Adaptive Linear Programming Decoding

TL;DR

This paper explores an adaptive approach to linear programming decoding that reduces complexity and enhances performance by selectively adding constraints, making decoding more efficient and effective.

Contribution

It introduces an adaptive method for LP decoding that significantly lowers complexity and improves decoding accuracy through dynamic constraint addition.

Findings

Adaptive LP decoding reduces complexity from exponential to manageable levels.

Combining parity checks with adaptive constraints improves decoding performance.

The method demonstrates substantial gains over traditional LP decoding approaches.

Abstract

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a first step in studying this method, and show that it can significantly reduce the complexity of the problem, which was originally exponential in the maximum check-node degree. We further show that adaptively adding new constraints, e.g. by combining parity checks, can provide large gains in the performance.