Quasi-cyclic unit memory convolutional codes
J. Justesen,E. Paaske,M. Ballan +2 more
TL;DR: Unit memory convolutional codes with generator matrices, which are composed of circulant submatrices, are introduced, and a number of good codes, some of which result from efficient computer search and some ofWhich result from known block codes are presented.
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Abstract: Unit memory convolutional codes with generator matrices, which are composed of circulant submatrices, are introduced. This structure facilitates the analysis of efficient search for good codes. Equivalences among such codes and some of the basic structural properties are discussed. In particular, catastrophic encoders and minimal encoders are characterized and dual codes treated. Further, various distance measures are discussed, and a number of good codes, some of which result from efficient computer search and some of which result from known block codes, are presented. >
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Citations
Strongly-MDS convolutional codes
TL;DR: A class of MDS convolutional codes is introduced whose column distances reach the generalized Singleton bound at the earliest possible instant, called strongly-MDS convolutionsal codes.
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Strongly MDS Convolutional Codes
TL;DR: In this article, a class of strongly MDS convolutional codes whose column distances reach the generalized Singleton bound at the earliest possible instant were introduced. But their free distance is maximal among all codes of the same rate and the same degree.
119
Bounded distance decoding of unit memory codes
TL;DR: Decoding methods for error patterns of bounded weight are described, and it is demonstrated that these methods offer a favorable combination of performance and complexity.
32
A Class of One-Dimensional MDS Convolutional Codes
TL;DR: In this paper, a class of one-dimensional convolutional codes is presented, and the extended row distances are computed, and they increase with slope at least n - δ. And the cyclicity of these codes is discussed.
27
On the MacWilliams Identity for Convolutional Codes
TL;DR: In this paper, the adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code and a MacWilliams identity conjecture is formulated, and an explicit formula for the transformation is stated.
25
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Solomon W. Golomb
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Convolutional codes I: Algebraic structure
TL;DR: Minimal encoders are shown to be immune to catastrophic error propagation and, in fact, to lead in a certain sense to the shortest decoded error sequences possible per error event.
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An updated table of minimum-distance bounds for binary linear codes
TL;DR: An updated table of upper and lower bounds on the maximum minimum-distance for binary linear error-correcting codes up to length 127 is presented, incorporating numerous improvements that have appeared since then.
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