Showing papers on "List decoding published in 1992"
TL;DR: This work generalizes the existing decoding algorithms by error location for BCH and algebraic-geometric codes to arbitrary linear codes and investigates the number of dependent sets of error positions.
115 citations
06 Dec 1992
TL;DR: It is shown that such a scheme can gain about 1 dB in signal-to-noise ratio compared to trellis coded modulation with a small increase of complexity.
Abstract: Coded modulation schemes based on multilevel codes have been proposed previously. Here, a sequence of subsets of the signal set is coded using block and/or convolutional codes. For complexity reasons the decoding is done in several stages (multistage decoding). Punctured convolutional codes and parity check codes are applied to this scheme in channel with additive white Gaussian noise. The usual decoder structure does not exploit the asymptotic gain of a code combination at a bit error rate of 10/sup -5/. The decoder structure is expanded by three means: interleaving between the coded bits of every level, use of reliability information about decoding, and iterative decoding. It is shown that such a scheme can gain about 1 dB in signal-to-noise ratio compared to trellis coded modulation with a small increase of complexity. The price to be paid is additional decoder delay. >
41 citations
TL;DR: In experiments using a single fiber between a transmitter and a receiver by orthogonal polarizations, delta -function inverse response was observed, and the ideal two-channel network with inverse decoding has no loss due to encoding/decoding, only inevitable lossDue to the broadcast network.
Abstract: Coherent fiber-optic networks are used to improve upon incoherent CDMA schemes. If a single-channel network is used between transmitters and receivers, standard coherent correlation takes place. If several parallel spatial channels (fibers and/or polarizations) are used, ideal inverse decoding can be implemented, with perfect delta -function response of the matched decoder. The two-channel case is studied in detail. The rules for finding inverses of a given coding network and the relationship between matched networks for one-channel decoding and two-channel inverse decoding are given. Phase and frequency differences among stations imply that unwanted signals add up incoherently. The ideal two-channel network with inverse decoding has no loss due to encoding/decoding, only inevitable loss due to the broadcast network. In experiments using a single fiber between a transmitter and a receiver by orthogonal polarizations, delta -function inverse response was observed. >
39 citations
TL;DR: A key equation of the remainder decoding algorithm is presented and it is shown that several key equations proposed by L. Welch and E.R. Berlekamp and others can be derived from the proposed key equation.
Abstract: A key equation of the remainder decoding algorithm is presented. It is noted that the key equation presents a general relationship between the errors on the received codeword and the coefficients of the remainder polynomial. It is shown that several key equations proposed by L. Welch and E.R. Berlekamp (1983) and others can be derived from the proposed key equation. Useful properties of the key equations in fast decoding of Reed-Solomon codes are given. >
28 citations
Book•
01 Aug 1992
TL;DR: This book discusses the structure and Uniqueness of the (81,20,1,6) Strongly Regular Graph, and some Aspects of the Information Theoretic Dialogue on Projective Geometry Codes, and local search in Coding Theory.
Abstract: Foreword. Publications of J.H. van Lint. Local Search in Coding Theory. Cyclic Affine Planes and Paley Difference Sets. On the Reed-Muller Codes. A Note on Binary Cyclic Codes of Blocklength 63. List Decoding. Locally K 3,3 or Petersen Graphs. Note on the Structure of Semiovals in Finite Projective Planes. On Some New Simple Perfect Squared Squares. Structure and Uniqueness of the (81,20,1,6) Strongly Regular Graph. Some 2-Ranks. An Observation on Certain Point-Line Configurations in Classical Planes. Penrose Patterns are Almost Entirely Determined by Two Points. Covering Machines. Almost All Quasigroups Have Rank 2. The Dimension of Projective Geometry Codes. Subplane Covered Nets and Semipartial Geometries. On the Number of Fixed Point Free Elements in a Permutation Group. Generalized Hexagons of Even Order. On the Covering Radius of Reed-Muller Codes. A New Authentication Scheme Based on Latin Squares. Extension Operations for Cuts. Binomial Coefficient Codes over GF(2). Some VLSI Decompositions of the de Bruijn Graph. On Spherical Codes Generating the Kissing Number in Dimensions 8 and 24. Weight Distributions for a Certain Class of Codes and Maximal Curves. Probability, Information Theory, and Prime Number Theory. Translation Nets: A Survey. Local Indecomposability of Certain Geometric Graphs. New Spherical 4-Designs. Projective Codes Meeting the Griesmer Bound. Searching with Lies: the Ulam Problem. On Simple Combinatorial Optimization Problems. On Lengthening of Covering Codes. Kerdock Codes and Related Planes. Some Fascinating Integer Sequences. Support Weight Distribution of Linear Codes. On Block Designs with Repeated Blocks. On the Inverse Fermat Equation. On Perfect Arithmetic Codes. Linear Codes with Complementary Duals. Fault-Detection in Networks. Completely Regular Codes. Orthogonal Arrays and Other Combinatorial Aspects in the Theory of Uniform Point Distributions in Unit Cubes. On Decoding by Error Location and Dependent Sets of Error Positions. Incidence Structures Applied to Cryptography. More on the Uniqueness of the Golay Codes. A Recursive Method for Construction of Designs. Some Aspects of the Information Theoretic Dialogue. Circuits in Graphs Embedded on the Torus. A Note on Path-Zero Graphs. The [18,9,6] Code is Unique. Is Taylor's Graph Geometric? Complete k -arcs in PG(n,q), q Even. On the Cardinality of Sets of Sequences with Given Maximum Correlation. Fire Codes Revisited. On the Weight Enumerator of Product Codes. Some Small Non-Embeddable Designs. On Kirkman Triple Systems of Order 33. Efficient Circuits for Multiplying in GF(2 m ) for Certain Values of m .
