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 > 2 L $P>2L$ . 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.
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