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On Maximally Recoverable Codes for Product Topologies

Shivakrishna, D and Rameshwar, Arvind V and Lalitha, V and Sasidharan, Birenjith (2018) On Maximally Recoverable Codes for Product Topologies. In: 2018 Twenty Fourth National Conference On Communications (NCC), FEB 25-28, 2018, Hyderabad, INDIA.

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Given a topology of local parity-check constraints, a maximally recoverable code (MRC) can correct all erasure patterns that are information-theoretically correctable. In a grid-like topology, there are a local constraints in every column forming a column code, b local constraints in every row forming a row code, and h global constraints in an (m x n) grid of codeword. Recently, Gopalan et al. initiated the study of MRCs under grid-like topology, and derived a necessary and sufficient condition, termed as the regularity condition, for an erasure pattern to be recoverable when a = 1; h = 0. In this paper, we consider MRCs for product topology (h = 0). First, we construct a certain bipartite graph based on the erasure pattern satisfying the regularity condition for product topology (any a; b, h = 0) and show that there exists a complete matching in this graph. We then present an alternate direct proof of the sufficient condition when a = 1; h = 0. We later extend our technique to study the topology for a = 2; h = 0, and characterize a subset of recoverable erasure patterns in that case. For both a = 1; 2, our method of proof is uniform, i.e., by constructing tensor product G(col) circle times G(row) of generator matrices of column and row codes such that certain square sub-matrices retain full rank. The full-rank condition is proved by resorting to the matching identified earlier and also another set of matchings in erasure sub-patterns.

Item Type: Conference Proceedings
Additional Information: 24th National Conference on Communications (NCC), Hyderabad, INDIA, FEB 25-28, 2018
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 11 Mar 2019 10:38
Last Modified: 11 Mar 2019 10:38
URI: http://eprints.iisc.ac.in/id/eprint/61975

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