Low Complexity Symmetric-coded Based Sphere Decoding for Low-rate Polar Codes

Abstract

In this paper, we propose a novel low complexity symmetric-coded based sphere decoding (SD) algorithm for short polar codes with low rate. At the encoding stage, the first N/2 sub-channels transmit the frozen bits, while the information bits are selected from the latter N/2 sub-channels. Two symmetric codes are generated due to the mathematical structure of the generator matrix, which is well conditioned to the SD search.At the decoding stage, the presented SD algorithm computes the ED value by the combined signals to estimate the latter N/2 input bits.Furthermore, the backtrack operation starts from the earlier (N/2+1)-th bit, which can significantly reduce the average visited nodes (AVN).Simulation results show that, compared to the original SD algorithm, the presented variant of the SD algorithm can reduce the AVN to 0.9% for the polar code P(64,14) at SNR = 1 dB with a performance loss within 0.2 dB.