A construction for girth‐8 QC‐LDPC codes using Golomb rulers

Abstract

Abstract In this paper, an algebraic construction of regular QC‐LDPC codes by using the modular multiplication table mod P and Golomb rulers are proposed. It is proved that the proposed QC‐LDPC codes based on a Golomb ruler of length L have girth at least 8 if P>2L$P>2L$. The error performance of the proposed QC‐LDPC codes are simulated with various Golomb rulers. The proposed codes of length around 300 from the optimal 6‐mark Golomb ruler have an additional coding gain of at least 0.1 dB over 5G NR LDPC codes, 0.5 dB over those given earlier by others, both at FER 10−3. Some non‐trivial techniques to increase the length of a given Golomb ruler with and without an additional mark for improving the performance of the codes from Golomb rulers up to 0.7 dB are also found.