On the Local Erasure Correction Capacity of Convolutional Codes

Ivanov, Fedor; Kreshchuk, Alexey; Zyablov, Victor

doi:10.23919/isita.2018.8664288

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…Binary tail-biting convolutional codes were proposed as LRCs in [7], [38], but sliding-window repair was not considered. Locality properties of more general (but still binary) convolutional codes were recently considered in [14]. However, LRCCs and sliding-window repair as considered in this work were not treated in [14].…”

Section: Main Contributionsmentioning

confidence: 99%

Locally Repairable Convolutional Codes with Sliding Window Repair

Martínez-Peñas

Napp

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, ∂ − 1 erasures per local group), and sliding-window global repair, which can correct erasure patterns with up to d c j −1 erasures in every window of j + 1 consecutive blocks of n nodes, where d c j is the jth column distance of the code. The parameter j can be adjusted, for a fixed LRCC, according to different catastrophic erasure patterns, requiring only to contact n(j + 1) − d c j +1 nodes, plus less than µn other nodes, in the storage system, where µ is the memory of the code. A Singleton-type bound is provided for d c j . If it attains such a bound, an LRCC can correct the same number of catastrophic erasures in a window of length n(j + 1) as an optimal locally repairable block code of the same rate and locality, and with block length n(j + 1). In addition, the LRCC is able to perform the flexible and somehow local sliding-window repair by adjusting j. Furthermore, by adjusting and/or sliding the window, the LRCC can potentially correct more erasures in the original window of n(j+1) nodes than an optimal locally repairable block code of the same rate and locality, and length n(j+1). Finally, the concept of partial maximum distance profile (partial MDP) codes is introduced. Partial MDP codes can correct all informationtheoretically correctable erasure patterns for a given locality, local distance and information rate. An explicit construction of partial MDP codes whose column distances attain the provided Singleton-type bound, up to certain parameter j = L, is obtained based on known maximum sum-rank distance convolutional codes.

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Section: Main Contributionsmentioning

confidence: 99%

Locally Repairable Convolutional Codes with Sliding Window Repair

Martínez-Peñas

Napp

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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“…Binary tail-biting convolutional codes were proposed as LRCs in [7,36], but sliding-window repair was not considered. Locality properties of more general (but still binary) convolutional codes were recently considered in [14]. However, LRCCs and sliding-window repair as considered in this work were not treated in [14].…”

Section: Introductionmentioning

confidence: 99%

“…Locality properties of more general (but still binary) convolutional codes were recently considered in [14]. However, LRCCs and sliding-window repair as considered in this work were not treated in [14]. Rateless streaming codes (e.g.…”

Section: Introductionmentioning

confidence: 99%

Locally Repairable Convolutional Codes With Sliding Window Repair

Martínez-Peñas

Napp

2020

IEEE Trans. Inform. Theory

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Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, ∂ −1 erasures per local group), and sliding-window global repair, which can correct erasure patterns with up to d c j −1 erasures in every window of j + 1 consecutive blocks of n nodes, where d c j is the jth column distance of the code. The parameter j can be adjusted, for a fixed LRCC, according to different catastrophic erasure patterns, requiring only to contact n(j + 1) − d c j +1 nodes, plus less than µn other nodes, in the storage system, where µ is the memory of the code. A Singleton-type bound is provided for d c j . If it attains such a bound, an LRCC can correct the same number of catastrophic erasures in a window of length n(j + 1) as an optimal locally repairable block code of the same rate and locality, and with block length n(j + 1). In addition, the LRCC is able to perform the flexible and somehow local sliding-window repair by adjusting j. Furthermore, by adjusting and/or sliding the window, the LRCC can potentially correct more erasures in the original window of n(j + 1) nodes than an optimal locally repairable block code of the same rate and locality, and length n(j + 1). Finally, the concept of partial maximum distance profile (partial MDP) codes is introduced. Partial MDP codes can correct all information-theoretically correctable erasure patterns for a given locality, local distance and information rate. An explicit construction of partial MDP codes whose column distances attain the provided Singleton-type bound, up to certain parameter j = L, is obtained based on known maximum sum-rank distance convolutional codes.

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