Turbo Codes Based on Time-Variant Memory-1 Convolutional Codes over Fq

TL;DR

This paper introduces novel turbo codes over high-order finite fields based on time-variant convolutional codes, offering efficient decoding methods and significant performance gains over existing binary codes in moderate-short block regimes.

Contribution

It presents two new classes of turbo codes derived from a specific protograph ensemble, with flexible encoding schemes and efficient decoding algorithms, including FFT-based MAP decoding.

Findings

Achieved approximately 1 dB gain over binary LDPC and turbo codes.

Developed efficient belief propagation and forward-backward decoding algorithms.

Provided a cycle graph representation for the proposed codes.

Abstract

Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a parallel concatenation of two non-binary, time-variant accumulators. The second construction is based on the serial concatenation of a non-binary, time-variant differentiator and of a non-binary, time-variant accumulator, and provides a highly-structured flexible encoding scheme for (dv=2,dc=4) ensemble codes. A cycle graph representation is provided. The proposed codes can be decoded efficiently either as low-density parity-check codes (via belief propagation decoding over the codes bipartite graph) or as turbo codes (via the forward-backward algorithm applied to the component codes trellis). The forward-backward algorithm for symbol maximum a posteriori decoding of the component codes is illustrated and simplified by means of the fast Fourier transform. The proposed codes provide remarkable gains (~ 1 dB) over binary low-density parity-check and turbo codes in the moderate-short block regimes.