Regular {4, 8} LDPC Codes and Their Lowerror Floors

Regular LDPC codes are a special class of low-density codes having an equal number of ones in each row and column of the parity check matrix describing the linear code. The uniform structure of regular LDPC codes allows a practical hardware implementation which can efficiently utilize the inherent parallelism of the message passing algorithm (MPA) commonly used to decode low-density codes. The class of {3,6} LDPC codes has been extensively studied and they have been proven to provide very good error performance, especially at lower SNR. {4,8} codes have not been analyzed nearly as much in the literature, mainly because their 'threshold,' the SNR where the waterfall region of the error performance curve begins, is typically a quarter of a dB or so worse than for comparable-length {3,6} codes. It has been proposed that {4,8} codes have better high SNR behavior, but until recently it was not possible to verify this conjecture. A new technique which can efficiently find error floors of LDPC codes now has the ability to illuminate just how good {4,8} codes are in the high SNR region-a result which is of great interest for many practical applications. This paper will analyze the error floor characteristics of some {4,8} codes and provide a simple algorithm for designing {4,8} codes with low error floors. A newly-designed rate-1/2 (1200,600) {4,8} code with a vastly superior error floor compared to codes of similar parameters is introduced