SCL-GCD of Short Polar Codes

This paper is concerned with the SCL-GCD algorithm of polar codes, which performs the successive-cancellation list (SCL) decoding algorithm for a lower rate sub-code and the guessing codeword decoding (GCD) algorithm for a higher rate sub-code. We propose to implement the GCD algorithm in a parallel way and design early stopping criteria for reducing complexity and decoding latency without sacrificing performance. Numerical results show that, when compared with the original SCL decoding algorithm, the SCL-GCD algorithm armed with the proposed early stopping criteria has lower computational complexity and decoding latency in the high signal-noise ratio (SNR) region.

I. Introduction

As a family of capacity-achieving codes based on the concept of channel polarization [1], polar codes have been adopted as the standard coding scheme for control channels of the fifth generation (5G) enhanced Mobile Broadband [2]. However, the successive cancellation (SC) decoding algorithm [1] does not perform well when the code length is finite. Later, the successive cancellation list (SCL) decoding algorithm [3] and the cyclic redundancy check (CRC) aided SCL (CA-SCL) decoding algorithm [4], [5] were proposed. It has been illustrated numerically that, with a moderate list size L, the successive cancellation list (SCL) decoding of polar codes can approach the maximum likelihood (ML) performance [3]. The main drawback of the SCL decoding is its sequentialness, where bits are decoded sequentially depending on the previous bits, resulting in high decoding latency.