Network Coding Based on Byte-wise Circular Shift and Integer Addition

Shum, Wai‐Ting; Hou, Hanxu

doi:10.1109/isit44484.2020.9174327

Cited by 5 publications

(2 citation statements)

References 15 publications

(15 reference statements)

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“…Example 2. Shum and Hou [14] designed an array code for distributed storage across 6 disks such that the original data can be recovered from any 4 disks. In the context of network coding, this is a code for the 6 4 combination network [17].…”

Section: A Network Modelmentioning

confidence: 99%

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Permute & Add Network Codes via Group Algebras

Natarajan¹,

Joy²

2021

Preprint

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A class of network codes have been proposed in the literature where the symbols transmitted on network edges are binary vectors and the coding operation performed in network nodes consists of the application of (possibly several) permutations on each incoming vector and XOR-ing the results to obtain the outgoing vector. These network codes, which we will refer to as permute-and-add network codes, involve simpler operations and are known to provide lower complexity solutions than scalar linear codes. The complexity of these codes is determined by their degree which is the number of permutations applied on each incoming vector to compute an outgoing vector. Constructions of permute-and-add network codes for multicast networks are known. In this paper, we provide a new framework based on group algebras to design permute-and-add network codes for arbitrary (not necessarily multicast) networks. Our framework allows the use of any finite group of permutations (including circular shifts, proposed in prior work) and admits a trade-off between coding rate and the degree of the code. Further, our technique permits elegant recovery and generalizations of the key results on permute-and-add network codes known in the literature.

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Section: A Network Modelmentioning

confidence: 99%

“…Circular-shift network codes were designed in [11]- [13] for multicast networks by lifting scalar linear network codes. A similar code over 256 was designed in [14]. Note that all prior work on permute-and-add network codes [7]- [13] propose solutions for multicast networks only.…”

Section: Introductionmentioning

confidence: 99%