23 citations
TL;DR: A permutation decoding procedure for abelian codes is introduced by using the Groebner bases theory and it is found that this method is valid for decoding all the binary abelsian codes.
Abstract: A permutation decoding procedure for abelian codes is introduced by using the Groebner bases theory. This method is valid for decoding all the binary abelian codes. Some examples are given to show how powerful this method can be. >
22 citations
TL;DR: A new decoding algorithm is proposed which is faster than the known one for the Zetterberg codes and requires, however, to solve a quadratic equation in order to decide whether 2 or 3 errors have occurred.
Abstract: The Zetterberg codes are one of the best known families of double-error correcting binary linear codes. Unfortunately, no satisfactory decoding algorithm has been known for them until recently when an algebraic decoding algorithm was described by P. Kallquist (1989). It requires, however, to solve a quadratic equation in order to decide whether 2 or 3 errors have occurred. A simple criterion is derived to determine whether 1, 2, or 3 errors have occurred when a Zetterberg code is used for data transmission. Based on criterion a new decoding algorithm is proposed which is faster than the known one. >
17 citations
01 Jan 1992
TL;DR: This work shows how to generalize Porter's ideas to all Algebraic-Geometric Codes and moreover, how to solve the key equation by simple linear algebra operations.
Abstract: The recent work about the problem of decoding Algebraic-Geometric Codes has led to an algorithm (e.g., see [2,3]). Another algorithm has been given by Porter, see [6,7,8,9,10], generalizing Berlekamp's decoding algorithm. The main step is to solve a so-called "key-equation". For this purpose, Porter gave a generalization of Euclid's algorithm for functions on curves. Unfortunately, therefore he had to impose some strong restrictions to the code and its underlying curve, such that the resulting algorithm works only for a very small class of Algebraic-Geometric Codes. Recently, the generalized Euclidian algorithm was investigated and corrected by Porter, Shen and Pellikaan ([11]) and Shen ([12]). Here, we will show how to generalize Porters ideas to all Algebraic-Geometric Codes and moreover, how to solve the key equation by simple linear algebra operations. Two observations on Porter's methods have motivated our work:
17 citations
TL;DR: Error-control codes for byte-oriented systems wherein the erroneous bits tend to be confined to a small number of bytes are presented and mathematical techniques developed for the construction of codes that can detect and correct such errors.
Abstract: Error-control codes for byte-oriented systems are presented. The proposed codes are intended for systems wherein the erroneous bits tend to be confined to a small number of bytes. Mathematical techniques are developed for the construction of codes that can detect and correct such errors. Among the various codes presented, the codes for detection and correction of errors confined to a single byte are of particular interest. A decoding algorithm for these codes is also presented. >
15 citations
TL;DR: This work has extended the result, which was up to a special case of the HT bound, obtained by P. Stevens (1990) on error-and-erasure decoding of binary cyclic codes.
