Quasi-Cyclic LDPC Codes for Short Block-Lengths

In wireless communication, transmission error can be caused by multi-path fading, shadowing, scattering, interference and noise. As a result, errors generated in digital communication can be classified as burst errors, random bit errors, crosstalk and echo. For reliable communication, channel coding is used which adds redundancy to the information bits. Reliable and low latency communication are crucial for future communication systems involving satellite constellations and 5G communication systems, which underscores the importance of channel coding. Various codes exist for channel coding, among which low-density parity-check (LDPC) codes, polar codes and tail biting convolution codes are mentioned for 5G ultra-reliable low latency communication and enhanced mobile broadband systems. In the literature, the performance of large block-length codes has been well-studied. But these codes lead to high latency. The design of short block-length codes remains an open problem due to the trade-off between latency and performance. In this paper, we develop a systematic procedure for construction of hybrid quasi-cyclic LDPC (QC-LDPC) codes and compare the performance of the proposed approach with random LDPC and existing QC-LDPC codes for short block-lengths and phase shift keying (PSK) signal characteristics. The proposed method exploits Euclidean geometry and circulant decomposition resulting in a QC-LDPC matrix that avoids shorter girths for iterative decoding cycles. We emphasize that the proposed approach is different from the protographic construction method, masking method, identity matrix replacement method, algebraic based construction method, and base graph method used for the construction of QC-LDPC codes.