Error-correction codes are indispensable to ensure reliable data transmission in various communication systems. Among these, Polar codes and PAC (Polarized Adjustable Convolutional) codes have gained significant attention due to their capacity-achieving properties and low encoding complexity. This thesis presents a novel decoding technique that combines the Targeted Parity Protection (TPP) algorithm and Dynamic Successive Cancellation List (SCL) decoding to achieve substantial performance improvements while maintaining much lower complexity compared to the conventional Fano decoder. The proposed technique focuses on leveraging Cyclic Redundancy Check (CRC) bits to protect critical information bits, leading to enhanced error correction capabilities. By applying TPP, the decoding process is accelerated by effectively reducing latency and saves computational resources by eliminating wrong codeword candidates at an earlier stage before the decoder favors them. The integration of Dynamic SCL introduces adaptability to the decoder, allowing it to adjust the list size based on the decoding requirements for different code rates and lengths. This adaptability enables efficient use of hardware resources by optimizing the utilization of the decoder storage but also tailors the decoder's performance to each specific scenario, yielding substantial error correction performance gains in both Polar and PAC codes. Extensive simulations and performance evaluations demonstrate the effectiveness of the proposed technique. The results indicate a gain of up to 0.4 dB for Polar codes and up to 0.6 dB for PAC codes compared to the standard SCL decoding approach. It is worth mentioning that such gains are considered substantial for fiber optical communications which is one of the target applications of the new technique. Furthermore, the technique showcases a reduction in decoding complexity, outperforming the traditional Fano decoder.
Error-correction codes are indispensable to ensure reliable data transmission in various communication systems. Among these, Polar codes and PAC (Polarized Adjustable Convolutional) codes have gained significant attention due to their capacity-achieving properties and low encoding complexity. This thesis presents a novel decoding technique that combines the Targeted Parity Protection (TPP) algorithm and Dynamic Successive Cancellation List (SCL) decoding to achieve substantial performance improvements while maintaining much lower complexity compared to the conventional Fano decoder. The proposed technique focuses on leveraging Cyclic Redundancy Check (CRC) bits to protect critical information bits, leading to enhanced error correction capabilities. By applying TPP, the decoding process is accelerated by effectively reducing latency and saves computational resources by eliminating wrong codeword candidates at an earlier stage before the decoder favors them. The integration of Dynamic SCL introduces adaptability to the decoder, allowing it to adjust the list size based on the decoding requirements for different code rates and lengths. This adaptability enables efficient use of hardware resources by optimizing the utilization of the decoder storage but also tailors the decoder's performance to each specific scenario, yielding substantial error correction performance gains in both Polar and PAC codes. Extensive simulations and performance evaluations demonstrate the effectiveness of the proposed technique. The results indicate a gain of up to 0.4 dB for Polar codes and up to 0.6 dB for PAC codes compared to the standard SCL decoding approach. It is worth mentioning that such gains are considered substantial for fiber optical communications which is one of the target applications of the new technique. Furthermore, the technique showcases a reduction in decoding complexity, outperforming the traditional Fano decoder.
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.
We investigate the cyclic redundancy check (CRC) codes aided successive cancellation list (SCL) decoding schemes to improve the performance of Polar codes. Distinguished from the existing literatures of Polar codes that only consider the error detection capability of CRC, we attempt to take advantage of the inherent error correction capability of CRC and we first devise a segmented CRC-error-correcting aided SCL decoding (SCC-SCL) framework. Based on this framework, an error-correcting table based SCC-SCL (ET-SCC-SCL) decoding scheme is proposed, by introducing the look-up-table based CRC error correction method into the segmented Polar SCL decoding process. Since the error correction capability is limited by the size of the look-up table, which in turn limits the performance gain, we further propose a deep learning based SCC-SCL (DL-SCC-SCL) decoding scheme. In this scheme, a long short-term memory (LSTM) network replaces the error correction table to perform error correction, combining the sequence of log likelihood ratios (LLRs) with the syndromes to determine the error patterns. Simulation results show that both of the proposed decoding schemes have significant performance gain over the classic CRC error-detection aided SCL decoding scheme. Especially for the DL-SCC-SCL, the performance gain at bit error rate of 10-5is about 0.5 dB.
By adopting successive cancellation list decoding (SCL), polar codes demonstrate competitive error correction performance over LDPC and Turbo codes. However, SCL decoding suffers from high computational complexity and long decoding latency, especially when the list size is very large. Successive cancellation flip (SCF), as another decoding algorithm that can achieve high error correction performance, has a complexity that is close to that of successive cancellation (SC) decoding. With the observation that SCL and SCF decoding are similar at giving more chances to inspect possible codewords simultaneously or sequentially, a novel hybrid decoder is proposed in this paper, which essentially combines the ideas of SCF and SCL decoders. Moreover, in order to compensate for the degradation of performance caused by the reduction of path splitting and further reduce the decoding latency, the convolutional polar codes are adopted with a designed bit-flipping set. Simulation results demonstrate that the proposed decoder achieves the reduction of decoding latency while attaining better performance than conventional CRC-aided SCL decoder.
Polar codes have attracted the attention of numerous researchers in the past decade due to their excellent performance. However, their performance at short block lengths under standard successive cancellation decoding is far from desirable. An effective method to improve the performance at short lengths is CRC precoding followed by successive-cancellation list decoding. Later, Arikan presented polarization-adjusted convolutional (PAC) codes, which further improve the performance of polar codes. In fact, bit-flipping is another post-processing method that can improve decoding performance. In this paper, we propose a novel SCL Bit-Flipping of PAC Codes. We show that better performance can be achieved using list decoding when the list size is the same for PAC codes (N=128, K=64). The decoding performance of our newly proposed PAC-SCLF with a list size of 32 is 0.3 dB better than that of the traditional PAC-SCL with a list size of 32. We set the maximum number of bit flips to 5. The performance of the list size (L=32) for PAC-SCLF is almost the same as the performance of the list size (L=128) for PAC-SCL.
Polar codes achieve outstanding error correction performance when using successive cancellation list (SCL) decoding with cyclic redundancy check. A larger list size brings better decoding performance and is essential for practical applications such as 5G communication networks. However, the decoding speed of SCL decreases with increased list size. Adaptive SCL (A-SCL) decoding can greatly enhance the decoding speed, but the decoding latency for each codeword is different so A-SCL is not a good choice for hardware-based applications. In this paper, a hardware-friendly two-staged adaptive SCL (TA-SCL) decoding algorithm is proposed such that a constant input data rate is supported even if the list size for each codeword is different. A mathematical model based on Markov chain is derived to explore the bounds of its decoding performance. Simulation results show that the throughput of TA-SCL is tripled for good channel conditions with negligible performance degradation and hardware overhead.
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.