Polar codes attract more and more attention of researchers in recent years, since its capacity achieving property. However, their error-correction performance under successive cancellation (SC) decoding is inferior to other modern channel codes at short or moderate blocklengths. SC-Flip (SCF) decoding algorithm shows higher performance than SC decoding by identifying possibly erroneous decisions made in initial SC decoding and flipping them in the sequential decoding attempts. However, it performs not well when there are more than one erroneous decisions in a codeword. In this paper, we propose a path metric aided bit-flipping decoding algorithm to identify and correct more errors efficiently. In this algorithm, the bit-flipping list is generated based on both log likelihood ratio (LLR) based path metric and bit-flipping metric. The path metric is used to verify the effectiveness of bit-flipping. In order to reduce the decoding latency and computational complexity, its corresponding pipeline architecture is designed. By applying these decoding algorithm and pipeline architecture, an improvement on error-correction performance can be got up to 0.25dB compared with SCF decoding at frame error rate of 10-4, with low average decoding latency.
Polar codes attract more and more attention of researchers in recent years, since its capacity achieving property. However, their error-correction performance under successive cancellation (SC) decoding is inferior to other modern channel codes at short or moderate blocklengths. SC-Flip (SCF) decoding algorithm shows higher performance than SC decoding by identifying possibly erroneous decisions made in initial SC decoding and flipping them in the sequential decoding attempts. However, it performs not well when there are more than one erroneous decisions in a codeword. In this paper, we propose a path metric aided bit-flipping decoding algorithm to identify and correct more errors efficiently. In this algorithm, the bit-flipping list is generated based on both log likelihood ratio (LLR) based path metric and bit-flipping metric. The path metric is used to verify the effectiveness of bit-flipping. In order to reduce the decoding latency and computational complexity, its corresponding pipeline architecture is designed. By applying these decoding algorithm and pipeline architecture, an improvement on error-correction performance can be got up to 0.25dB compared with SCF decoding at frame error rate of 10-4, with low average decoding latency.
Bit flipping was first used to improve the decoding performance of successive cancellation (SC) decoder. Since SC decoding process is serial, so the first bit that goes wrong in the decoding process will cause several subsequent bits to go wrong, which will suffer from higher decoding delay than belief propagation (BP) parallel decoding. In order to meet the performance of 5G low latency and high reliability, BP decoding algorithm have received a lot of attention. However, at medium and high signal-to-noise ratios (SNR), BP decoding does not perform as well as the SC list (SCL) decoding algorithm. Hence, BP decoding algorithm borrows bit-flip strategies from SC bit flip (SCF) decoder to improve the performance. The performance of BP bit flip (BPF) decoding depends on whether the construction of the flip set is correct, so this letter proposes a flip set construction approach based on the standard deviation of the log-likelihood ratio (LLR) and the reliability weight of polarized channels, which is comparable to the existing BPF decoding, the improved algorithm can identify the error-prone bits more efficiently and improve the decoding performance.
Successive cancellation (SC) decoding of polar codes may bring about error propagation that needs to be mitigated. In this paper, we present a new SC Flipping (SCFlip) decoder, named bit error rate (BER) evaluation based SCFlip (BER-SCFlip), which can accurately target the first error bit and correct it with a high probability. Thus, a high error correction capability and a low decoding complexity can be achieved. First, we propose a new criterion to find out the most suspicious error bit. Those non-frozen bits that have higher decoding BERs derived from log-likelihood-ratios (LLRs) after SC decoding than the corresponding expected ones estimated via Gaussian Approximation (GA), are collected into the flip-bits set. These candidate bits will be flipped one by one according to their SC decoding orderings in extra decoding attempts until the decoded codeword passes cyclic redundancy check (CRC) or a predetermined maximum number of extra attempts is reached. We then propose an extended version of BER-SCFlip, named BER-SCFlip-w with the capability to correct up to w error bits in each extra decoding attempt. By combining our criterion for the flip-bits selection with that of Dynamic SCFlip (D-SCFlip), the proposed BER-SCFlip-w significantly reduces decoding complexity and latency while maintaining the superior error-correction performance close to that of D-SCFlip-w. The simulation results show that the proposed schemes are competitive among existing SCFlip algorithms and could achieve the error-correction performance approaching that of CRC-aided SCL decoding under list size L = 16 while maintaining low complexity.
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.
Although the SC-Flip decoder can significantly avoids the effects of cumulative errors by flipping the first erroneous bit of the traditional SC decoder, the computational complexity of the SCF increases simultaneously. In this letter, to reduce the computational complexity of the SCF decoder, we investigate the log-likelihood ratio (LLR) values and their distribution related to the erroneous bit-channels, then replace the LLR sorting method of SC-Flip with a new value. By setting a threshold for the bits to flip, we proposed a SC-Flip decoder using effective flip bits (SCF-EF). Simulation results demonstrate that for practical code lengths (1024, 512), SCF-EF can achieve 21.37% complexity reduction at SNR of 0.5dB with negligible loss compared with the BLER performance when correcting all single-errors.
Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity.