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International Conference on Electrical, Electronic and Computing Engineering (IcETRAN)

Quantization Analysis for the CRC Aided Successive Cancellation List Polar Decoder

Nikola Borović, Dragomir El Mezeni, Vladimir L. Petrović

Published Jun 9, 2025• 0 citations
Publisher

Abstract

Polar codes have recently found application as error correction codes for the control information in 5 G wireless communication. Stringent requirements for decoding latency, power consumption, and communication reliability demand efficient hardware implementation of communication modules. One of the key aspects of efficient hardware implementation is a robust quantization scheme. In this paper, we present an empirical approach to analyzing quantization for the Cyclic Redundancy Check-Aided Successive Cancellation List (CA-SCL) decoding algorithm, which is used in the 5 G standard. The paper gives detailed quantization analysis of the CA-SCL algorithm for 11-bit CRC and 4 lists. We proposed a quantization scheme with decoding performance within 0.1 dB of the floating point performance for positive Signal-to-noise ratios (SNRs). It is shown that a decoder with one extra bit achieves performance within 0.1 dB of the floating-point model over a wide range of SNRs and code rates.

DOI
10.1109/icetran66854.2025.11114217

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Polar codes have recently found application as error correction codes for the control information in 5 G wireless communication. Stringent requirements for decoding latency, power consumption, and communication reliability demand efficient hardware implementation of communication modules. One of the key aspects of efficient hardware implementation is a robust quantization scheme. In this paper, we present an empirical approach to analyzing quantization for the Cyclic Redundancy Check-Aided Successive Cancellation List (CA-SCL) decoding algorithm, which is used in the 5 G standard. The paper gives detailed quantization analysis of the CA-SCL algorithm for 11-bit CRC and 4 lists. We proposed a quantization scheme with decoding performance within 0.1 dB of the floating point performance for positive Signal-to-noise ratios (SNRs). It is shown that a decoder with one extra bit achieves performance within 0.1 dB of the floating-point model over a wide range of SNRs and code rates.
Novel successive cancellation list (SCL) decoding schemes of Polar codes by exploiting the error correction (EC) capability of the cyclic redundancy check (CRC) codes are proposed in this paper. Different from the schemes in the literature that only considered the error detection capability of CRC, the proposed schemes aim to improve the performance of CRC-aided Polar decoding to the most by benefiting from the potential EC capability of CRC. Specifically, we first propose a basic decoding scheme, named CRC error-correction-aided successive cancellation list (CRC-EC-SCL) decoding, by introducing the look-up-table-based CRC EC method into the Polar SCL decoding process. Then, based on the basic scheme, we further propose the segmented-CRC-EC-SCL decoding scheme. By segmented-CRC, the information block is divided into multiple segments and each segment is attached with a shorter CRC sequence. By conducting the CRC-EC-aided coding for each of the segments, multiple erroneous bits can be corrected early and error propagation can, thus, be efficiently suppressed. The simulation results show that both of the proposed decoding schemes have a significant performance gain over the classic CRC-EC-SCL decoding scheme. Especially for the segmented-CRC-EC-SCL, the performance gain at a frame error rate of 10−4is about 0.4 dB. Moreover, the average computation complexity of the segmented-CRC-EC-SCL is close to the classic scheme.
An improved CA-SCL (CRC-Aided Successive Cancellation List) decoding algorithm for Polar codes is proposed in this paper. By introducing the global cyclic redundancy check and local parity check, a lower bit error rate is obtained comparing with the known results. The new algorithm constructs a prune decoding path by the parity check in the local processing. Since the parity check can only detect an odd number of errors, the global CRC is used to increase the error detection ability and the decoding accuracy. The performance of the improved decoding algorithm is better than the known results, especially when the code length is either less than or equal to 512, and the code rate is not greater than 0.5 in case of the signal-to-noise ratio (SNR) higher than 3dB. In particular, when the code length is 256 with code rate of 0.5 and decoding list size of 32 under the condition of bit error rate 10-5on the AWGN channel, the proposed algorithm has around 0.25dB and 0.55dB performance gain comparing with that of the CA-SCL and SCL algorithms, respectively.
Although iterative decoding of polar codes has recently made huge progress based on the idea of permuted factor graphs, it still suffers from a non-negligible performance degradation when compared to state-of-the-art CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show that iterative decoding of polar codes based on the belief propagation list (BPL) algorithm can approach the error-rate performance of CA-SCL decoding and, thus, can be efficiently used for decoding the standardized 5G polar codes. Rather than only utilizing the cyclic redundancy check (CRC) as a stopping condition (i.e., for error-detection), we also aim to benefit from the error-correction capabilities of the outer CRC code. For this, we develop two distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv (BCJR)-based approach and a sum product algorithm (SPA)-based approach. Further, an optimized selection of permuted factor graphs is analyzed and shown to reduce the decoding complexity significantly. Finally, we benchmark the proposed CRC-aided belief propagation list (CA-BPL) decoding to state-of-the-art 5G polar codes under CA-SCL decoding and, thereby, showcase an error-rate performance not just close to the CA-SCL but also close to the maximum likelihood (ML) bound as estimated by ordered statistic decoding (OSD).
Cyclic redundancy check (CRC)-aided successive cancellation list (CA-SCL) decoding algorithm has brought good error performance. Recently, some researchers utilized multiple CRC codes to reduce decoding complexity of CA-SCL decoding algorithm. However, based on CA-SCL decoding frame, we not only reduce decoding complexity but also improve error performance. We divide polar codeword into independent sub-blocks during the process of encoding. Meanwhile, locations of multiple CRC are optimized according to a value of each average Bhattacharyya parameter. Finally, for CA-SCL decoding, results indicate that our constructed polar codes show an admirable error performance and low decoding complexity than that of equal sub-block codewords.
In this letter, three post-processing schemes for cyclic redundancy check (CRC-)aided successive cancellation list (CA-SCL) decoding are presented for polar codes. The re-decoding based on our post-processing schemes can effectively alleviate both the channel and decision errors encountered via CA-SCL decoding. Simulation results show that our schemes perform better than conventional re-decoding schemes and can be incorporated into a polar decoder that has a small list size to achieve a performance that is expected for a large list size.
A successive cancellation list (SCL) decoder with the assistance of a cyclic redundancy check (CRC) can provide competitive decoding performance for polar codes compared with the state-of-the-art codes. In this paper, we adopt a bit-flip algorithm for the CRC-assisted SCL decoder to further improve the error-correcting performance. We first introduce a new bit-flip criterion for the SCL decoder. To support this criterion, we give the metric to identify the positions that need to be flipped. To verify the superiority of the proposed bit-flip criterion, we also consider a kind of SCL-flip decoder whose criterion is very similar with the existing one and we will prove that its performance is worse than the decoder with the proposed bit-flip criterion. The simulation results show that the decoder with the proposed bit-flip criterion outperforms both the standard CRC-assisted SCL decoder and the existing SCL-based bit-flip decoder.