Permute and Add Network Codes via Group Algebras

Natarajan, Lakshmi Prasad and Joy, Smiju Kodamthuruthil (2022) Permute and Add Network Codes via Group Algebras. IEEE Transactions on Communications, 70 (5). pp. 2951-2963. ISSN 0090-6778

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Abstract

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 network 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 works) 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. © 1972-2012 IEEE.

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IITH Creators:

IITH Creators	ORCiD
Natarajan, Lakshmi Prasad	http://orcid.org/0000-0003-1552-5240

Item Type:

Article

Additional Information:

The work of Lakshmi Prasad Natarajan was supported by the SERB-DST research grant MTR/2019/001454. An earlier version of this paper was presented in part at the 2021 IEEE International Symposium on Information Theory (ISIT 2021), Melbourne, Australia [DOI: 10.1109/ISIT45174.2021.9517898].

Uncontrolled Keywords:

Circular shifts; group algebra; network coding; permutations

Subjects:

Electrical Engineering
Mathematics > Algebra

Divisions:

Department of Electrical Engineering

Depositing User:

. LibTrainee 2021

Date Deposited:

28 Jun 2022 09:22

Last Modified:

29 Jun 2022 10:31