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.
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.
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.
SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct bit-flipping position in SCF decoding limits its improvements. Due to its improved bit-flipping criterion, Thresholded SCF (TSCF) decoding algorithm exhibits a superior error-correction performance and lower computational complexity than SCF decoding. However, the parameters of TSCF decoding depend on multiple channel and code parameters, and are obtained via Monte-Carlo simulations. Our main goal is to realize TSCF decoding as a practical polar decoder implementation. To this end, we first realize an approximated threshold value that is independent of the code parameters and precomputations. The proposed approximation has negligible error-correction performance degradation on the TSCF decoding. Then, we validate an alternative approach for forming a critical set that does not require precomputations, which also paves the way to the implementation of the Fast-TSCF decoder. Compared to the existing fast SCF implementations, the proposed Fast-TSCF decoder has 0.24 to 0.41 dB performance gain at frame error rate of 10−3, without any extra cost. Compared to the TSCF decoding, Fast-TSCF does not depend on precomputations and requires 87% fewer decoding steps. Finally, implementation results in TSMC 65nm CMOS technology show that the Fast-TSCF decoder is 20% and 82% more area-efficient than the state-of-the-art fast SCF and fast SC-List decoder architectures, respectively.
SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct bit-flipping position in SCF decoding limits its improvements. Due to its improved bit-flipping criterion, Thresholded SCF (TSCF) decoding algorithm exhibits a superior error-correction performance and lower computational complexity than SCF decoding. However, the parameters of TSCF decoding depend on multiple channel and code parameters, and are obtained via Monte-Carlo simulations. Our main goal is to realize TSCF decoding as a practical polar decoder implementation. To this end, we first realize an approximated threshold value that is independent of the code parameters and precomputations. The proposed approximation has negligible error-correction performance degradation on the TSCF decoding. Then, we validate an alternative approach for forming a critical set that does not require precomputations, which also paves the way to the implementation of the Fast-TSCF decoder. Compared to the existing fast SCF implementations, the proposed Fast-TSCF decoder has 0.24 to 0.41 dB performance gain at frame error rate of 10-3, without any extra cost. Compared to the TSCF decoding, Fast-TSCF does not depend on precomputations and requires 87% fewer decoding steps. Finally, implementation results in TSMC 65nm CMOS technology show that the Fast-TSCF decoder is 20% and 82% more area-efficient than the state-of-the-art fast SCF and fast SC-List decoder architectures, respectively.
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.
Although original successive cancellation flip (SCF) decoding of the polar codes can identify the first error position and flip the error, decoding still fails when other errors occur after the corrected error bit. Therefore, the improvement of the block error rate (BLER) performance is limited. In this paper, we present an improved algorithm that can correct multiple error bits, named as improved multiple bit-flipping successive cancellation decoding algorithm. First, multiple sets are constructed by calculating the log likelihood ratio (LLR) of each information bit. Then, a bit is selected and corrected from the first set when original decoding fails; two bits are selected and flipped from the second set when all bits in the first set cannot be successfully decoded; when all bits combinations in the second set are flipped but the output vector still does not match the input vector, three bits are selected and corrected from the third set. Simulation results show that the BLER performance of the improved algorithm is better than that of the successive cancellation list decoding (SCL) decoding algorithm with a list size of L = 8 for N = 256. When N = 1024 and SNR = 3 dB, the BLER performance of improved algorithm is slightly better than that of SCL decoding algorithm with a list size of L = 4.
Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e., BP bit-flip (BP-BF), generalized BP-flip (GBPF), cyclic redundancy check (CRC)-aided (CA-SCL) decoding, and ordered statistic decoding (OSD), algorithms. Simulation results showed that the FL-BP had an excellent block error rate (BLER) performance gain up to 0.7 dB compared with BP, BP-BF, and GBPF decoder. Besides, the computational complexity was reduced considerably in the high signal-to-noise ratio (SNR) regime compared with the BP-BF and GBPF decoding methods.