The dynamic perturbation (DP) decoding algorithm of Cyclic Redundancy Check (CRC) concatenated polar codes over Additive White Gaussian Noise (AWGN) channel is proposed. CRC concatenated polar codes append the CRC bits at the end of information bits and then feeds the resulting vector as input to the polar encoder. This paper improves the CRC-aided decoding method of polar codes based on perturbation, and proposes a dynamic perturbation decoding method for Polar-CRC concatenation code by controlling the interference noise dynamically. The proposed dynamic perturbation decoding is better than the original method with successive cancellation (SC) decoding.
The dynamic perturbation (DP) decoding algorithm of Cyclic Redundancy Check (CRC) concatenated polar codes over Additive White Gaussian Noise (AWGN) channel is proposed. CRC concatenated polar codes append the CRC bits at the end of information bits and then feeds the resulting vector as input to the polar encoder. This paper improves the CRC-aided decoding method of polar codes based on perturbation, and proposes a dynamic perturbation decoding method for Polar-CRC concatenation code by controlling the interference noise dynamically. The proposed dynamic perturbation decoding is better than the original method with successive cancellation (SC) decoding.
Polar codes have emerged as a powerful error correction technique for reliable data transmission in various communication systems. The addition of cyclic redundancy check (CRC) can significantly enhance the reliability of polar codes by providing an additional layer of error detection and correction. Without CRC, a system will lack a mechanism that detects and corrects decoding errors. By appending CRC bits to the polar-encoded data, the receiver with a belief propagation (BP) decoder can perform CRC to verify the correctness of the received information, enabling error detection beyond the capabilities of polar codes alone. This paper mainly focuses on incorporating CRC codes into polar codes and evaluating performance after the codes were transmitted into an additive white Gaussian channel. The CRC-aided BP decoder was simulated using MATLAB. The block length, N, was set to 256 and 1024 bits, and CRC varied between 12 and 16 bits for each N. The decoder system was tested with different numbers of iterations (50, 100, 200, and 500) to verify the performance in terms of bit error rate and frame error rate. Overall, this research provides a comprehensive analysis of the utilization of CRC for polar codes, considering different CRC sizes, numbers of iterations for BP decoding, and various block lengths. The average number of iterations of 200 and increasing CRC shows the lowest error rate readings throughout an increase in noise. The use of 12 and 16 bits of CRC further enhances the decoder’s error detection and correction capability.
Due to the unsatisfactory block error rate (BLER) performance of short or moderate block , the further development of polar codes is limited. In this paper, the parity-check codes concatenated cyclic redundancy check aided successive cancellation list (CA-SCL) decoding algorithms are studied. Then, an efficient concatenated method, double-parity-check CA-SCL (DP-CA-SCL) polar codes, is proposed according to exiting parity-check decoding algorithms. Not only can this new method improve the BLER performance in short or moderate block, but also it can guarantee the reduction of complexity relative to original CA-SCL method. The simulations in additive white Gaussian noise channel with binary phase shift keying modulation reveal that the DP-CA-SCL polar codes can provide significant performance gains. Comparing to the original CA-SCL decoding, there are 0.5 dB performance gains using proposed method at BLER of 10-3with (128, 64) polar codes. For another moderate block (256, 128) polar codes, it can also guarantee performance gains at least 0.18 dB.
Cyclic redundancy check (CRC) assisted list successive cancellation decoding (SCLD) makes polar codes competitive with the state-of-art codes. In this letter, we try to find the optimal CRC for polar codes to further improve its performance. We first analyze the undetected error probability of CRC-aided SCLD as well as the characteristics of Hamming weight distribution of polar codes. Based on these characteristics, a multilevel SCLD-based searching strategy with moderate list size is proposed to compute the minimum Hamming weight distribution (MHWD) of different CRC-concatenated polar codes. Using the searched MHWD, the optimal CRC for polar codes are presented in this letter. Simulation results show that the performance of optimal CRC-aided SCLD significantly outperforms the standard one, especially at high code rate.
In this paper, two decoding algorithms based on Successive-Cancellation (SC) are proposed to improve the error-correction performance of cyclic redundancy check (CRC)-aided polar codes while aiming for a low-complexity implementation. Comparisons with Dynamic SC Flip (DSCF) and SC Perturbation (SCP) are carried out since the proposed DSCF and Perturbation (DSCFP) and Perturbed DSCF (PDSCF) algorithms combine both methods. The analysis includes comparisons with several code lengthsNand various number of decoding attemptsTmax. ForN=1024and the coding rateR=1/2, the DSCF and the SCP algorithms withTmax=17are bested by approximately 0.1 dB at block-error rate (BLER) of 0.001. At BLER = 10−6and forTmax=64, the gain is of 0.375 dB and > 0.5 dB with respect to DSCF and SCP, respectively. At high signal-to-noise ratio, the average computational complexity of the proposed algorithms is virtually equivalent to that of SC.
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.
Soft information perturbations can significantly improve the successive cancellation (SC) decoding performance of polar codes. This is an effective method for realizing low-latency yet high performance for long polar codes, since each perturbation-based SC (PSC) decoding can be performed in parallel. However, little theoretical insight has been revealed so far regarding its work rationale. This paper provides the theoretical analysis of the soft information perturbation. It reveals that PSC decoding improves the SC decoding performance through correcting the erroneous bit estimations, especially the first erroneous bit (FEB). It further validates that perturbing the soft information does not degrade the error-correction capability of SC decoding. Such revelations lead to the design of optimal perturbations that maximizes the FEB correction probability, resulting in an enhanced PSC decoding performance. Based on this, a novel hybrid PSC (HPSC) decoding is proposed. By introducing the random and biased perturbations, the HPSC decoding can better divert from the initial erroneous estimation and converge to the intended one. Our simulation results demonstrate that with the optimal perturbation, the HPSC decoding can achieve a similar performance as the cyclic redundancy check (CRC) aided SC list (CA-SCL) decoding, while avoiding path sorting and expansion.