http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:1839 This paper extends the class of low-density parity-check (LDPC) codes that can be algebraically constructed. We present regular LDPC codes based on resolvable Steiner 2-designs which have Tanner graphs free of four-cycles. The resulting codes are (3, ρ)-regular or (4, ρ)-regular for any value of ρ and for a flexible choice of code lengths. 2010-04-27T06:35:24.936Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:1840 This paper presents a construction of low-density parity-check (LDPC) codes based on the incidence matrices of oval designs. The new LDPC codes have regular parity-check matrices and Tanner graphs free of 4-cycles. Like the finite geometry codes, the codes from oval designs have parity-check matrices with a large proportion of linearly dependent rows and can achieve significantly better minimum distances than equivalent length and rate randomly constructed LDPC codes. Further, by exploiting the resolvability of oval designs, and also by employing column splitting, we are able to produce 4-cycle free LDPC codes for a wide range of code rates and lengths while maintaining code regularity. 2010-04-27T06:35:14.954Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:2737 Gallager introduced low-density parity-check (LDPC) codes in 1962, presenting a construction method to randomly allocate bits in the parity-check matrix subject to certain structural constraints. Since then improvements have been made to Gallager's construction method and some analytic constructions for LDPC codes have been presented. However analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. That is, we construct (3, ρ)-regular codes whose Tanner (1981) graph is free of 4-cycles for any integer ρ. 2010-04-27T06:30:58.500Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:2740 The paper presents a construction of very high-rate low-density parity-check (LDPC) codes based on incidence matrices of unital designs. Like the projective geometry and oval designs, unital designs exist with incidence matrices which are significantly rank deficient. Thus high-rate LDPC codes with a large number of linearly dependent parity-check equations can be constructed. The LDPC codes from unitals have Tanner graphs free of 4-cycles and perform well with iterative decoding, offering new LDPC codes at rates and lengths not available with existing algebraic LDPC codes. 2010-04-27T06:30:47.346Z ]]>