A simple high-speed decoding algorithm for the [24, 12, 8] extended Golay code suitable for implementation in combinational circuits is described. The proposed decoding algorithm corrects all patterns of three or fewe...
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A simple high-speed decoding algorithm for the [24, 12, 8] extended Golay code suitable for implementation in combinational circuits is described. The proposed decoding algorithm corrects all patterns of three or fewer errors and detects quadruple errors using the Turyn construction of the extended Golay code. It is proved that the [24, 12, 8] Golay code can correct all patterns of three or fewer random errors as well as certain patterns of quadruple errors such as four-bit cyclic single-burst and two-dimensional burst errors.
A reduced-complexity modified decoding algorithm for turbo trellis-coded modulation (TTCM) is proposed and evaluated in terms of complexity and bit error rate (BER) performance in an additive white Gaussian noise chan...
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A reduced-complexity modified decoding algorithm for turbo trellis-coded modulation (TTCM) is proposed and evaluated in terms of complexity and bit error rate (BER) performance in an additive white Gaussian noise channel. The algorithm uses an optimal approximation of the Jacobian logarithm, used in the so-called Log-MAP decoding, by means of the max operation and three piecewise-linear terms. Further computational complexity savings are obtained by applying this approximation only to the two largest values within the decoding step. To improve performance, the algorithms are also investigated using a scaling factor for the extrinsic information. Computer-simulated BER performance evaluation results and complexity comparisons are reported showing the near-optimal performance as well as noticeable implementation advantages of the proposed algorithms with respect to the Log-MAP decoding.
Based on the breadth-first search manner and the level-compression technique, this letter first presents a new ai ray data structure to represent the classical Huffman tree. Then, the decoding algorithm is given. Both...
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Based on the breadth-first search manner and the level-compression technique, this letter first presents a new ai ray data structure to represent the classical Huffman tree. Then, the decoding algorithm is given. Both the memory and the decoding time required in the proposed method are less than those of previous methods. Some experimentations are carried out to demonstrate the advantages of the proposed method. In fact, the proposed algorithm can be applied to the canonical Huffman tree.
Previous algorithms for decoding AG codes up to the designed distance all assumed existence of an extra rational place on the base algebraic curve. The place is used to solve the decoding problem by linear algebra ove...
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Previous algorithms for decoding AG codes up to the designed distance all assumed existence of an extra rational place on the base algebraic curve. The place is used to solve the decoding problem by linear algebra over the base field of the curve. The rationality of the place is essential, and therefore AG codes supported by all rational places on the curve are excluded from the domain of applicability of the decoding algorithms. This paper presents a decoding algorithm for those AG codes using an extra place of higher degree. Hence finally all AG codes, as Goppa defined 40 years ago, are equipped with a fast decoding algorithm.
A decoding algorithm, based on Venn diagrams, for decoding the (23, 12, 7) Golay code is presented. The decoding algorithm is based on the design properties of the parity sets of the code. As for other decoding algori...
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A decoding algorithm, based on Venn diagrams, for decoding the (23, 12, 7) Golay code is presented. The decoding algorithm is based on the design properties of the parity sets of the code. As for other decoding algorithms for the Golay code, decoding can be easily done by hand.
In this correspondence, it is proved that Hermitian code is a direct sum of concatenated Reed-Solomon codes over GF (q(2)). Based on this discovery, first, a new method for computing the dimension and tightly estimati...
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In this correspondence, it is proved that Hermitian code is a direct sum of concatenated Reed-Solomon codes over GF (q(2)). Based on this discovery, first, a new method for computing the dimension and tightly estimating the minimum distance of the Hermitian code is derived. Secondly, a new decoding algorithm, which is especially effective in dealing with burst errors with complexity O(n(5/3)), is described. Finally, some possible approaches for optimization of Hermitian codes are discussed.
The binary QR codes are well known for their good behavior. The proposed algebraic decoding algorithm for decoding the (31, 16, 7) QR code with reducible generator polynomial is able to correct up to three errors in t...
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ISBN:
(纸本)9781424435197
The binary QR codes are well known for their good behavior. The proposed algebraic decoding algorithm for decoding the (31, 16, 7) QR code with reducible generator polynomial is able to correct up to three errors in the finite field GF(2(5)). The proposed algorithm is based on an application of the decoding algorithm given by Truong et al. and Chen et al. to modify the decoding algorithm proposed by Reed el al. All syndromes in the error-locator polynomial are computed in the finite field GF(2(5)). Thus, the decoding time can be reduced. Moreover, the simulation results for comparing the proposed decoding algorithm with decoding algorithm given by Reed et al. are given. This algorithm is suitable for implementation in a programmable microprocessor or special-purpose VLSI chip.
Channel coding always plays an important role In communication systems. decoding complexity is one factor which needs to be considered in its implementation. In this paper the decoding algorithm for MTCM is studied. V...
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ISBN:
(纸本)9781424421077
Channel coding always plays an important role In communication systems. decoding complexity is one factor which needs to be considered in its implementation. In this paper the decoding algorithm for MTCM is studied. Viterbi decoding algorithm for MTCM contains much more computations per trellis state transition. A most applicable decoding scheme for MTCM Is proposed, which can achieve reduced computational complexity. The BER performance can approach that of the maximum likelihood decoding algorithm quickly by increasing the value of one parameter of MTCM.
Low-density generator matrix with iterative belief propagation decoding and comma-free source codes are natural choices for noisy channel encoding and source coding, respectively. In earlier work, We found that avoidi...
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ISBN:
(纸本)0780344081
Low-density generator matrix with iterative belief propagation decoding and comma-free source codes are natural choices for noisy channel encoding and source coding, respectively. In earlier work, We found that avoiding 6 cycles had little impact on the performance of a code established by performing a fixed number of decoding algorithm iterations. In this work, we carried on a more detailed investigation of the decoding algorithm and found that the comma-free codes call be effectively used as an outer error-detection-correction-code for a low-density generator matrix inner code.
We present a new approach of the decoding algorithm for Gabidulin Codes. In the same way as efficient erasure decoding for Generalized Reed Solomon codes by using the structure of the inverse of the VanderMonde matric...
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