A Double Maximization Approach for Optimizing the LM Rate of Mismatched Decoding

TL;DR

This paper introduces a novel double maximization approach to optimize the LM rate in mismatched decoding, transforming a complex non-convex problem into a series of convex optimizations, resulting in improved performance bounds.

Contribution

It proposes a dual formulation and an alternating maximization algorithm for optimizing the LM rate, enabling efficient and effective rate maximization in mismatched decoding scenarios.

Findings

Noticeable rate gains achieved with the proposed method

The dual form simplifies the optimization problem into convex subproblems

Efficient closed-form iterative steps facilitate practical implementation

Abstract

An approach is established for maximizing the Lower bound on the Mismatch capacity (hereafter abbreviated as LM rate), a key performance bound in mismatched decoding, by optimizing the channel input probability distribution. Under a fixed channel input probability distribution, the computation of the corresponding LM rate is a convex optimization problem. When optimizing the channel input probability distribution, however, the corresponding optimization problem adopts a max-min formulation, which is generally non-convex and is intractable with standard approaches. To solve this problem, a novel dual form of the LM rate is proposed, thereby transforming the max-min formulation into an equivalent double maximization formulation. This new formulation leads to a maximization problem setup wherein each individual optimization direction is convex. Consequently, an alternating maximization algorithm is established to solve the resultant maximization problem setup. Each step of the algorithm only involves a closed-form iteration, which is efficiently implemented with standard optimization procedures. Numerical experiments show the proposed approach for optimizing the LM rate leads to noticeable rate gains.