Performance Comparison of LDPC Block and Spatially Coupled Codes over GF(q)

TL;DR

This paper compares the finite-length performance of protograph-based spatially coupled LDPC codes and LDPC block codes over GF(q), showing that non-binary SC-LDPC codes outperform traditional codes under various regimes and analyzing their computational complexity.

Contribution

It introduces a sliding window decoding method for q-ary SC-LDPC codes and provides a comprehensive performance and complexity comparison with LDPC block codes.

Findings

Non-binary SC-LDPC codes outperform LDPC-BCs and binary SC-LDPC codes in simulations.

Decoding regimes with equal constraint length and equal latency are analyzed.

Complexity analysis shows differences under equal performance and latency conditions.

Abstract

In this paper, we compare the finite-length performance of protograph-based spatially coupled low-density parity-check (SC-LDPC) codes and LDPC block codes (LDPC-BCs) over GF(q). In order to reduce computational complexity and latency, a sliding window decoder with a stopping rule based on a soft bit-error-rate (BER) estimate is used for the q-ary SC-LDPC codes. Two regimes are considered: one when the constraint length of q-ary SC-LDPC codes is equal to the block length of q-ary LDPC-BCs and the other when the two decoding latencies are equal. Simulation results confirm that, in both regimes, (3,6)-, (3,9)-, and (3,12)-regular non-binary SC-LDPC codes can significantly outperform both binary and non-binary LDPC-BCs and binary SC-LDPC codes. Finally, we present a computational complexity comparison of q-ary SC-LDPC codes and q-ary LDPC-BCs under equal decoding latency and equal decoding performance assumptions.