Reliability ratio based weighted bit-flipping decoding for low-density parity-check codes - Electronics Letters

Introduction: The family of low-density parity-check (LDPC) codes proposed by Gallager [1] has attracted substantial research interest in the information theory community. LDPC codes can be decoded using various decoding schemes [1–4] such as hard-decisions, softdecisions and hybrid decoding schemes. The high-complexity sum-product algorithm (SPA) was shown to achieve a near-capacity performance [4]. However, the weighted bit-flipping (WBF) algorithm [2] strikes a good trade-off between the associated decoding complexity and the achievable performance. The attractive property of the WBF algorithm is that during each iteration the weighted sum of the same values is computed, resulting in a significantly lower decoding in comparison to the SPA. An improved WBF (I-WBF) algorithm was proposed by Zhang and Fossorier [3]. In this Letter, the following problems of the WBF and the I-WBF algorithm are addressed. 1. Both the WBF and I-WBF algorithms attribute the violation of a particular parity check to only the least reliable bit. 2. If the weighting factor a utilised in the I-WBF algorithm [3] is not optimum, the BER performance may be significantly degraded. Thus in this contribution, the BER performance of the I-WBF algorithm is further improved by using more sophisticated bit-flipping, while avoiding any preprocessing such as finding the optimal weighting factor a of the I-WBF algorithm. An (N, K, j) LDPC code can be uniquely represented by an M N parity-check matrix (PCM), where M1⁄4N K and each column of the PCM has an average weight of j. By representing the PCM using the Tanner graph [5], each column of the PCM corresponds to a message node in the Tanner graph and each row of the PCM is associated with a check node. We will use the notation H for representing the PCM of the LDPC code, and Hmn denotes the binary entry in the mth row and the nth column. We denote the set of bits participating in the mth check by N (m)1⁄4 {n: Hmn1⁄4 1}. The term {n: Hmn1⁄4 1} indicates the specific set of values for the column index n, where the value of the PCM entry Hmn at the mth row and nth column is one. Similarly, the set of checks in which the nth bit participates is denoted asM(n)1⁄4 {m: Hmn1⁄4 1}. When an information block of size K is encoded by an LDPC encoder, a codeword c of length N will be produced, and the coded bits will be mapped using BPSK modulation onto the corresponding constellation point x. When the Gaussian noise is added to the transmitted signal, a noise-contaminated received sequence y will be obtained. Based on the sequence y, an initial hard decision can be made and we arrive at a binary sequence z of length N.