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International Symposium on Turbo Codes and Iterative Information Processing

Balanced Incomplete Block Designs, Partial Geometries, and Their Associated QC-LDPC Codes

Juane Li, Yi Gong, Shu Lin, Khaled Abdel-Ghaffar

Published Aug 30, 2021• 5 citations
Publisher

Abstract

This paper presents two classes of partial geometries (PaGs) derived from balanced incomplete block designs (BIBDs) of a special type. Based on these two classes of partial geometries, quasi-cyclic (QC) LDPC codes can be constructed. These codes not only perform well over AWGN channels (AWGNCs) but also can correct bursts of erasures over binary erasure channels (BECs) effectively.

DOI
10.1109/istc49272.2021.9594122

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This paper presents two classes of partial geometries (PaGs) derived from balanced incomplete block designs (BIBDs) of a special type. Based on these two classes of partial geometries, quasi-cyclic (QC) LDPC codes can be constructed. These codes not only perform well over AWGN channels (AWGNCs) but also can correct bursts of erasures over binary erasure channels (BECs) effectively.
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This paper constructs Partially Balanced Incomplete Block Designs (PBIBD) based on finite fields,and uses them to construct regular Low-Density Parity-Check(LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for the choosing of the code rate.Further,the paper even constructs QC-LDPC codes with girth at least 8,they can also be quasi-cyclic.Simulation results show that some of the codes can have slightly better performance than random regular LDPC codes over AWGN channel.