efficient Computation of Marton's Error Exponent via Constraint Decoupling

TL;DR

This paper introduces an efficient algorithm for computing Marton's error exponent in lossy source coding by decoupling constraints and using alternating maximization, significantly reducing computational complexity.

Contribution

It develops a novel composite maximization framework with constraint decoupling and an alternating algorithm for efficient Marton's error exponent computation.

Findings

The proposed method outperforms existing grid search algorithms in efficiency.

The algorithm guarantees global convergence.

Numerical experiments validate the superior performance on various sources.

Abstract

The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation methods of the Marton's error exponent remain underdeveloped due to its formulation as a non-convex optimization problem with limited efficient solvers. While a recent grid search algorithm can compute its inverse function, it incurs prohibitive computational costs from two-dimensional brute-force parameter grid searches. This paper proposes a composite maximization approach that effectively handles both Marton's error exponent and its inverse function. Through a constraint decoupling technique, the resulting problem formulations admit efficient solvers driven by an alternating maximization algorithm. By fixing one parameter via a one-dimensional line search, the remaining subproblem becomes convex and can be efficiently solved by alternating variable updates, thereby significantly reducing search complexity. Therefore, the global convergence of the algorithm can be guaranteed. Numerical experiments for simple sources and the Ahlswede's counterexample, demonstrates the superior efficiency of our algorithm in contrast to existing methods.