Two reliability-based iterative majority-logic decoding algorithms for LDPC codes

Cyclic and quasi-cyclic LDPC codes: New developments

“…Theorems 2 and 3 can be used to determine the roots of the generator polynomials of type-1 and type-2 cyclic descendant LDPC codes of C EG . Also included in Figure 1 is the error performance of the code decoded with a soft-reliability based iterative majoritylogic decoding (SRBI-MLGD) (a binary message-passing decoding algorithm) proposed in [16]. We see that, at the biterror rate (BER) of 10 −6 , the SRBI-MLGD performs only 0.6 dB from the scaled MS with 50 iterations.…”

“…The SRBI-MLGD requires only integer and binary logical operations with a computational complexity much less than that of the SPA and the MS-algorithm. It offers more effective trade-off between error-performance and decoding complexity compared to the other reliability-based iterative decoding, such as the weighted bit-flipping (WBF) algorithms [10], [16]. …”

“…The descendant circulants Ψ 0 and Ψ 2 both have column EG (X) of this code has β = α 3 , β 2 , ..., β 16 and their conjugates as roots. By extensive computer search, we find that C (1) EG has no trapping set with size smaller than 17, however, we do find a (17,0) trapping set which gives a codeword of weight 17.…”

The modified reliability-based iterative majority-logic decoding algorithm for structured LDPC codes

“…In 2009, Huang et al proposed a reliability-based iterative majority-logic decoding (RBI-MLGD) algorithm [4], which requires only logical operations and integer additions. For the RBI-MLGD algorithm, specific soft reliability messages are defined from the received quantized symbols and iteratively updated in the decoding process.…”

“…In this paper, we present a modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for the structured LDPC codes based on the work in [4]. The presented MRBI-MLGD algorithm is an integer message passing algorithm and mainly requires the logical and integer operations.…”