Abstract
This paper presents a novel hard decision decoding algorithm for low‐density parity‐check (LDPC) codes, in which the stand matching pursuit (MP) is adapted for error pattern recovery from syndrome over GF(2). In this algorithm, the operation of inner product can be converted into XOR and accumulation, which makes the matching pursuit work with a high efficiency. In addition, the maximum iteration is theoretically explored in relation to sparsity and error probability according to the sparse theory. To evaluate the proposed algorithm, two MP‐based decoding algorithms are simulated and compared over an AWGN channel, i.e., generic MP (GMP) and syndrome MP (SMP). Simulation results show that the GMP algorithm outperforms the SMP by 0.8 dB at BER = 10−5.
Highlights
Low-density parity-check (LDPC) code is known for its capacity-approaching performance and belief propagation (BP) decoding algorithms [1–6]
Simulation is conducted via BPSK modulation over an AWGN channel to test the validity of MPbased algorithm in decoding of LDPC codes
Based on the compressed sensing theory, the number of maximum iterations in relation to sparsity and error probability was derived theoretically, which could provide a guide in practice
Summary
Low-density parity-check (LDPC) code is known for its capacity-approaching performance and belief propagation (BP) decoding algorithms [1–6]. This kind of soft decision algorithm has high implementation complexity, which may not be tolerated in some applications, for example, space optical communications. Literature [8] introduced a MP-based algorithm to decode hard decision LDPC code and called it the syndrome matching pursuit (SMP). In binary LDPC decoding, as there tends to be more than one atom (a column of the parity-check matrix) that generates the maximum inner product between residual and the dictionary (parity-check matrix), it is very difficult to recognize which is the matching one. The syndrome can be expressed as the form of linear measurements
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