On Existence of Girth-8 QC-LDPC Code with Large Column Weight: Combining Mirror-sequence with Classification Modulo Ten
Guohua Zhang, Xiangya Liu, Jianhua Zhang, Yi Fang

TL;DR
This paper introduces algebraic methods combining mirror-sequence and classification modulo ten to construct short-length QC-LDPC codes with girth 8 and large column weights, improving bounds significantly.
Contribution
It proposes a novel algebraic construction for QC-LDPC codes with girth 8 and large column weights using mirror-sequence and row-regrouping within the GCD framework.
Findings
Improved lower bounds on circulant sizes by about 20%.
Constructed codes with smaller circulant sizes than existing benchmarks.
Applicable to arbitrary row weights for short-length codes.
Abstract
Quasi-cyclic (QC) LDPC codes with large girths play a crucial role in several research and application fields, including channel coding, compressed sensing and distributed storage systems. A major challenge in respect of the code construction is how to obtain such codes with the shortest possible length (or equivalently, the smallest possible circulant size) using algebraic methods instead of search methods. The greatest-common-divisor (GCD) framework we previously proposed has algebraically constructed QC-LDPC codes with column weights of 5 and 6, very short lengths, and a girth of 8. By introducing the concept of a mirror sequence and adopting a new row-regrouping scheme, QC-LDPC codes with column weights of 7 and 8, very short lengths, and a girth of 8 are proposed for arbitrary row weights in this article via an algebraic manner under the GCD framework. Thanks to these novel…
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Taxonomy
TopicsError Correcting Code Techniques · Advanced Wireless Communication Techniques · PAPR reduction in OFDM
