Towards An Exact Combinatorial Algorithm for LP Decoding of Turbo Codes

TL;DR

This paper introduces an exact combinatorial algorithm for LP decoding of turbo codes that guarantees finite convergence and significantly outperforms generic LP solvers in speed, especially at high SNRs.

Contribution

The paper proposes a novel finite-step algorithm based on Euclidean distance minimization and shortest path computations in the trellis graph for turbo code LP decoding.

Findings

Algorithm outperforms commercial LP solvers by up to a factor of 100 in speed.

Guarantees finite convergence unlike previous heuristic methods.

Effective especially for high SNR values.

Abstract

We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the turbo code. Previous attempts to exploit the combinatorial graph structure only led to algorithms which are either of heuristic nature or do not guarantee finite convergence. A numerical study shows that our algorithm clearly beats the running time, up to a factor of 100, of generic commercial LP solvers for medium-sized codes, especially for high SNR values.