Showing papers on "List decoding published in 1988"
TL;DR: The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters.
Abstract: Practically all known good constructive coding techniques for bandlimited channels, including lattice codes and various trellis-coded modulation schemes, can be characterized as coset codes. A coset code is defined by a lattice partition Lambda / Lambda ' and by a binary encoder C that selects a sequence of cosets of the lattice Lambda '. The fundamental coding gain of a coset code, as well as other important parameters such as the error coefficient, the decoding complexity, and the constellation expansion factor, are purely geometric parameters determined by C Lambda / Lambda '. The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters. >
676 citations
TL;DR: Shannon's zero-error channel capacities C/sub OF/C/sub O/ with and without noiseless feedback are generalized to list decoding: the receiver lists L messages, erring if the correct one is not listed.
Abstract: Shannon's zero-error channel capacities C/sub OF/, C/sub O/ with and without noiseless feedback are generalized to list decoding: the receiver lists L messages, erring if the correct one is not listed. The corresponding capacities C/sub OF/(L), C/sub O/(L) are nondecreasing in L. For an I-letter input alphabet, C/sub OF/(L) attains its maximum at L=I-1. A lower bound to C/sub O/(L) approaches that maximum as L increases. >
66 citations
TL;DR: A decoding method is proposed for the redundant residue polynomial codes, a class that includes Reed-Solomon codes, based on properties of Euclid's algorithm, which is suitable for decoding concatenated codes whose outer codes are redundant residue Poole's algorithm.
Abstract: A decoding method is proposed for the redundant residue polynomial codes, a class that includes Reed-Solomon codes. The method is based on properties of Euclid's algorithm. The advantage of the method is that the computation of both the error-locator polynomial and the error-evaluator polynomial needed in conventional decoding methods can be avoided. The method is suitable for decoding concatenated codes whose outer codes are redundant residue polynomial codes, since they are easily decoded by ignoring erasures detected in the inner codes. >
46 citations
TL;DR: A construction is given which allows error correction of a code for the T-user binary adder channel with two codewords per user to allow a greater freedom in choosing the parameters of the code without decreasing the rate sum.
Abstract: A construction is given which allows error correction of a code for the T-user binary adder channel with two codewords per user. The construction for a noisy channel is generalized to allow a greater freedom in choosing the parameters of the code without decreasing the rate sum. An example which illustrates an efficient decoding algorithm for the noisy channel is given. >
22 citations
TL;DR: The BCH algorithm is extended to correct more errors than indicated by the BCH bound, and a measure for the worst-case number of field elements of an extension field GF(2/sup m/) that must be tested for this purpose is given.
Abstract: The BCH algorithm is extended to correct more errors than indicated by the BCH bound. In the first step of the decoding procedure, a number of errors corresponding to a particular case of the Hartmann-Tzeng bound are corrected. In the second step full error correction is the goal. A measure for the worst-case number of field elements of an extension field GF(2/sup m/) that must be tested for this purpose is given for binary cyclic linear unequal error protection codes as well as for conventional binary cyclic codes. >
18 citations
Patent•
05 Feb 1988TL;DR: Disclosed as discussed by the authors is a coding and decoding method, in which a certain promised nonzero symbol is appended for decoding, thereby disallowing the presence of a codeword with all-"0" data after coding.
Abstract: Disclosed is a coding and decoding method, in which a certain promised nonzero symbol is appended for coding and decoding, thereby disallowing the presence of a codeword with all-"0" data after coding. The method enables the detection of a fault in an external circuitry by checking the occurrence of an all-"0" received word attributable to the external circuitry.
18 citations
TL;DR: The method for linear MDS codes saves the computation of the weight distribution and yields upper bounds for the probability of erroneous decoding and for the symbol error rate by the cumulative binomial distribution.
Abstract: When a block code is used on a discrete memoryless channel with an incomplete decoding rule that is based on a generalized distance, the probability of decoding failure, the probability of erroneous decoding, and the expected number of symbol decoding errors can be expressed in terms of the generalized weight enumerator polynomials of the code. For the symmetric erasure channel, numerically stable methods to compute these probabilities or expectations are proposed for binary codes whose distance distributions are known, and for linear maximum distance separable (MDS) codes. The method for linear MDS codes saves the computation of the weight distribution and yields upper bounds for the probability of erroneous decoding and for the symbol error rate by the cumulative binomial distribution. Numerical examples include a triple-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) code of length 63 and a Reed-Solomon code of length 1023 and minimum distance 31. >
11 citations
13 Jun 1988
TL;DR: The channel is assumed to be a multiaccess OR channel and the decoding problem is considered for a certain class of superimposed codes and a decoding algorithm is proposed and analyzed in terms of maximal decoding complexity.