Abstract: Procedures are presented for error-and-erasure decoding of cyclic codes up to the Hartmann-Tzeng (HT) bound. Emphasis is placed on converting the problem of error-and-erasure decoding to an error-only decoding problem so that the Berlekamp-Massey or the Feng-Tzeng multisequence shift-register synthesis algorithms can be applied. This work has thus extended the result, which was up to a special case of the HT bound, obtained by P. Stevens (1990) on error-and-erasure decoding of binary cyclic codes. >
01 Aug 1992
TL;DR: It has been shown that the proposed decoding strategies for Reed-Solomon product codes give a significant performance improvement over the conventional decoder.
Abstract: The authors propose two decoding strategies for Reed-Solomon product codes, and analyze their performance on a random error channel. The performance measures of interest are the probability of undetected error at the inner decoder output and that of decoding failure at the outer decoder output. It has been shown that the proposed decoding strategies give a significant performance improvement over the conventional decoder. >
27 May 1992
TL;DR: An efficient algorithm for GMD (generalized minimum distance) decoding is presented, which requires an algebraic errors-and-erasures decoding procedure to execute only one time.
Abstract: An efficient algorithm for GMD (generalized minimum distance) decoding is presented. It requires an algebraic errors-and-erasures decoding procedure to execute only one time. The Welch-Berlekamp iterative method is efficiently used to reduce the number of algebraic decoding procedures. A method for hardware implementation of this GMD decoding is shown. >
TL;DR: Five new combined error-correcting (d, k) codes for use on bandwidth limited channels are presented and these new codes are compared to known codes with similar parameters.
Abstract: Five new combined error-correcting (d, k) codes for use on bandwidth limited channels are presented. These new codes are compared to known codes with similar parameters. The error behaviour of the new codes after Viterbi decoding on the binary symmetric channel is evaluated by simulation. The power spectral densities are also measured and the results presented.
16 Nov 1992
TL;DR: This method provides a robust alternative for decoding of convolutional codes on fast fading (especially frequency-selective) channels where the estimation of channel parameters becomes more and more difficult.
Abstract: For decoding of convolutional codes by the Viterbi algorithm, the knowledge of channel parameters on non-Gaussian channels is either essential or preferable. When the considered channel is fast time-varying, reliable and robust estimation of the channel parameters by the conventional decision-directed adaptive algorithms is hardly possible. In the present paper, the Viterbi algorithm is applied in a modified way. Firstly a new trellis diagram is constructed at the receiver side according to modified definitions of trellis state and branch. Secondly a new branch metric is defined so that its expression does not explicitly depend on the channel parameters. With these modifications, decoding can be achieved without the knowledge of channel parameters. This method provides a robust alternative for decoding of convolutional codes on fast fading (especially frequency-selective) channels where the estimation of channel parameters becomes more and more difficult. >
TL;DR: Two decoding algorithms for double-byte error correcting-triple-bytes error detecting (DBEC-TBED) Reed-Solomon (RS) codes are implemented using Turbo-Pascal and several executions of the software show that the algorithm of Deng-Costello fails in the detection of some triple-byte errors, whereas the standard reference algorithm succeeds in detection always.
Abstract: Two decoding algorithms for double-byte error correcting-triple-byte error detecting (DBEC-TBED) Reed-Solomon (RS) codes are implemented using Turbo-Pascal. The first one is the noniterative decoding algorithm developed by R.H. Deng and D.J. Costello (ibid., vol.C-36, p.1359-63, Nov. 1987). The second one is a frequency-domain RS decoding method given by R.E. Blahut (Theory and Practice of Error Control Codes, Reading, MA, Addison-Wesley, 1983), which implements a standard Berlekamp-Massey algorithm; it is used as reference. Several executions of the software show that the algorithm of Deng-Costello fails in the detection of some triple-byte errors, whereas the standard reference algorithm succeeds in detection always. An example is presented in which the algorithm of Deng-Costello cannot detect a triple-error pattern. The authors also propose a modification to the algorithm of Deng-Costello for its proper operation and make a comparison between the two algorithms. >
TL;DR: It is shown that the reliability performance of Reed-Muller and other majority logic decodable codes can be substantially improved at the expense of a very small reduction in throughput.
Abstract: Reliability information provided by sets of orthogonal check sums in a majority logic decoder for block codes is used in a type-I hybrid automatic-repeat-request (ARQ) error control scheme. The reliability information is obtained through a simple modification of the majority logic decoding rule. It is shown that the reliability performance of Reed-Muller and other majority logic decodable codes can be substantially improved at the expense of a very small reduction in throughput. The simplicity of the decoding circuit permits implementation in systems with very high data rates. >
11 Oct 1992
TL;DR: The authors describe optimum decoding algorithms that can be useful for channels with various forms of interference, and demonstrate that the formulation considered here is solvable for many channels.
