Symbol flipping decoding (SFD) of non-binary low-density parity-check (NB-LDPC) codes has lower implementation complexity at a cost of performance degradation, when compared with other belief propagation decoding algorithms. This paper proposes modified SFD algorithms based on prediction (SFDP) for NB-LDPC codes by introducing random penalty items into the flipping metrics. Two types of noise with uniform and Gaussian distributions are considered. A probabilistic analysis shows theoretically that the randomly penalized SFDP algorithms can be advantageous in the correct flipping probability over their original versions. Simulation results show that the proposed penalizing methods exhibit significant performance gains for both regular and irregular NB-LDPC codes with different rates and alphabet sizes in both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC).
The main challenge for hardware implementation of non-binary LDPC decoding is the high computational complexity and large memory requirement. To address this challenge, five new low complexity LDPC decoding algorithms are proposed in this paper. The proposed algorithms are developed specifically towards the low complexity, yet effective, decoding of the NB LDPC codes. The proposed decoding algorithms update, iteratively, the hard decision received vector to search for the valid codeword in the vector space of Galois field
(GF) . The selection criterion for least reliable symbol positions is based on the information from the failed checks and the reliability information from the Galois field structure as well as from the received channel soft information. To choose the correct value for the candidate symbol, two methods are used. The first method is based on the prediction of the error symbol from the set of Galois field symbols which maximize an objective function. In the second method, individual bits are flipped based on the reliability information obtained from the channel. Algorithms 1 and 2 flip a single symbol per iteration whilst the other three algorithms 3, 4 and 5 flip multiple symbols in each iteration. The proposed voting based Algorithms 1, 2 and 5 first short list the unreliable positions using a majority voting scheme and then choose the candidate symbol value from the set of the symbols in
GF(q) while not violating the field order
q . These methods simplify the decoding complexity in terms of computation and memory. Results and analysis of these algorithms show an appealing tradeoff between computational complexity and bit error rate performance for NB LDPC codes.
To speed up the convergence rate of non-binary low-density parity check codes and reduce decoding computational complexity of decoding algorithm, a weighted symbol flipping decoding algorithm based on iterative stopping criteria is proposed. The algorithm determines the position and amplitude of the flipped symbol according to the weight of the information node and the flipping function in the check equation, and selects the optimal value of the weighting factor through simulation. At the same time, the iteration stop criterion is introduced, and the iteration is stopped by setting the number of parity equations without satisfying the different signal-to-noise ratio. The simulation results show that the channel additive white Gauss noise, the algorithm ensures the invariant properties of weighted symbol flipping decoding algorithm under the condition that can accelerate the convergence speed, reduce the average number of iterations, so the decoding performance and complexity trad-off between effective.