The Successive Cancellation decoder cannot provide satisfactory error correcting performance for finite length polar codes. The error performance can be improved by using Successive Cancellation Flip decoders at the expense of higher complexity. In line with this, a novel decoding approach has been developed in this paper, where distributed parity bits are used to divide the codeword into multiple segments having equal probability of error occurrence, allowing early termination. The proposed Segmented Parity Successive Cancellation Flip (SP-SC Flip) Decoder achieves lower normalized complexity and average decoding latency compared to some related existing decoders, without degrading the error correcting performance. Further improvement in decoder performance is observed when code words are divided into a greater number of segments.
The Successive Cancellation decoder cannot provide satisfactory error correcting performance for finite length polar codes. The error performance can be improved by using Successive Cancellation Flip decoders at the expense of higher complexity. In line with this, a novel decoding approach has been developed in this paper, where distributed parity bits are used to divide the codeword into multiple segments having equal probability of error occurrence, allowing early termination. The proposed Segmented Parity Successive Cancellation Flip (SP-SC Flip) Decoder achieves lower normalized complexity and average decoding latency compared to some related existing decoders, without degrading the error correcting performance. Further improvement in decoder performance is observed when code words are divided into a greater number of segments.
Polar Codes achieve average error correction performance at finite code lengths, when decoded using Successive Cancellation (SC) decoding. Successive Cancellation Flip (SC-Flip) based decoders provide a viable low complexity substitute of the high performing high complexity Successive Cancellation List (SCL) decoders, providing a considerable improvement in the performance. A novel approach to identify and flip multiple erroneous bits in each decoding attempt has been aimed in this paper. Moreover, a faster version of the proposed decoder is also presented, which provides better performance throughout the entire decoding range. The performance of the proposed decoders have been evaluated with respect to frame error correction rate along with average normalized complexity and then compared with some of the existing works for validating the outperformance.
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.
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 are a class of error-correcting codes that provably achieve the capacity of practical channels. The successive-cancellation flip (SCF) decoder is a low-complexity decoder that was proposed to improve the performance of the successive-cancellation (SC) decoder as an alternative to the high-complexity successive-cancellation list (SCL) decoder. The SCF decoder improves the error-correction performance of the SC decoder, but the variable execution time and the high worst-case execution time pose a challenge for the realization of receivers with fixed-time algorithms. The dynamic SCF (DSCF) variation of the SCF decoder further improves the error-correction performance but the challenge of decoding delay remains. In this work, we propose a simplified restart mechanism (SRM) that reduces the execution time of SCF and DSCF decoders through conditional restart of the additional trials from the second half of the codeword. We show that the proposed mechanism is able to improve the execution time characteristics of SCF and DSCF decoders while providing identical error-correction performance. For a DSCF decoder that can flip up to 3 simultaneous bits per decoding trial, the average execution time, the average additional execution time and the execution-time variance are reduced by approximately 31%, 37% and 57%, respectively. For this setup, the mechanism requires approximately 3.9% additional memory.
The decoding performance of successive cancellation (SC) can be improved by correcting the error bits caused by channel noises. In order to identify and correct those error bits, we propose an improved progressive bit-flipping (IPBF) decoding algorithm. First, a more efficient method of constructing the set of error bit positions (EBPs) is proposed. It can significantly reduce the size of the set of EBPs, especially at medium to high signal to noise ratio (SNR). Second, a pruning technique of reducing the number of error bit-flipping combinations (EBFCs) is presented. In the case of ensuring that the decoding performance of PBF algorithm is not degraded, the decoding complexity is reduced as much as possible with the help of the pruning scheme. From the simulation results, compared to the conventional PBF algorithm, the proposed IPBF algorithm not only significantly reduces the average decoding complexity, but also has a slight improvement in decoding performance. At 2.0dB, the decoding complexity can be reduced by 63.6%, 87.5%, and 97.6% when ω is equal to 2, 3 and 4, respectively.
Polar codes have attracted significant attention in the field of communication, for the capacity-achieving under binary-input discrete memoryless channels (BDMCs). On the basis of successive cancellation (SC) decoding algorithm, many excellent methods have been developed to improve the decoding performance on short and medium codes. In this paper, an LLR-based segmented flipped successive cancellation list (LLR-based SF-SCL) decoding algorithm is proposed, where the information bits are divided into segments for early bit-flipping and termination. In order to make the unreliable bits evenly distributed in each sub-block, an LLR-based segmentation scheme is applied. Simulation results show that the proposed segmented flipped algorithm is superior to CRC-aided successive cancellation list (CA-SCL) algorithm in the block error rate (BLER) performance, and LLR-based segmentation scheme has better performance compared to uniform segmentation scheme.