Abstract: The authors describe optimum decoding algorithms that can be useful for channels with various forms of interference. These algorithms consider constrained receiver complexity in the following sense. For a fixed number of decoders or demodulators, or for a fixed tolerable time delay for multiple decoding attempts, what is the best decoding algorithm? Optimality is defined as the maximum least cost incurred by a jammer to cause a decoding error (or failure). The design of the decoders or demodulators is determined by a set of thresholds, each of which determines an erasure region. It is demonstrated that the formulation considered here is solvable for many channels including the simple M-ary input-output channel with the Hamming distance as the cost function, the additive channel where the cost function corresponds to Euclidean distance, and a noncoherent channel with ratio-threshold-like decision rules and difference metric decision rules. >
01 Aug 1992
TL;DR: The decoding delay is proposed to replace the commonly used scheme length as a criterion for evaluating orchard codes and the ever approachable lower bound of the decode delay is derived to be 2τ for τ-error correcting orchard code.
Abstract: To evaluate an orchard code, a standard measure of how well the orchard code works is necessary. In the paper we propose the decoding delay to replace the commonly used scheme length as a criterion for evaluating orchard codes. The ever approachable lower bound of the decoding delay is derived to be 2τ for τ-error correcting orchard codes. With the help of the concept of the decoding delay, the performances of several orchard codes are compared. Also given are some very interesting new orchard codes.
TL;DR: Decoding algorithms in which unpruned codeword trees are generated from an ordered list of parity checks are investigated and it is suggested that for the small erasure probability, the method is computationally feasible at rates above the computational cutoff rate.
Abstract: Decoding algorithms in which unpruned codeword trees are generated from an ordered list of parity checks are investigated. The order is computed from the received message, and low-density parity-check codes are used to help control the growth of the tree. Simulation results are given for the binary erasure channel. They suggest that for the small erasure probability, the method is computationally feasible at rates above the computational cutoff rate. >
TL;DR: A decoding method for binary two-error correcting cyclic codes whose generator polynomials have at most two irreducible factors is presented.
Abstract: A decoding method for binary two-error correcting cyclic codes whose generator polynomials have at most two irreducible factors is presented. This class includes binary narrow-sense BCH codes with designed distance 5. The decoding algorithm uses the Zech logarithm for the finite field in which the roots of the code lie. >
01 Jan 1992
TL;DR: The purpose of this report is to discuss TCM architectural considerations in general, and to present the design, at the logic gate level, or a specific TCM decoder which applies these considerations to achieve high-speed decoding.
Abstract: Since 1971, when the Viterbi Algorithm was introduced as the optimal method of decoding convolutional codes, improvements in circuit technology, especially VLSI, have steadily increased its speed and practicality. Trellis-Coded Modulation (TCM) combines convolutional coding with higher level modulation (non-binary source alphabet) to provide forward error correction and spectral efficiency. For binary codes, the current stare-of-the-art is a 64-state Viterbi decoder on a single CMOS chip, operating at a data rate of 25 Mbps. Recently, there has been an interest in increasing the speed of the Viterbi Algorithm by improving the decoder architecture, or by reducing the algorithm itself. Designs employing new architectural techniques are now in existence, however these techniques are currently applied to simpler binary codes, not to TCM. The purpose of this report is to discuss TCM architectural considerations in general, and to present the design, at the logic gate level, or a specific TCM decoder which applies these considerations to achieve high-speed decoding.
19 Oct 1992
TL;DR: The authors evaluated the performances of a Reed-Solomon coded 64-QAM modulation on a Rayleigh fading channel and found that when the spectral efficiency is not close to 6, the gain of soft decision decoding over erasure decoding and the loss of erasure decode over hard decision decoding are not so large.
Abstract: The authors propose the design of a coded transmission system for the terrestrial urban radio channel, with a 4 bit-spectral efficiency. They evaluated the performances of a Reed-Solomon coded 64-QAM modulation on a Rayleigh fading channel. Three decoding algorithms are considered: a hard decision and an erasure Berlekamp-Massey decoding algorithm and a soft decision maximum likelihood decoding algorithm. By computing the cutoff rate they found that when the spectral efficiency is not close to 6, the gain of soft decision decoding over erasure decoding and the gain of erasure decoding over hard decision decoding are not so large. However, this gain must increase when the spectral efficiency becomes closer to 6 bits. >
17 Sep 1992
TL;DR: A method to utilize the reliability of decoded data for equalization and an adaptive decoding scheme based on the combined decoding and equalization are proposed and theoretical error probability and simulation results are given.
