Analysis and Design of Partially Information- and Partially Parity-Coupled Turbo Codes

TL;DR

This paper introduces partially information- and parity-coupled turbo codes, demonstrating their near-capacity performance and flexible rate adjustment, with improved decoding thresholds as coupling memory increases.

Contribution

The work provides construction methods, density evolution analysis, and rate-compatible design strategies for partially coupled turbo codes, achieving near-capacity thresholds.

Findings

Thresholds within 0.0002 of BEC capacity for various rates

Decoding performance improves with larger coupling memory

Flexible rate adjustment without changing component code architectures

Abstract

In this paper, we study a class of spatially coupled turbo codes, namely partially information- and partially parity-coupled turbo codes. This class of codes enjoy several advantages such as flexible code rate adjustment by varying the coupling ratio and the encoding and decoding architectures of the underlying component codes can remain unchanged. For this work, we first provide the construction methods for partially coupled turbo codes with coupling memory $m$ and study the corresponding graph models. We then derive the density evolution equations for the corresponding ensembles on the binary erasure channel to precisely compute their iterative decoding thresholds. Rate-compatible designs and their decoding thresholds are also provided, where the coupling and puncturing ratios are jointly optimized to achieve the largest decoding threshold for a given target code rate. Our results show that for a wide range of code rates, the proposed codes attain close-to-capacity performance and the decoding performance improves with increasing the coupling memory. In particular, the proposed partially parity-coupled turbo codes have thresholds within 0.0002 of the BEC capacity for rates ranging from $1/3$ to $9/10$, yielding an attractive way for constructing rate-compatible capacity-approaching channel codes.