A New Construction of Structured Binary Regular LDPC Codes Based on Steiner Systems with Parameter t %26gt; 2

作者：Falsafain Hossein^*; Esmaeili Morteza

来源：IEEE Transactions on Communications, 2012, 60(1): 74-80.

DOI：10.1109/TCOMM.2011.101011.110120

• LDPC codes
• combinatorial design
• Steiner quadruple system (SQS)
• inversive geometry

This paper presents a novel method for constructing structured regular low-density parity-check (LDPC) codes based on a special type of combinatorial designs, known as Steiner systems. This code design approach can be considered as a generalization of the well-known method which uses the point-block incidence matrix of a Steiner 2-design for the code construction. Though the given method can be applied on any Steiner system S(t, k, v), in this paper we focus only on Steiner systems with t %26gt;= 3. Furthermore, we show that not only a Steiner system (X, B) itself, but also its residual design with respect to an arbitrary point x is an element of X can be employed for code construction. We also present a technique for constructing binary and non-binary QC-LDPC codes from Steiner systems. The Tanner graph of the constructed codes is free of 4-cycles and hence the codes have girth at least six. Simulation results show that the so constructed codes perform well over the AWGN channel with iterative message-passing decoding.

• 出版日期2012-1