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Showing papers on "List decoding published in 1986"


Journal ArticleDOI
TL;DR: This work introduces exceptionally simple decoding algorithms for the two extended Golay codes based on recent methods of Conway and Curtis of finding the unique blocks containing five points in either the (5,8,24) Steiner system or the ( 5,6,12) Steiners system.
Abstract: We introduce exceptionally simple decoding algorithms for the two extended Golay codes The algorithms are based on recent methods of Conway and Curtis of finding the unique blocks containing five points in either the (5,8,24) Steiner system or the (5,6,12) Steiner system These decoding methods are simple enough to enable decoding extended Golay codes by hand Both of the methods involve relations between the extended Golay codes and other self-dual codes Proofs are given explaining these relationships and why the decoding methods work The decoding algorithms are explained and illustrated with many examples [3 , chap 12] has facts about the Mathieu group and some details about decoding the Golay codes

71 citations


Journal ArticleDOI
TL;DR: A decoding algorithm for linear codes that uses the minimum weight words of the dual code as parity checks is defined and is able to correct beyond the half minimum distance and has the capability of including soft-decision decoding.
Abstract: 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.

45 citations


Patent
Katsutoshi Hisada1, Nobuaki Kokubu1, Shigeki Sakurai1, Yukio Murata1, Tatsuo Okano1 
04 Aug 1986
TL;DR: In this paper, a decoder for two-dimensional image codes such as modified Reed or modified modified Reed codes is disclosed, which ensures fast decoding operation by outputting reference codes in parallel manner while serially discriminating input codes and monitoring the relationship of both codes.
Abstract: There is disclosed a decoder for two-dimensionally encoded image codes such as modified Reed or modified modified Reed codes. The decoder ensures fast decoding operation by outputting reference codes in parallel manner while serially discriminating input codes and monitoring the relationship of both codes.

10 citations


Patent
21 Nov 1986

7 citations


01 Jan 1986
TL;DR: A Reed-Solomon code decoding algorithm based on Newton's interpolation to speed up Generalized-Minimum-Distance decoding and it can be shown that this GMD decoding complexity is asymptotically minimal.
Abstract: We propose a Reed-Solomon code decoding algorithm based on Newton’s interpolation to speed up Generalized-Minimum-Distance (GMD) decoding. This algorithm uses a modified Berlekamp-Massey algorithm to perform all necessary GMD decoding steps in only one run. The solutions generated by a Berlekamp-Massey algorithm if i least reliable symbols are erased are used to generate the solutions for 2 erasures less. By then using a time domain decoder the overall asymptotic GMD decoding complexity becomes O(dn) with n the length and d the distance of the code. It can be shown that this GMD decoding complexity is asymptotically minimal. Summary Up to now the coding and decoding of Reed-Solomon codes is based on the Fourier transform. The approach proposed here uses Newton’s interpolation. To use interpolation for coding was already proposed by Mandelbaum [4] back in 1979. Newton’s interpolation has the advantage that if one wants to add a new interpolation value then only one additional coefficient has to be calculated. We use this for GMD decoding. We assume that the distance of the Reed-Solomon code is odd (d=2t+1) and w.1.o.g. that the Reed-Solomon codewords over GF(q) are defined by the evaluation of polynomials of degree less or equal n-1-2t with n

5 citations


DOI
01 Aug 1986
TL;DR: The paper presents a maximum-likelihood consistent bounded distance decoding algorithm for convolutional codes, in which the decoder exploits the fact that only certain error sequences need to be corrected.
Abstract: The paper presents a maximum-likelihood consistent bounded distance decoding algorithm for convolutional codes. The algorithm correctly decodes all error sequences which fall within the error-correcting sphere. A class of codes is defined, in which the decoder exploits the fact that only certain error sequences need to be corrected. For these codes the decoding is based on a reduced encoder state diagram. Thus, only a subset of the trellis or tree has to be searched in order to find the error pattern. An exact characteristication of the reduced state diagram is given in the paper along with an example.

4 citations


DOI
01 Feb 1986
TL;DR: An upper bound is presented for the decoding time improvement factor of the reduced search algorithm compared to exhaustive table look-up decoding.
Abstract: A reduced search soft-decision decoding algorithm for binary block codes is presented. It is based on the weight distribution of the code and the transition probabilities of a binary input Q-ary output channel in sequencing the codeword classes during a table look-up operation. An upper bound is presented for the decoding time improvement factor of the reduced search algorithm compared to exhaustive table look-up decoding.

1 citations


Proceedings ArticleDOI
01 Oct 1986
TL;DR: A new approach to mitigate the effects of interference is derived that modifies conventional interleaving, detects and deletes burst errors, and corrects random errors.
Abstract: Based on the fact that performance of random error correction decoding is insensitive to code symbols erased before its decoding process, a new approach to mitigate the effects of interference is derived. This approach consists of three basic functions: it modifies conventional interleaving, it detects and deletes burst errors, and it corrects random errors. Therefore, this approach minimizes effects of jamming, antenna switching, and nuclear fading. We shall first describe a tactic of integrating coding and interleaving. Then, derivation and application of a special rate-1/4 convolutional code are illustrated. Finally, some preliminary computer simulation results on a rate-1/2 code are utilized to verify the effectiveness of the proposed technique.

1 citations




ReportDOI
10 Nov 1986
TL;DR: A new pruned-trellis search algorithm for high-rate convolutional code is developed, and the search time and memory size is significantly reduced from standard search techniques.
Abstract: : A new pruned-trellis search algorithm for high-rate convolutional code is developed. The search time and memory size is significantly reduced from standard search techniques. Some new high-rate systematic optimum convolutional codes of rate up to 7/8 have been found by this new search technique, and with constraint length up to 15. These newly found high-rate convolutional codes can be efficiently decoded using pruned, error-trellis, syndrome decoding. The real advantage of the pruned error-trellis decoding over the conventional Viterbi decoding algorithm is the reduction of the memory size required. Simulation shows that the error trellis performance of pruned error-trellis decoding suffers only a 0.2 dB loss for some systematic high-rate convolutional codes compared with conventional, full trellis decoding. Keywords: Integrated circuits; Architectures; Bibliographics; Abstracts.

Journal ArticleDOI
TL;DR: Maximal distance binary codes that are composed of individual characters from the residues of pairwise prime polynomials are constructed and compared to Reed-Solomon codes to allow faster decoding and greater data rates.
Abstract: Maximal distance binary codes that are composed of individual characters from the residues of pairwise prime polynomials are constructed and compared to Reed-Solomon codes. Although these binary residue codes are not as efficient as R-S codes in that codeword lengths are shorter, error decoding involves only binary and not finite field operations and thus allows faster decoding and greater data rates. Data rates of hundreds of megabits per second are feasible if decoding is implemented with VLSI array logic. Constructions of array logic for use in decoding are described. These codes lend themselves for use in a concatenated coding scheme.