Abstract: A combined technique of equalization and decoding of an error-correcting code is introduced. It is very useful for achieving highly reliable communications in channels corrupted by noise and intersymbol interference, such as a telephone subscriber channel and a mobile communications channel. Two types of structures and algorithms for combined equalization and decoding are presented. Equalization can achieve stable adaptation for unknown characteristics and/or variance of a channel by using some information obtained in decoding, while decoding can be modified to adapt to the condition of a channel by exploiting information from equalization. In particular, a method to utilize the reliability of decoded data for equalization and an adaptive decoding scheme based on the combined decoding and equalization are proposed. Theoretical error probability and simulation results are given to evaluate the communication system using the combined technique. >
TL;DR: A maximum-likelihood decoding algorithm which is highly efficient for the cyclic code on the Z-channel and shows that by providing a certain threshold for the algorithm, a higher-speed decoding is realized and the computational complexity can be improved without sacrificing the maximum- likelihood property.
Abstract: This paper considers the Z-channel, which is known as a channel model for photon communication or semiconductor memory. A new decoding algorithm is proposed and discussed.
Recently, studies have been made from various viewpoints on the asymmetrical error-correcting code suited to the Z-channel, which is considered interesting. One of the basic problems in the Z-channel is the performance and the decoding method when the cyclic code with various features is applied, but it has been investigated little.
This paper presents first a maximum-likelihood decoding algorithm which is highly efficient for the cyclic code on the Z-channel. It is then shown that by providing a certain threshold for the algorithm, a higher-speed decoding is realized. It is shown also that by setting the threshold above a certain value, the computational complexity can be improved without sacrificing the maximum-likelihood property. Finally, it is demonstrated by numerical calculation that the decoding error probability is improved greatly by the decoding algorithm proposed in this paper, together with a drastic improvement in the computational complexity.
10 May 1992
TL;DR: A method is presented for computing a bound on the probability of error for maximum-likelihood decoding of trellis codes on channels with intersymbol interference and a reduced-state bound under the assumption of no error propagation is presented.
Abstract: A method is presented for computing a bound on the probability of error for maximum-likelihood decoding of trellis codes on channels with intersymbol interference. In general, computing such bounds requires the solution of a system of 2/sup 2(v+kL)/ equations, where v is the constraint-length of a rate k/n trellis code and L is the length of the channel impulse response. Direct solution of this set of equations is unreasonable for many cases of interest, and therefore an alternative method for computing a bound is presented. A bound on the probability of error for reduced-state decoding under the assumption of no error propagation is presented. This reduced-state bound can be formulated as the solution of a system of 2/sup 2(v+kL)/ equations, and this bound can be computed using the same method given for the maximum-likelihood bound. >
14 Jun 1992
TL;DR: The analytical results show that significant coding gain can be achieved by using the erasing technique with an ML Viterbi decoder.
Abstract: The authors study different strategies for decoding the concatenated inner code, applied in the case of multilevel coding with a multistage decoding procedure. The first strategy recapitulates the classical method of decoding the concatenated code. The second strategy is based on an erasing technique using hard detection. Maximum likelihood (ML) detection is applied in a third strategy. A fourth strategy is the combination of the second and the third strategies using an ML decoding and the erasing technique. For each decoding strategy, the overall performance of the system is derived analytically and the criterion of erasing is defined. The analytical results show that significant coding gain can be achieved by using the erasing technique with an ML Viterbi decoder. >
10 May 1992
TL;DR: A new version of the time domain algorithm which has only about 40% of the multiplications of published time domain techniques is presented and it is shown that this algorithm can also be used very efficiently for decoding truncated Reed-Solomon codes.
Abstract: Reed-Solomon decoding can be carried out in the time domain or frequency domain. The authors present a new version of the time domain algorithm which has only about 40% of the multiplications of published time domain techniques. The approach adopted in the algorithm development is as follows: obtain a new frequency domain decoding algorithm, with the number of Galois field multiplications and polynomial shift operations minimized; and take the Galois field inverse and discrete Fourier transforms of all the sequences and operators of this frequency domain decoding algorithm. Methods of mapping these algorithms into regular and flexible VLSI architectures are described. Both parallel and pipelined architectures are considered. It is shown that this algorithm can also be used very efficiently for decoding truncated Reed-Solomon codes. >