Received Value Flipping Based Sphere Decoding Algorithm for Polar Codes

Polar codes are considered as one of the most competitive channel coding schemes for the future wireless communication system. To improve the performance of polar codes with short code-length for control channels, a sphere decoding algorithm based on received value flipping is proposed in this paper. When a codeword fails the cyclic redundancy check, the algorithm flips the received value with low reliability and forms a new received sequence. Then, this new sequence is sent to the decoder for another decoding attempt. In addition, we also compare the performance of different flipping sets and evaluate the influence of the associated flipping set sizes. Simulation results show that, the proposed algorithm can achieve performance improvement over additive white Gaussian noise channel with acceptable complexity. For the (64, 16) polar code, the proposed algorithm can achieve about 0.23 dB performance gain at frame error rate = <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10^{-3}$</tex>, compared to the conventional sphere decoding algorithm. Finally, we also verify the applicability of the proposed algorithm over Rayleigh fading channel and observe similar results.