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Physical Communication

Fast successive-cancellation list decoding of parity-check polar codes with special nodes

Lijuan Xing, Zhuo Li

Published Jul 1, 2026• 0 citations
Publisher
DOI
10.1016/j.phycom.2026.103238

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Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. To reduce the decoding latency, developing tailored fast and efficient list decoding algorithms of specific polar constituent codes (special nodes) is a promising solution. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming to further speedup the SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) nodes and sequence rate one or single-parity-check (SR1/SPC) nodes. In particular, we develop two classes of fast list decoding algorithms for these nodes, where the first class uses a sequential decoding procedure to yield decoding latency that is linear with the list size, and the second further parallelizes the decoding process by pre-determining the redundant candidate paths offline. Simulation results show that the proposed list decoding algorithms are able to achieve up to 70.7% lower decoding latency than state-of-the-art fast SCL decoders, while exhibiting the same error-correction performance.

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In the case of short code, polar code demonstrates superior performance compared with Low Density Parity Check (LDPC) code. Particularly in low coding rate scenario, the complexity of Polar code encoding and decoding is significantly lower than that of LDPC code. The technological advantage of Polar code makes it of great value in special application scenarios such as satellite communication and ocean communication. The polar coding scheme can significantly improve the transmission reliability of the communication system, because the satellite spread spectrum communication system generally adopts short code design.In the research of decoding algorithm, the original Serial Cancellation (SC) decoding algorithm has simple rules, but the decoding effect is not ideal under the limited code length, and the serial decoding mechanism leads to large decoding delay. The Successive Cancellation List (SCL) decoding algorithm improves decoding performance by increasing the number of decoding search path. However, maintaining multiple decoding paths can multiply the decoding complexity. Fast node-based decoding algorithm aims to accelerate decoding and reduce latency by defining and simplifying the decoding process for specific nodes, yet they do not optimize the decoding paths. In view of the above problems, this paper proposes a Simplified Parity Check-based Cyclic Redundancy Check (CRC)-Aided Successive Cancellation List (S-PC-CASCL) decoding algorithm. Simulation results demonstrate that the proposed S-PC-CASCL maintains excellent error correction performance while reducing the average list size by up to 16 % under low Signal Noise Ratio (SNR) conditions, thereby lowering computational complexity and decoding latency compared with other widely used polar decoding methods.

IEEE Access•Jan 1, 2025•0 citations
Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. To reduce the decoding latency, developing tailored fast and efficient list decoding algorithms of specific polar constituent codes (special nodes) is a promising solution. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming to further speedup the SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) nodes and sequence rate one or single-parity-check (SR1/SPC) nodes. In particular, we develop two classes of fast list decoding algorithms for these nodes, where the first class uses a sequential decoding procedure to yield decoding latency that is linear with the list size, and the second further parallelizes the decoding process by pre-determining the redundant candidate paths offline. Simulation results show that the proposed list decoding algorithms are able to achieve up to 70.7% lower decoding latency than state-of-the-art fast SCL decoders, while exhibiting the same error-correction performance.
Being able to provide excellent error-correction performance for polar codes with short-to-moderate code length, successive-cancellation list (SCL) is regarded as one of the most promising decoding algorithms. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming at achieving further speedup for SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) and sequence rate-1(SRI) nodes, based on the minimum-combinations set (MCS) which is able to significantly narrow the search space of candidate paths. Typically, SPC nodes can be directly decoded within one round of path splitting procedure, whereas SR1 nodes, as a group of parallel SPC nodes, can also be decode efficiently. Simulation results show that the proposed fast SCL decoder is able to reduce the decoding latency by 68.4% as compared to the state of the art, without any error-correction performance degradation.
In the case of short code, polar code demonstrates superior performance compared with Low Density Parity Check (LDPC) code. Particularly in low coding rate scenario, the complexity of Polar code encoding and decoding is significantly lower than that of LDPC code. The technological advantage of Polar code makes it of great value in special application scenarios such as satellite communication and ocean communication. The polar coding scheme can significantly improve the transmission reliability of the communication system, because the satellite spread spectrum communication system generally adopts short code design.In the research of decoding algorithm, the original Serial Cancellation (SC) decoding algorithm has simple rules, but the decoding effect is not ideal under the limited code length, and the serial decoding mechanism leads to large decoding delay. The Successive Cancellation List (SCL) decoding algorithm improves decoding performance by increasing the number of decoding search path. However, maintaining multiple decoding paths can multiply the decoding complexity. Fast node-based decoding algorithm aims to accelerate decoding and reduce latency by defining and simplifying the decoding process for specific nodes, yet they do not optimize the decoding paths. In view of the above problems, this paper proposes a Simplified Parity Check-based Cyclic Redundancy Check (CRC)-Aided Successive Cancellation List (S-PC-CASCL) decoding algorithm. Simulation results demonstrate that the proposed S-PC-CASCL maintains excellent error correction performance while reducing the average list size by up to 16 % under low Signal Noise Ratio (SNR) conditions, thereby lowering computational complexity and decoding latency compared with other widely used polar decoding methods.