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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.
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Abstract: MDS convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper we introduce a class of MDS convolutional codes whose column distances reach the generalized Singleton bound at the earliest possible instant. We call these codes strongly MDS convolutional codes. It is shown that these codes can decode a maximum number of errors per time interval when compared with other convolutional codes of the same rate and degree. These codes have also a maximum or near maximum distance profile. A code has a maximum distance profile if and only if the dual code has this property.
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Citations
Layered Constructions for Low-Delay Streaming Codes
TL;DR: In this article, a new class of error correction codes for low-delay streaming communication is proposed, called MiDAS codes, which achieve a near optimal rate for an online setup where a source packet arrives at the encoder every $M$ channel uses, and needs to be decoded with a maximum delay of $T$ packets.
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Decoding of Convolutional Codes over the Erasure Channel
TL;DR: In this paper, the decoding capabilities of convolutional codes over the erasure channel were studied and two subclasses of MDP codes were defined: reverse-MDP and complete MDP convolutions.
Perfecting Protection for Interactive Multimedia: A survey of forward errror correction for low-delay interactive applications
TL;DR: Many current and emerging applications require low-latency communication, including interactive voice and video communication, multiplayer gaming, multiperson augmented/virtual reality, and various Internet of Things (IoT) applications.
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Convolutional Codes with Maximum Distance Profile
TL;DR: The main result shows that maximum distance profile codes form a generic set inside the variety which parametrizes the set of convolutional codes of a fixed rate and a fixed degree.
Superregular matrices and applications to convolutional codes
TL;DR: In this article, it was shown that a matrix is superregular if all of its rows are nonzero and any linear combination of its columns, with nonzero coefficients, has at least a − b + 1 nonzero entries.
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Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
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Polynomial weights and code constructions
TL;DR: It is shown that the polynomials (x - c)^i, i = 0,1,2,\cdots, have the "weight-retaining" property that any linear combination of these polynmials with coefficients in GF(q) has Hamming weight at least as great as that of the minimum degree polynomial included.
Maximum Distance Separable Convolutional Codes
TL;DR: The main result of the paper shows that this upper bound for the free distance generalizing the Singleton bound can be achieved in all cases if one allows sufficiently many field elements.
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On generator matrices of MDS codes (Corresp.)
Ron M. Roth,Gadiel Seroussi +1 more
TL;DR: By taking rectangular subarrays of the described triangles, it is possible to construct generator matrices [I|A] of maximum distance separable codes, where A is a Hankel matrix.
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