Showing papers on "Burst error-correcting code published in 1980"
TL;DR: Two new computationally efficient algorithms are developed for finding the exact burst-correcting limit of a cyclic code based on testing the colmn rank of certain submatrices of the parity-check matrix of the code.
Abstract: Two new computationally efficient algorithms are developed for finding the exact burst-correcting limit of a cyclic code. The first algorithm is based on testing the colmn rank of certain submatrices of the parity-check matrix of the code. An auxiliary result is a proof that every cyclic (n,k) codes with a minimum distance of at least three, corrects at least all bursts of length \lfloor (n - 2k + 1)/2 \rfloor or less. The second algorithm, which requires somewhat less computation, is based on finding the length of the shortest linear feedback shift-register that generates the subsequences of length n - k of the sequence formed by the coefficients of the parity-check polynomial h(x) , augmented with \lfloor (n-k)/2 \rfloor -1 leading zeros and trailing zeros. Tables of the burst-correcting limit for a large number of binary cyclic codes are included.
32 citations
TL;DR: Lower and upper bounds on the number of parity-check digits required for a linear code that corrects errors which are bursts of length b (fixed) of a specified type are presented.
Abstract: This paper presents lower and upper bounds on the number of parity-check digits required for a linear code that corrects errors which are bursts of length b (fixed) of a specified type.
21 citations
TL;DR: A decoding algorithm is given and the efficiency of these codes is discussed and the design parameters that specify the length of correctable successive timing errors are specified.
Abstract: Binary block codes are constructed that are capable of correcting successive timing errors such as the deletion or insertion of s bits (s\leq D) within a single additive burst of errors of length b or less (b=f+g+2D) , where f and D are the design parameters that specify the length of correctable successive timing errors and g is the length of the correctable additive burst. A decoding algorithm is given and the efficiency of these codes is discussed.
7 citations
TL;DR: The use of the General Column and Diagonal Matrix Burst Correcting Codes (GCDM3CC) for burst and random correction errors of noisy digital communication channels and synchronization of messages used in a computer communication network.
Abstract: This paper deals with : The use of the General Column and Diagonal Matrix Burst Correcting Codes (GCDM3CC) for burst and random correction errors of noisy digital communication channels and synchronization of messages used in a computer communication network. Statistics for the GCDMBCC, The construction strategies for the protocol packets used for a computer communication network with the aid of the redundancy cyole.
4 citations
TL;DR: A class of linear matrix codes for compound channels with memory that can be used to transmit information from fixed–rate sources through fixed-rate compound channels and analysis techniques to study error propagation in the proposed codoa are given.
Abstract: A class of linear matrix codes for compound channels with memory (i.e. channels on which burst, cluster and random errors occur) ia given. Explicit formulas are given for the number of burst, cluster and random errors that can be corrected with tlicso codes. Decoding nchcmes and analysis techniques to study error propagation in the proposed codoa are given. In particular, a new decoding algorithm for a concatenated matrix codo is given. The algorithm utilizes the decoding algorithm for the corresponding concatenated matrix code. A coding–decoding procedure is first, followed. The codes can bo used to transmit information from fixed–rate sources through fixed–rate compound channels. Tho channel probabilities are related to channel error propagation.
2 citations
TL;DR: Several new B 1 codes which meet the Wyner-Ash bound for minimum guard space are given and one simplified decodhg scheme is described which uses simple logic for error correction.
Abstract: A new class of B 1 codes which have an information rate of (b-1)/b for b=2,3,4, \cdots is presented. These codes correct error bursts up to b bits long when followed by a guard space of 3b^{2} - 2b - 1 bits. It is assumed that a hard decision is made on the fii sub-block of b bits after one constraint length of the code is received and then feedback is used to modify the syndrome bits. One simplified decodhg scheme is described which uses simple logic for error correction. A detailed example is presented showing an application of the results. Several new B 1 codes which meet the Wyner-Ash bound for minimum guard space are given. These codes were found by computer search.
2 citations
Patent•
28 Aug 1980
TL;DR: In this paper, a correction system codes and decodes f-blockwise for automatic correction of burst errors of lengths up to be symbols such that the multiplication matrix used for coding is also used for syndrome generation and error correction in that the c = bc+f-1 consecutive symbols in the burst selection region of the syndrome register only checks 2(f 1) symbols against a criterion independent of the generator polynomial and from bc whilst the remaining symbols are only checked to ascertain whether they contain zeros.
Abstract: The correction system codes and decodes f-blockwise for automatic correction of burst errors of lengths up to be symbols such that the multiplication matrix used for coding is also used for syndrome generation and error correction in that the c = bc+f-1 consecutive symbols in the burst selection region of the syndrome register only checks 2(f-1) symbols against a criterion independent of the generator polynomial and from bc whilst the remaining symbols are only checked to ascertain whether they contain zeros. In a certain region of the syndrome register, the two distances L1 and L2 of symbols differing from zero are determined by the region's boundaries and then checked to ensure that L1 + L2 is greater than or equal to f-1.
2 citations
TL;DR: The approach of this paper is to compare the properties of burst error correcting codes to provide a simplified and direct application of the known information theory behind those codes which are commonly found in the literature.
Abstract: The approach of this paper is to compare the properties of burst error correcting codes. It provides a simplified and direct application of the known information theory behind those codes which arr commonly found in the literature. For applications in which large coding is tolerable matrix codes have advantages over other burst correcting codes. Perhaps more important and certainly more surprising is the fact that matrix codes become comparatively more efficient and simpler to mechanize for increasing length n.
2 citations
1 citations
1 Nov 1980
TL;DR: Borders on the number of parity check digits required for a linear code that corrects random and burst errors separately and simultaneously are presented.
Abstract: The paper presents bounds on the number of parity check digits required for a linear code that corrects random and burst errors separately and simultaneously.
TL;DR: Separable error-correcting/detecting codes are developed that provide protection against combinations of both unidirectional and random errors.
Abstract: Separable error-correcting/detecting codes are developed that provide protection against combinations of both unidirectional and random errors. Specifically, codes are presented which can both: 1) correct (detect) some t random errors, and 2) detect any number of unidirectional errors which may also contain t or fewer random errors. Necessary and sufficient conditions for the existence of these codes are also developed. Decoding algorithms for these codes are presented, and implementations of the algorithms are also discussed.