A Class of High-rate, Low-complexity, Well- structured LDPC Codes from Combinatorial Designs and their Applications on ISI Channels

We present a systematic construction of a class of highrate, well-structured low density parity check (LDPC) codes based on combinatorial designs. We show that the proposed -design results in a class of -regular LDPC codes, which are systematic, quasicyclic, free of length-4 and length-6 cycles, linear-time encodable and decodable, and which have high code rates of . Analysis from the maximum likelihood perspective shows that the distance spectrum of the proposed LDPC codes are better than that of the Gallager ensemble codes for the same code length and rate. The proposed codes are then applied to several inter-symbol interference channels, where 2 high code rates and 3 block sizes from short to mediumn are evaluated. For best performance gain, the i.i.d. capacity is computed to choose the best precoder and iterative decoding and equalization is performed The proposed LDPC codes demonstrate performance that is slightly (but noticeably) better than an average random LDPC code of column weight 3. Unlike random codes, well-structured LDPC codes can lend themselves to a very low-complexity implementation for highspeed applications.