Application of Beyond Bound Decoding for High Speed Optical Communications
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This paper studies the application of beyond bound decoding method for high speed optical communications. This hard-decision decoding method outperforms traditional minimum distance decoding method, with a total net coding gain of 10.36 dB.Keywords:
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BP decoding algorithm is usually used to realize decoding of RA codes,but the hardware circuit of BP decoding algorithm is complicated.Minimum-sum decoding algorithm can simplify BP decoding algorithm,but it is achieved by sacrificing performance.A modified RA decoding algorithm is proposed in order to have a good tradeoff between complexity and decoding performance.The proposed algorithm is approximate to BP decoding algorithm by the method of offset approximation,which can decrease the complexity of BP decoding algorithm.The simulation results show that,compared with BP decoding algorithm,the modified RA decoding algorithm can decrease algorithm complexity and keep good decoding performance.Compared with minimum-sum decoding algorithm,the complexity of modified RA decoding algorithm is almost unchanged,but the decoding performance improves significantly.
Berlekamp–Welch algorithm
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Iterative Viterbi decoding
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Purpose The purpose of this paper is to research the traditional belief‐propagation (BP) decoding algorithm of low‐density parity‐check code. The big computation load is a shortcoming of traditional BP decoding algorithm. Accordingly, the paper provides an improved BP decoding algorithm which raises the decoding efficiency and reduces decoding time delay. Design/methodology/approach An improved BP decoding algorithm is studied and the error correction performance of the improved BP decoding algorithm in the Gaussian channel is provided. Findings The simulation result shows the improved BP decoding algorithm has lower computational complexity and higher decoding speed based on the premise of a little decoding performance loss. Research limitations/implications The improved BP decoding algorithm has lower computational complexity and higher decoding speed based on the premise of a little decoding performance loss. Practical implications The improved BP decoding algorithm raises the decoding efficiency and reduces decoding time delay. Originality/value The decoding algorithm only needs to update the wrong bit information which might arise, but not update the bit information whose reliability is very high. The improved BP decoding algorithm raises the decoding efficiency and reduces decoding time delay.
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BP decoding algorithm is usually used to realize decoding of IRA codes,but the hardware circuit of BP decoding algorithm is complicated. A modified IRA decoding algorithm is proposed in order to have a good tradeoff between complexity and decoding performance. The proposed algorithm is approximate to BP decoding algorithm by the method of offset approximation ,which can simplify the complexity of BP decoding algorithm. The simulation results show that,compared with BP decoding algorithm,the modified IRA decoding algorithm can decrease algorithm complexity and keep good decoding performance. Compared with minimum-sum decoding algorithm,the complexity of modified IRA decoding algorithm is almost unchanged,but the decoding performance improves significantly.
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A novel minimum sequential increase decoding is presented, which is equivalent to the minimum Euclidean distance decoding. A new generalized threshold is also built up for the test sequence. The decoding problem is converted into a search progress on a direct tree. Then A algorithm with the new generalized threshold is applied to search on this tree. With the ability of heuristic search, A decoding algorithm can improve the decoding speed while the decoding performance remains optimal. Our computer simulations show the great advantages in decoding speed of A decoding algorithm over other soft decision decoding algorithms.
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Tree (set theory)
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The soft-decision decoding of polar codes is a trend that will be extensively applied in modern complex communication systems. However, the existing soft-decision decoding of polar codes is not satisfied due to the poor performance and high complexity. In this paper, a novel adjustable list decoding and its soft-decision type are proposed. Some bounds are given to depict the features of the decoding list with a correct path, which provides a guide to adjust the decoding list. The proposed adjustable list decoding scheme can achieve an equivalent performance to conventional SCL with significant lower complexity. Moreover, the soft adjustable list decoding can also outperform than the conventional soft-decision decoding schemes in concatenated structures.
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Sphere polar decoding can achieve the maximum likelihood (ML) bound. Existing sphere polar decoding ignores that the Euclidean distance of the frozen bits can be determined at earlier decoding levels. In this article, efficient sphere polar decoding is proposed to reduce the complexity. The set-by-set decoding process via synchronous determination is applied to the sphere polar decoding with fixed lower bounds and its multiple-searches version. Numeric results show the proposed decoding reduces much complexity on the low-rate codes compared with the existing sphere decoding while maintaining the same performance. At high signal-to-noise ratios, the latency of the proposed decoding is comparable with the successive cancellation list decoding.
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Successive cancellation (SC) decoding algorithm and successive cancellation list (SCL) decoding algorithm are two common decoding methods for polar codes. The SC decoding algorithm has low complexity, but in its decoding process, the bits with small channel indices are used to assist the decoding of the bits with large channel indices. Therefore, the bit being decoded depends on the bits that have already been decoded which causes error propagation. On the basis of SC decoding, the SCL decoding algorithm overcomes the problem of error propagation by widening the path search width and retaining multiple paths at the same time in the decoding process. However, the complexity of SCL decoding is higher than that of SC decoding. Without changing the performance of the SCL decoding algorithm, we propose a low-complexity SCL decoding algorithm based on path metric (PM). After the last frozen bit is decoded, the path with the smallest PM is selected, and the subsequent nodes adopt SC decoding. Through this combination of SCL decoding and SC decoding, the complexity of the SCL decoding algorithm can be effectively reduced while the SCL decoding performance remains unchanged, especially in the case of high code rates.
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Soft decision decoding is a decoding method which can cut the decoding error probability as compared with hard decision decoding by utilizing the channel measurement information effectively. In this paper, a new soft decision decoding method by which decoding operations can be efficiently carried out by utilizing the hierarchy of linear block codes is proposed. In addition, an improved algorithm which can reduce significantly the maximum computational complexity is also proposed. The proposed decoding algorithm utilizing the hierarchical structure of codes is a decoding method by which decoding is carried out sequentially from codes with high coding rates or codes of higher hierarchy in the inclusion order, and soft decision decoding can be efficiently carried out by utilizing a number of classes of codes having inclusion relationships in a manner which is superior to Chase algorithm 2 in the decoding error probability and the computational complexity for decoding. Computer simulation results confirm that the proposed algorithm realizes decoding error probability characteristics close to those of the maximum likelihood decoding method and that decoding can be carried out efficiently at a lower computational complexity than Chase algorithm 2 when the SNR is large. In addition, the improved algorithm which can reduce significantly the maximum computational complexity can realize decoding error probability characteristics close to those of the maximum likelihood decoding method on practical communication channels with relatively large SNR. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(3): 108–114, 2000
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Abstract An adaptive decoding scheme is introduced that achieves efficient soft—decision decoding for row—and—column parity array codes. The special structure of array codes is exploited to make effective use of hard—decision methods to realize soft—decision decoding. This leads to considerable reduction in decoding complexity as the amount of soft—decision computation varies with channel conditions. It is shown that the new decoding algorithm guarantees bounded distance performance. Simulation results indicate that the actual improvement of decoding performance over uncoded systems and previous decoding methods is significant.
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This paper describes an iterative method of decoding (for convolutional codes) that obtains soft-estimate decoding performances in-between BP decoding and optimal MAP decoding. The idea is to replace an original even-parity function (which is used in BP decoding) with a "reduced" core function and a corresponding multistate trellis. The result is a soft-decoding performance that can be better than the performance for recursive BP decoding. The decoding method does not achieve the optimal MAP performance due to dependencies within the recursive algorithm. The benefit is that the trellis may have far fewer states than the full 2 m -state trellis which is required for MAP decoding
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Trellis (graph)
Convolutional code
Berlekamp–Welch algorithm
Belief Propagation
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