共查询到20条相似文献,搜索用时 15 毫秒
1.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》2009,55(9):4108-4118
2.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(5):709-714
A decoding algorithm for linear codes that uses the minimum weight words of the dual code as parity checks is defined. This algorithm is able to correct beyond the half minimum distance and has the capability of including soft-decision decoding. Results on applying this algorithm to quadratic residue (QR) codes, BCH codes, and the Golay codes (with and without soft-decision decoding) are presented. 相似文献
3.
Lee Soo-Woong Vijaya Kumar B. V. K. 《Selected Areas in Communications, IEEE Journal on》2010,28(2):181-187
Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel. 相似文献
4.
Gross W.J. Kschischang F.R. Gulak P.G. 《Very Large Scale Integration (VLSI) Systems, IEEE Transactions on》2007,15(3):309-318
Reed-Solomon codes are powerful error-correcting codes that can be found in many digital communications standards. Recently, there has been an interest in soft-decision decoding of Reed-Solomon codes, incorporating reliability information from the channel into the decoding process. The Koetter-Vardy algorithm is a soft-decision decoding algorithm for Reed-Solomon codes which can provide several dB of gain over traditional hard-decision decoders. The algorithm consists of a soft-decision front end to the interpolation-based Guruswami-Sudan list decoder. The main computational task in the algorithm is a weighted interpolation of a bivariate polynomial. We propose a parallel architecture for the hardware implementation of bivariate interpolation for soft-decision decoding. The key feature is the embedding of both a binary tree and a linear array into a 2-D array processor, enabling fast polynomial evaluation operations. An field-programmable gate array interpolation processor was implemented and demonstrated at a clock frequency of 23 MHz, corresponding to decoding rates of 10-15 Mb/s 相似文献
5.
Justesen J. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2007,53(8):2881-2885
By introducing a few simplifying assumptions we derive a simple condition for successful decoding using the Koetter-Vardy algorithm for soft-decision decoding of Reed-Solomon codes. We show that the algorithm has a significant advantage over hard decision decoding when the code rate is low, when two or more sets of received symbols have substantially different reliabilities, or when the number of alternative transmitted symbols is very small. 相似文献
6.
Takata T. Ujita S. Kasami T. Lin S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1993,39(4):1204-1218
Multistage decoding of multilevel block multilevel phase-shift keying (M -PSK) modulation codes for the additive white Gaussian noise (AWGN) channel is investigated. Several types of multistage decoding, including a suboptimum soft-decision decoding scheme, are devised and analyzed. Upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes. Error probabilities of some specific multilevel block 8-PSK modulation codes are evaluated and simulated. The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity. In one example, it is shown that the difference in performance between the proposed suboptimum multistage soft-decision decoding and the single-stage optimum decoding is small, only a fraction of a dB loss in SNR at the block error probability of 10-6 相似文献
7.
An efficient algorithm is presented for maximum-likelihood soft-decision decoding of the Leech lattice. The superiority of this decoder with respect to both computational and memory complexities is demonstrated in comparison with previously published decoding methods. Gain factors in the range of 2-10 are achieved. The authors conclude with some more advanced ideas for achieving a further reduction of the algorithm complexity based on a generalization of the Wagner decoding method to two parity constraints. A comparison with the complexity of some trellis-coded modulation schemes is discussed. The decoding algorithm presented seems to achieve a computational complexity comparable to that of the equivalent trellis codes 相似文献
8.
Simplified correlation decoding by selecting possible codewords using erasure information (Corresp.)
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1983,29(5):743-748
Correlation decoding is an optimal scheme of soft-decision decoding for error-correcting codes in the sense of minimum block-error probability. However, it is very difficult to apply the scheme when the number of information digits is large because of decoding complexity. A new algorithm for soft-decision decoding is presented, simplifying the correlation scheme by selecting certain codewords and decreasing decoding complexity by using erasure information. Any desired block-error probability between the error Probabilities of correlation and hard-decision decoding can be realized by setting up a suitable threshold value 0 for erasure decision. Computer simulation has been performed for Golay(23,12,7) code and BCH(15,7,5) code. 相似文献
9.
Low-density parity check codes over GF(q) 总被引:2,自引:0,他引:2
Gallager's (1962) low-density binary parity check codes have been shown to have near-Shannon limit performance when decoded using a probabilistic decoding algorithm. We report the empirical results of error-correction using the analogous codes over GF(q) for q>2, with binary symmetric channels and binary Gaussian channels. We find a significant improvement over the performance of the binary codes, including a rate 1/4 code with bit error probability <10-5 at Eb/N0=0.2 dB 相似文献
10.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1982,28(2):349-355
Algorithms for the soft-decision decoding of linear block codes are presented. These algorithms perform a reduced complexity search through a trellis derived from the parity check matrix of an(n, k) linear block code. The computational complexity of the algorithms is considerably reduced from that of a full maximum-likelihood algorithm. We demonstrate the trade-off between complexity and efficiency of the algorithms through computer simulation. 相似文献
11.
TETRA数字集群移动通信系统的物理层协议中采用了缩短Reed-Muller(RM)码,它与经典RM码的差异极大,无法采用Reed大数逻辑译码算法.根据正交校验矩阵的特点,提出了一种一般线性分组码的正交校验矩阵的穷举搜索算法.使用该算法搜索了缩短RM码的正交校验矩阵,对搜索速度进行了分析.证明了该码是两步完全可正交码,给出了它的Massey大数逻辑译码方法.仿真结果表明,无论是硬判决还是软判决,该译码方法的纠错性能都优于伴随式译码方法. 相似文献
12.
