Polar-coded perturbation sphere decoding algorithm over Rayleigh fading channel

Abstract

A perturbation sphere decoding algorithm for control channels with small payload size is proposed in this paper. When a codeword fails the cyclic redundancy check (CRC), the algorithm performs a perturbation operation by adding noise to the codeword and achieves a new received sequence. Subsequently, this perturbed sequence is sent to the decoder for another decoding attempt. Moreover, a partial perturbation algorithm is proposed to further reduce the resource consumption, which only applies perturbation for those rows having relative low weights, resulting in improved performance and reduced complexity. Simulation results show that, the two proposed algorithms exhibit excellent performance over Rayleigh fading channel and the performance gain increases with the maximum perturbation number. For (64,22) polar codes, the two algorithms can achieve about 0.58 dB and 0.71 dB performance gain, respectively, with maximum perturbation number = 4 and FER = $10^{-3}$, compared to the conventional sphere decoding algorithm. Meanwhile, the complexity of partial perturbation algorithm is reduced to about 77.66% compared to the perturbation algorithm at the SNR = 5 dB.