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

J. Li and E. Kurtas (USA)


low density parity check (LDPC) codes, combinatorial design, distance spectrum, intersymbol interference (ISI), iterative decoding and equalization (IDE), turbo equalization, binary precoding


We present a systematic construction of a class of high rate, well-structured low density parity check (LDPC) codes based on combinatorial designs. We show that the proposed (2ρ, ρ2 , ρ, 2, {0, 1})-design results in a class of (2, ρ)-regular LDPC codes, which are systematic, quasi static, free of length-4 and length-6 cycles, linear-time en codable and decodable, and which have high code rates of R = (1− 1 ρ )2 . Analysis from the maximum likelihood per spective shows that the distance spectrum of the proposed LDPC codes are better than that of the Gallager ensem ble codes for the same code length and rate. The pro posed codes are then applied to several inter-symbol in terference channels, where 2 high code rates and 3 block sizes from short to mediumn are evaluated. For best per formance 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 per formance 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 them selves to a very low-complexity implementation for high speed applications.

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