Low complexity symmetric-coded based sphere decoding for low-rate polar codes

The sphere decoding (SD) algorithm can provide (sub)optimal solutions with reduced computational complexity of maximum likelihood (ML) detection for multi-input multi-output (MIMO) communication systems. In this paper, we propose a novel low complexity symmetric-coded based 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 Euclidean distance value by the combined signals to estimate the latter N/2 input bits. Furthermore, the backtrack operation starts from the earlier [Formula: see text]-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 [Formula: see text] for the polar code P(64, 14) at SNR = 1  dB with a performance loss within 0.2 dB. The presented SD algorithm may find applications in MIMO systems where the complexity of the standar ML detection increases exponentially with the transmitting antennas.