A Quasi-Cyclic LDPC Generator Polynomial for Navigation Signals of NavIC

This paper proposes a novel method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes with short block lengths for satellite navigation applications requiring enhanced error correction capabilities. The method constructs sparse base matrices, ensuring a parity check matrix girth greater than four, using a correlation-based method and an adaptive probability density function to avoid regular patterns in the parity check matrix. Investigations reveal that the proposed QC-LDPC codes achieve a low bit error rate of \(10^{- 7}\) at 4 dB energy per bit per unit noise density (\(E_{b}/N_{0}\)), compared to the Global Positioning Service L1C band LDPC codes, which show a bit error rate of \(5 \times 10^{- 7}\) at the same \(E_{b}/N_{0}\) for the shortest block length of 274 uncoded bits under consideration. This method is used for constructing LDPC parity check matrices for India’s NavIC satellites by the Indian Space Research Organisation.