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IEEE Communications Letters

Guessing Error Pattern Ordered Statistic Decoding for Short Polar Codes

Yuxin Han, Kai Niu, Xuanyu Li

Published Sep 28, 2023• 3 citations
Publisher

Abstract

Polar codes have been used to guarantee high reliability in communication due to their excellent performance. In this letter, we propose a guessing error pattern ordered statistic decoding (GEPOSD) algorithm to further improve the performance of short polar codes. It outperforms the widely used cyclic redundancy check-aided successive cancellation list (CA-SCL) decoding under a code length of 64. The GEPOSD algorithm utilizes a strategy based on the maximum a posteriori probability rule to select the error pattern on the most reliable independent bits. Subsequently, an error pattern set is extended using a tree search approach. To minimize computational complexity, we introduce two early stopping criteria that limit the number of error patterns tested in decoding. The simulation results show that the complexity of GEPOSD is significantly reduced compared to the original OSD algorithm.

DOI
10.1109/lcomm.2023.3320153

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Applied Sciences•Feb 26, 2019•2 citations
Polar codes have been used to guarantee high reliability in communication due to their excellent performance. In this letter, we propose a guessing error pattern ordered statistic decoding (GEPOSD) algorithm to further improve the performance of short polar codes. It outperforms the widely used cyclic redundancy check-aided successive cancellation list (CA-SCL) decoding under a code length of 64. The GEPOSD algorithm utilizes a strategy based on the maximum a posteriori probability rule to select the error pattern on the most reliable independent bits. Subsequently, an error pattern set is extended using a tree search approach. To minimize computational complexity, we introduce two early stopping criteria that limit the number of error patterns tested in decoding. The simulation results show that the complexity of GEPOSD is significantly reduced compared to the original OSD algorithm.
In this paper, we propose a pre-configured error pattern ordered statistics decoding (PEPOSD) algorithm and discuss its application to short cyclic redundancy check (CRC)-polar codes. Unlike the traditional OSD that changes the most reliable independent symbols, we regard the decoding process as testing the error patterns, like guessing random additive noise decoding (GRAND). Also, the pre-configurator referred from ordered reliability bits (ORB) GRAND can better control the range and testing order of EPs. An offline-online structure can accelerate the decoding process. Additionally, we also introduce two orders to optimize the search order for testing EPs. Compared with CRC-aided OSD and list decoding, PEPOSD can achieve a better trade-off between accuracy and complexity.
With the advent of 5th generation (5G) mobile communication era, higher requirements are put forward for ultra-reliable and low-latency transmission compared with 4G, especially in the field of short packet communication. In this paper, we propose a segmented cyclic redundancy check aided order statistical decoding algorithm with multiple biases (BIAS- SCRC-OSD) for short polar codes. This algorithm constructs multiple information sets by repeatedly adding bias value, and selects more effective information sets to improve the decoding performance. For further improving the decoding performance, we change the original cyclic redundancy check (CRC) into segment check. The simulation results show that a suitable bias value can significantly improve the decoding performance with a small increase in computational complexity. Compared with the original CRC-aided order statistical decoding (OSD) algorithm, the proposed algorithm has a gain of about 0.8 dB at target bit error rate (BER) 10-4with code rate R = 0.5 and code length N = 64.
This paper is concerned with a guessing codeword decoding (GCD) of linear block codes, which is optimal and typically requires a fewer number of searches than the naive exhaustive search decoding (ESD). Compared with the guessing random additive noise decoding (GRAND), which is only efficient for high-rate codes, the GCD is efficient for not only high-rate codes but also low-rate codes. We prove that the GCD typically requires a fewer number of queries than the GRAND. Compared with the conventional ordered statistics decoding (OSD), the GCD does not require the online Gaussian elimination (GE). In addition to limiting the maximum number of searches, we suggest limiting the radius of searches in terms of soft weights or tolerated performance loss to further reduce the decoding complexity, resulting in the so-called truncated GCD. The performance gap between the truncated GCD and the optimal decoding can be upper bounded approximately by the saddlepoint approach or other numerical approaches. The derived upper bound captures the relationship between the performance and the decoding parameters, enabling us to balance the performance and the complexity by optimizing the decoding parameters of the truncated GCD. We also introduce a parallel implementation of the (truncated) GCD algorithm to reduce decoding latency without compromising performance. Another contribution of this paper is the application of the GCD to the polar codes. We propose a multiple-bit-wise decoding algorithm over a pruned tree for the polar codes, referred to as the successive-cancellation list (SCL) decoding algorithm by GCD. First, we present a strategy for pruning the conventional polar decoding tree based on the complexity analysis rather than the specific bit patterns. Then we apply the GCD algorithm in parallel aided by the early stopping criteria to the leaves of the pruned tree. Simulation results show that, without any performance loss as justified by analysis, the proposed decoding algorithm can significantly reduce the decoding latency of the polar codes.
In this letter, the ordered statistic decoding (OSD) is considered to decode short polar codes. Since the number of tested codewords is high in the original OSD, a threshold-based OSD is proposed to reduce the complexity. The analysis shows that the threshold affects the OSD in two ways. One is the error floor in high signal-to-noise ratio (SNR) region while the other is the reduction of the number of tested codewords. The estimation on the BLER performance in high SNR region and the average number of tested codewords are discussed. After that, CRC-aided OSD is proposed to further improve the performance of polar codes. Simulation results show that a well-designed threshold-based OSD can reduce the complexity without significant performance loss. And a higher order OSD decoder is needed if OSD is used to decoding moderate or long polar codes. It is also illustrated that the CRC-aided OSD outperforms the CRC-aided list decoding when the code rate is high. When code rate is low, the result inverses.
Polar codes have garnered significant attention since they were proposed due to their capacity-achieving properties and their low-complexity decoding process, and they were selected as the coding scheme for the control channel in 5G mobile communication technology. A successive cancellation list (SCL) decoder, aided by a cyclic redundancy check (CRC), performs the competitive error correcting performance for polar codes compared to other sophisticated codes. The SCL-Flip decoding algorithm is proposed to enhance the error correction performance of the SCL. However, the SCL-Flip is hampered by a high decoding complexity due to the necessary selection and sorting process of path metrics (PMs). Additionally, it requires a large number of iterations to achieve a good error correction performance. In this paper, we propose the error segment bit-flip (ES-SCL-Flip) decoding algorithm, a simplified bit-flip approach for the SCL decoder based on analyzing the distributions of the first error bit. Firstly, we construct an index set with a high probability of the first erroneous bit. Second, a bit-flip criterion is introduced to prevent the costly operation of the PM selection and sorting without compromising the error correction performance. Finally, a search strategy is employed that utilizes segmented error indication to target and rectify the initial error segment sequentially. The simulation results demonstrate that the ES-SCL-Flip decoder provides an improved error correction performance with only a minimal increase in decoding complexity compared to the conventional CRC-aided SCL decoder. This algorithm attains a commendable equilibrium between the error correction performance and decoding complexity.
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.