Designing Nonlinear Turbo Codes with a Target Ones Density

TL;DR

This paper introduces a systematic method for designing nonlinear turbo codes with non-uniform ones densities, optimizing performance on channels like Z-channels and BBSC, achieving near-capacity results.

Contribution

It presents a novel design technique for nonlinear turbo codes supporting non-50% ones densities, tailored for specific asymmetric and broadcast channels.

Findings

Nonlinear turbo codes can be designed to support non-uniform ones densities.

Designed codes are within 0.02 bits of channel capacity.

Simulation results validate the effectiveness of the proposed design method.

Abstract

Certain binary asymmetric channels, such as Z-channels in which one of the two crossover probabilities is zero, demand optimal ones densities different from 50%. Some broadcast channels, such as broadcast binary symmetric channels (BBSC) where each component channel is a binary symmetric channel, also require a non-uniform input distribution due to the superposition coding scheme, which is known to achieve the boundary of capacity region. This paper presents a systematic technique for designing nonlinear turbo codes that are able to support ones densities different from 50%. To demonstrate the effectiveness of our design technique, we design and simulate nonlinear turbo codes for the Z-channel and the BBSC. The best nonlinear turbo code is less than 0.02 bits from capacity.