Optimization of Polar Code BP Bit-Flipping Decoding Based on an Adaptive Genetic Algorithm

Abstract —Polar codes, as capacity-achieving error-correcting codes, have become a cornerstone of modern communication systems due to their excellent theoretical performance. Compared with the Successive Cancellation (SC) decoding algorithm, the Belief Propagation (BP) decoding algorithm for polar codes offers advantages such as parallel output and ease of hardware implementation. However, the bit-flipping decoding schemes based on BP still exhibit a significant performance gap in frame error rate (FER) compared to the Successive Cancellation List (SCL) decoding. To address the demand for high reliability and low power consumption in practical applications, this paper proposes an optimized bit-flipping scheme in which the flipping set is constructed using an adaptive genetic algorithm. The proposed method first reduces the computational complexity of the initial BP decoding process by adopting the Offset Min-Sum (OMS) approximation. During the construction of the flipping set, an adaptive mechanism dynamically adjusts the crossover and variational probabilities based on the fitness of individuals in the population. The indices of the information bits are used as individuals in the genetic algorithm, enabling the fitness values to gradually evolve from local optima toward a global optimum. This approach allows for more accurate identification of bit positions prone to decoding errors. For a polar code with a length of 1024 and a code rate of 0.5, the proposed AGA-OMS-BPF decoder achieves approximately 1.3 dB BER performance gain at a BER of 10 −5 compared with the conventional BPF decoder. Simulation results demonstrate that the proposed method effectively reduces the number of unsuccessful BP decoding attempts by constructing a more efficient flipping set, thereby achieving performance gains with reduced computational complexity.