Abstract: Ways of sharing a common channel without feedback are considered. The channel is assumed to be a multiaccess OR channel and the decoding problem is considered for a certain class of superimposed codes. A decoding algorithm is proposed and analyzed in terms of maximal decoding complexity. The robustness of the decoding algorithm is tested by simulations of decoding beyond the designed capability of the code. >
8 citations
01 Jun 1988
7 citations
01 Dec 1988
TL;DR: This report reviews soft decision techniques from simple eraser reconstruction through generalized minimum distance decoding and its extensions and those which seem most suited for Improved Iterated Codes are identified.
Abstract: : An open problem in communications is the construction and decoding os asymptotically good block codes - those which drive the probability or error to zero while bounding the code rate form below as the block length becomes infinite The author's Improved Iterated Codes have these properties, but larger rate bounds and simpler decoding would be useful Soft decision decoding promises some of each This report reviews soft decision techniques from simple eraser reconstruction through generalized minimum distance decoding and its extensions Those which seem most suited for Improved Iterated Codes are identified Author
3 citations
12 Jun 1988
TL;DR: A new class of error-correcting codes, with random and burst error correcting capability is described, with extreme simplicity of design of the decoder as well as the encoder and ease of implementation.
Abstract: The codes presented, which are majority-logic decodable, are created by simple geometric constructions. An iterative decoding scheme is given. The decoder differs significantly from bounded distance decoders commonly used for decoding block codes in that many error patterns having weight greater than the code minimum distance are correctable. This feature contributes to the codes' high efficiency in an automatic-repeat-request (ARQ) system. The decoding algorithm is also capable of burst error correction, and of detecting decoding faults, so that many patterns not correctable may be so indicated to the data sink. Although the code structure is essentially geometric, codes also have an algebraic structure that permits them to be used with classical algebraic codes, especially cyclic codes. The codes discussed can use encoder and decoder functions based entirely on shift registers. >
11 May 1988
TL;DR: A fast microprocessor-based decoding algorithm for high-rate Reed-Solomon codes is introduced to decrease the error location calculation time and hence increase the decoding speed.
Abstract: Applications of error control coding in mobile communications are considered. Statistical information required to choose a proper coding scheme to combat bursty errors is discussed. A consideration of implementation aspects such as cost, flexibility, reliability, size, and power consumption leads to a universal Reed-Solomon decoder structure suitable for mobile communications. A fast microprocessor-based decoding algorithm for high-rate Reed-Solomon codes is introduced to decrease the error location calculation time and hence increase the decoding speed. >
02 Nov 1988
TL;DR: This work considers maximum-likelihood decoding of binary linear codes from the viewpoint of space complexity, and discusses the concept of projecting set, enabling MLD by a gradient-like algorithm, and some extensions.
Abstract: We consider maximum-likelihood decoding (MLD) of binary linear codes from the viewpoint of space complexity. We discuss the concept of projecting set, enabling MLD by a gradient-like algorithm, and some extensions.
TL;DR: A way of using sequential decoding to exploit the memory of a Gilbert channel that alleviates this problem is presented, using a Fano-like metric matched to this channel.
Abstract: It is well known that the computational performance of sequential decoding deteriorates greatly when channel errors occur in clusters, as in Gilbert channels. A way of using sequential decoding to exploit the memory of a Gilbert channel that alleviates this problem is presented. A Fano-like metric matched to this channel is used. The method is investigated by simulating sequential decoding utilizing the stack algorithm. The simulations confirm the feasibility of the technique. >
Journal Article•
01 Apr 1988
TL;DR: This report investigates conventional decoding algorithms for BCH codes and inversionless forms of the algorithms are considered and the results are extended to provide for decoding of erasures as well as errors.
Abstract: : This report investigates conventional decoding algorithms for BCH codes. The algorithm of Sugiyama, Kasahara, Hirasawa and Namekawa, Mills' continued fraction algorithm, and the Berlekamp-Massey algorithm are all viewed as slightly differing variants of Euclid's algorithm. An improved version of Euclid's algorithm for polynomials is developed. The Berlekamp-Massey algorithm is extended within the Euclidean framework to avoid computation of vector inner products. Inversionless forms of the algorithms are considered and the results are extended to provide for decoding of erasures as well as errors. Keywords: Bose Chaudhuri Hocquenghem code; Very large scale integration; Two dimensional systolic arrays; Communications; Coding; Error correction codes.
