Convolutional codes with maximum column sum rank for network streaming

Mahmood, Rafid; Badr, Ahmed; Khisti, Ashish

doi:10.1109/isit.2015.7282860

Cited by 22 publications

(49 citation statements)

References 8 publications

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“…We follow previous approaches and regard the symbols v v v i as packets and consider that losses occur on a packet level [5,18,26]. In the transmission of a stream of information at each time instant i we receive a symbol packet v v v i ∈ F n .…”

Section: Delay In Burst Erasure Channelsmentioning

confidence: 99%

“…Thus, the proposed construction admits an optimal delay decoding when only bursts of erasures of length up to L occur. Note that this construction requires only binary entries, whereas previous contributions (see for instance [18,19]) require larger finite fields. As a consequience, the decoding of our construction is computationally more efficient.…”

Section: Our Constructionmentioning

confidence: 99%

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Block Toeplitz matrices for burst-correcting convolutional codes

Climent

Napp

Requena

2019

RACSAM

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In this paper we study a problem in the area of coding theory. In particular, we focus on a class of error-correcting codes called convolutional codes. We characterize convolutional codes that can correct bursts of erasures with the lowest possible delay. This characterization is given in terms of a block Toeplitz matrix with entries in a finite field that is built upon a given generator matrix of the convolutional code. This result allows us to provide a concrete construction of a generator matrix of a convolutional code with entries being only zeros or ones that can recover bursts of erasures with low delay. This construction admits a very simple decoding algorithm and, therefore, simplifies the existing schemes proposed recently in the literature.

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Section: Delay In Burst Erasure Channelsmentioning

confidence: 99%

Section: Our Constructionmentioning

confidence: 99%

Block Toeplitz matrices for burst-correcting convolutional codes

Climent

Napp

Requena

2019

RACSAM

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show abstract

Section: Theoremmentioning

confidence: 99%

“…In [17] a construction of an (n, k, δ) convolutional code with optimal rank sum column distance profile satisfying d j SR = (n − k)(j + 1) + 1 was proposed. The codes in [17] are sum rank metric analogs of MDP codes [1,8]. One disadvantage of these codes is the requirement of very large fields requiring double exponential size in the code degree δ.…”

Section: Theoremmentioning

confidence: 99%

Concatenation of convolutional codes and rank metric codes for multi-shot network coding

Napp

Pinto

Sidorenko

2017

Des. Codes Cryptogr.

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In this paper we present a novel coding approach to deal with the transmission of information over a network. In particular we make use of the network several times (multi-shot) and impose correlation in the information symbols over time. We propose to encode the information via an inner and an outer code, namely, a Hamming metric convolutional code as an outer code and a rank metric code as an inner code. We show how this simple concatenation scheme can exploit the potential of both codes to produce a code that can correct a large number of error patterns.

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“…Thus, a convolutional code is associated with a sequence of column distances at different time instants, and such a sequence is termed the distance profile of the convolutional code. In view of this, the distance profile of a convolutional code is particularly helpful for evaluating the error correction capability of the code when it is used for streaming over erasure channels [9], [10]. A comprehensive study of convolutional codes with the largest possible column distances was presented in [11].…”

Section: Introductionmentioning

confidence: 99%