Can Punctured Rate-1/2 Turbo Codes Achieve a Lower Error Floor than their Rate-1/3 Parent Codes?

TL;DR

This paper investigates whether punctured rate-1/2 turbo codes can outperform their rate-1/3 counterparts in error floors, proposing partially-systematic codes to improve convergence under iterative decoding.

Contribution

It introduces partially-systematic rate-1/2 turbo codes that can achieve lower error floors than rate-1/3 codes, addressing convergence issues with non-systematic codes.

Findings

Non-systematic rate-1/2 codes can have lower error floors under maximum-likelihood decoding.

Partially-systematic codes improve iterative decoding convergence.

Simulation results confirm lower error floors with proposed codes.

Abstract

In this paper we concentrate on rate-1/3 systematic parallel concatenated convolutional codes and their rate-1/2 punctured child codes. Assuming maximum-likelihood decoding over an additive white Gaussian channel, we demonstrate that a rate-1/2 non-systematic child code can exhibit a lower error floor than that of its rate-1/3 parent code, if a particular condition is met. However, assuming iterative decoding, convergence of the non-systematic code towards low bit-error rates is problematic. To alleviate this problem, we propose rate-1/2 partially-systematic codes that can still achieve a lower error floor than that of their rate-1/3 parent codes. Results obtained from extrinsic information transfer charts and simulations support our conclusion.