28 Nov 1988
TL;DR: A synchronization method for short length words that uses message dependent synchronization digits that can be used to achieve symbol synchronization for length-255 Reed-Solomon codes and Simulation results are given for hard as well as soft decision decoding.
Abstract: The authors describe a synchronization method for short length words that uses message dependent synchronization digits. To each message to be transmitted, redundant digits at the encoder side are assigned. The redundant digits depend on two neighbor messages and are chosen so that at the decoder side maximum separation can be detected between the synchronized and unsynchronized modes. They analyze the decoding performance for transmission over an AWGN (additive white Gaussian noise) channel with synchronization transition errors. If the length of the messages is taken as equal to 8, then the method can be used to achieve symbol synchronization for length-255 Reed-Solomon codes. Simulation results are given for hard as well as soft decision decoding. >
TL;DR: A bit-slice microprocessor-based real-time decoder has been proposed in this paper and the design is versatile since different decoding algorithms can be executed by changing the microprogram.
13 Jun 1988
TL;DR: The algorithm investigated is basically a further adaptation of the Blokh-Zyablov algorithm to the case of soft decision decoding and is investigated with respect to error correcting capability and complexity of implementation.
Abstract: The authors investigate and compare two different soft decoding schemes. The first approach considered is the algorithm devised by D. Chase (1972). The second approach is based on the idea of generalized minimum distance decoding proposed by D. Forney (1966). This idea was further developed by Blokh-Zyablov (1973) and Zinoviev (1979), who devised a decoding algorithm for concatenated codes. Coding in combination with modulation can be seen as a concatenation with the modulation scheme as an inner code. The algorithm investigated is basically a further adaptation of the Blokh-Zyablov algorithm to the case of soft decision decoding. Both algorithms are investigated with respect to error correcting capability and complexity of implementation. >
16 Mar 1988
TL;DR: A modified Viterbi algorithm is developed to improve the output error probability and prove superior performance of maximum-likelihood decoding over conventional bit-by-bit detection.
Abstract: To control the level of intersymbol interferences while providing synchronization for read-back data, run-length-limited codes are widely used in modern recording systems. The feasibility of utilizing the redundancies introduced by these codes and the intrinsic correlative aspects of magnetic recording channels is used to improve the output error probability. To accomplish this, a modified Viterbi algorithm is developed. Computer simulation models are used to evaluate the performance of the algorithm. The results prove superior performance of maximum-likelihood decoding over conventional bit-by-bit detection. >
TL;DR: A r-ary symmetric channel has as transition probability matrix the r×r matrix qxy=p if x≠y andqxy=1−(r−1)p=q if x=y, and MLD here reduces to majority decoding.
Abstract: A r-ary symmetric channel has as transition probability matrix the r×r matrix qxy=p if x≠y and qxy=1−(r−1)p=q if x=y. Given a set Y of r symbols, the code here consists of r codewords, each one of them is made up of n identical symbols. Whenever q is larger than p, maximum likelihood decoding amounts to find out in the received vector which symbol is repeated most. Thus MLD here reduces to majority decoding.
12 Jun 1988
TL;DR: Closest coset decoding (CCD) is an efficient soft-decoding technique for block codes that achieves the same asymptotical coding gain as a maximum-likelihood decoder with significantly less computational effort.
Abstract: Closest coset decoding (CCD) is an efficient soft-decoding technique for block codes. The decoding procedure introduced, which is based on the concept of coset decoding, achieves the same asymptotical coding gain as a maximum-likelihood decoder with significantly less computational effort. Detailed functions of CCD are presented for decoding Reed-Muller codes. >
01 Jun 1988
TL;DR: A weighted-output symbol-by-symbol soft-decision decoding algorithm for convolutional codes is described, which relies on Bayesian estimation and shows that the latter is a special case of the former.
Abstract: A weighted-output symbol-by-symbol soft-decision decoding algorithm for convolutional codes is described. Its main intended use concerns concatenation schemes. If a convolutional code is used as inner code, it makes soft-decision decoding of the outer code possible, which improves the overall error rate. This algorithm relies on Bayesian estimation. Its comparison with Battail algorithm using cross-entropy minimisation shows that the latter is a special case of the former.