An Efficient Software Stack Sphere Decoder for Polar Codes

Abstract

Proved to achieve the symmetric capacity of the binary-input discrete memoryless channels, polar codes have been chosen for the eMBB control channels in the 5th generation mobile communication systems. Besides the main decoding algorithms like successive cancellation (SC) decoding and CRC-aid SC list (CA-SCL) decoding, sphere decoder (SD) and list SD (LSD) are the alternatives for short codes with less required memory bits. Existing SD and LSD attain high calculation complexity, for SD requires a back-tracking process and LSD needs a large list size $L$ to achieve satisfying performance. To reduce complexity, an efficient software stack sphere decoder (ESSD) based on the synchronous determination is firstly proposed in this article. With the dynamic set-by-set decoding in the stack structure, it achieves the lowest complexity in SD-based decoders (SD/LSD/ESSD) while sharing the same performance on low-rate codes and high-rate codes. Compared with the CA-SCL decoder, the complexity and latency of the proposed ESSD are also competitive at high signal-to-noise-ratio on the displayed codes. Implemented on C++ , the proposed ESSD reduces $\text{44.77}\%$ latency compared with CA-SCL-32 for $\mathcal {P}(128,120)$ at the BER of $10^{-5}$ with $E_b/N_0 = \text{7}$ dB.