Adams S.S. Karst N. Pollack J. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2007,53(8):2677-2684
The growing demand for efficient wireless transmissions over fading channels motivated the development of space-time block codes. Space-time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum-likelihood decoding algorithm while achieving full transmit diversity. The two main research problems for these complex orthogonal space-time block codes (COSTBCs) have been to determine for any number of antennas the maximum rate and the minimum decoding delay for a maximum rate code. The maximum rate for COSTBCs was determined by Liang in 2003. This paper addresses the second fundamental problem by providing a tight lower bound on the decoding delay for maximum rate codes. It is shown that for a maximum rate COSTBC for 2m - 1 or 2m antennas, a tight lower bound on decoding delay is r = (m-1 2m) . This lower bound on decoding delay is achievable when the number of antennas is congruent to 0, 1, or 3 modulo 4. This paper also derives a tight lower bound on the number of variables required to construct a maximum rate COSTBC for any given number of antennas. Furthermore, it is shown that if a maximum rate COSTBC has a decoding delay of r where r < r les 2r, then r=2r. This is used to provide evidence that when the number of antennas is congruent to 2 modulo 4, the best achievable decoding delay is 2(m-1 2m_). 相似文献
13.
Schnabl G. Bossert M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1995,41(1):304-308
Constructs Reed-Muller codes by generalized multiple concatenation of binary block codes of length 2. As a consequence of this construction, a new decoding procedure is derived that uses soft-decision information. The algorithm is designed for low decoding complexity and is applicable to all Reed-Muller codes. It gives better decoding performance than soft-decision bounded-distance decoding. Its decoding complexity is much lower than that of maximum-likelihood trellis decoding of Reed-Muller codes, especially for long codes 相似文献
14.
In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft-decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity-check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation-based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation-based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of RS codes. 相似文献
15.
Hammons A.R. Jr. Kumar P.V. Calderbank A.R. Sloane N.J.A. Sole P. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1994,40(2):301-319
Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson (1967), Kerdock (1972), Preparata (1968), Goethals (1974), and Delsarte-Goethals (1975). It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z 4, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z 4 domain implies that the binary images have dual weight distributions. The Kerdock and “Preparata” codes are duals over Z 4-and the Nordstrom-Robinson code is self-dual-which explains why their weight distributions are dual to each other. The Kerdock and “Preparata” codes are Z 4-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z 4, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the “Preparata” code and a Hadamard-transform soft-decision decoding algorithm for the I(Kerdock code. Binary first- and second-order Reed-Muller codes are also linear over Z 4 , but extended Hamming codes of length n⩾32 and the Golay code are not. Using Z 4-linearity, a new family of distance regular graphs are constructed on the cosets of the “Preparata” code 相似文献
16.
Mizuochi T. Konishi Y. Miyata Y. Inoue T. Onohara K. Kametani S. Sugihara T. Kubo K. Yoshida H. Kobayashi T. Ichikawa T. 《Photonics Technology Letters, IEEE》2009,21(18):1302-1304
The concatenation of low-density parity-check and Reed-Solomon codes for forward error correction has been experimentally demonstrated for the first time in this letter. Using a 2-bit soft-decision large-scale integration and high-speed field-programmable gate arrays, a net coding gain of 9.0 dB was achieved with 20.5% redundancy with four iterative decoding for an input bit-error rate of 8.9 times 10-3 at 31.3 Gb/s. 相似文献
17.
We present a simple soft-decision decoding algorithm that modifies Sipser and Spielman's (see IEEE Trans, Inform. Theory, vol.42, p.1710-22, Nov. 1996) hard-decision sequential “bit-flipping” algorithm for decoding expander codes. The algorithm incorporates symbol reliability information and a simple “taboo” function that avoids repeated flipping of the same bit. The two algorithms have comparable simplicity, but simulations show that the soft-decision algorithm results in both improved performance and-because fewer decoding iterations are necessary-improved speed 相似文献
18.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》2008,54(9):3907-3928
19.
Calderbank A.R. McGuire G. Kumar V.P. Helleseth T. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1996,42(1):217-226
Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock (1972) and Preparata (1968) codes that can be very simply constructed as binary images, under the Gray map, of linear codes over Z4 that are defined by means of parity checks involving Galois rings. This paper describes how Fourier transforms on Galois rings and elementary symmetric functions can be used to derive lower bounds on the minimum distance of such codes. These methods and techniques from algebraic geometry are applied to find the exact minimum distance of a family of Z 4. Linear codes with length 2m (m, odd) and size 2(2m+1-5m-2). The Gray image of the code of length 32 is the best (64, 237) code that is presently known. This paper also determines the exact minimum Lee distance of the linear codes over Z4 that are obtained from the extended binary two- and three-error-correcting BCH codes by Hensel lifting. The Gray image of the Hensel lift of the three-error-correcting BCH code of length 32 is the best (64, 232) code that is presently known. This code also determines an extremal 32-dimensional even unimodular lattice 相似文献
20.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(1):76-80
It is shown that soft decision maximum likelihood decoding of any(n,k) linear block code overGF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more thanq^{(n-k)} states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer thanq^{n-k} . For a binary(n,n - 1) single parity check code, the Viterbi algorithm is equivalent to the Wagner decoding algorithm. 相似文献