A Low-Complexity Ordered Statistics Decoding Algorithm for Short Polar Codes

Yusheng Xing,Guofang Tu

doi:10.3390/app9050831

Abstract

In this paper, we propose a low-complexity ordered statistics decoding (OSD) algorithm called threshold-based OSD (TH-OSD) that uses a threshold on the discrepancy of the candidate codewords to speed up the decoding of short polar codes. To determine the threshold, we use the probability distribution of the discrepancy value of the maximal likelihood codeword with a predefined parameter controlling the trade-off between the error correction performance and the decoding complexity. We also derive an upper-bound of the word error rate (WER) for the proposed algorithm. The complexity analysis shows that our algorithm is faster than the conventional successive cancellation (SC) decoding algorithm in mid-to-high signal-to-noise ratio (SNR) situations and much faster than the SC list (SCL) decoding algorithm. Our addition of a list approach to our proposed algorithm further narrows the error correction performance gap between our TH-OSD and OSD. Our simulation results show that, with appropriate thresholds, our proposed algorithm achieves performance close to OSD’s while testing significantly fewer codewords than OSD, especially with low SNR values. Even a small list is sufficient for TH-OSD to match OSD’s error rate in short-code scenarios. The algorithm can be easily extended to longer code lengths.

Highlights

Since polar coding’s introduction by Arikan in 2009, the method has attracted a considerable amount of research attention as the first theoretically proven method for achieving channel capacity.In his pioneering paper, Arikan proposed a decoding algorithm called “successive cancellation” (SC)to prove the capacity-achieving property of polar codes [1]
We propose a threshold-based ordered statistics decoding (OSD) decoding algorithm by setting a threshold on the discrepancy value of a codeword to reduce complexity while maintaining a word error rate (WER) close to Maximum likelihood decoding (MLD) for short liner block codes and apply this algorithm on short polar codes
We propose a threshold-based flexible OSD decoding algorithm to reduce the complexity of the OSD algorithm while maintaining an acceptable WER under various thresholds of short polar codes

Summary

Introduction

Since polar coding’s introduction by Arikan in 2009, the method has attracted a considerable amount of research attention as the first theoretically proven method for achieving channel capacity.In his pioneering paper, Arikan proposed a decoding algorithm called “successive cancellation” (SC)to prove the capacity-achieving property of polar codes [1]. Since polar coding’s introduction by Arikan in 2009, the method has attracted a considerable amount of research attention as the first theoretically proven method for achieving channel capacity. In his pioneering paper, Arikan proposed a decoding algorithm called “successive cancellation” (SC). To prove the capacity-achieving property of polar codes [1]. The SC decoding algorithm uses the recursive structure of polar codes to achieve a complexity of O( N log N ), where N is the codeword length. The performance of polar codes with a finite code length is unsatisfactory with the suboptimal SC decoding algorithm. Several alternative decoding methods have been proposed to improve performance. The list SC decoding method (SCL) [2] and the stack SC decoding method (SCS) [3] show the most significant improvement in the word error rate (WER)

Methods

Results

Conclusion