A class of (γργ-1,ργ,ρ,γ,{0,1}) combinatorially designed LDPC codes with application to ISI channels

A systematic construction of regular low density parity check (LDPC) codes based on (γρ^γ-1,ρ^γ,ρ,γ,{0,1}) combinatorial designs is investigated. From one particular view point, the proposed codes are "loosened" finite geometry codes where some lines are systematic removed. The loosened design rules offer at least two advantages: a lower decoding complexity and a richer code set. We show that the proposed codes contain a good combination of structure and pseudorandomness, where the former enables low-cost implementation in hardware and the latter ensures reasonable performance by avoiding certain recurrent error patterns (e.g. rectangular error patterns). One possible application for the proposed structured LDPC codes is the digital recording systems. Simulations show that with proper preceding, the proposed codes can perform as well as or slightly better than the random codes. Unlike random codes, the proposed structured LDPC codes can lend themselves to a low-complexity implementation for high-speed applications.