A Discrete Polymatroidal Framework for Differential Error-Correcting Index Codes

Thomas, Anoop and Rajan, B Sundar (2019) A Discrete Polymatroidal Framework for Differential Error-Correcting Index Codes. In: IEEE TRANSACTIONS ON COMMUNICATIONS, 67 (7). pp. 4593-4604.

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Abstract

In the conventional index coding problem, the messages transmitted by the source to satisfy the demands of the receivers are error-free. However, in practice, the messages may be error prone which led to the introduction of error-correcting index codes. An error-correcting index code is an encoding scheme which enables every receiver to decode its demanded message even in the presence of certain number of transmission errors. Formally, an index code capable of correcting at most delta errors at all its receivers is defined as a delta-error-correcting index code. In this paper, we explore the connections between vector linear error-correcting index codes and discrete polymatroids. This is motivated from the connections between linear network error-correcting codes and matroids. It is shown that a vector linear error-correcting index code exists if and only if there exists a representable discrete polymatroid satisfying certain conditions. Differential error-correcting index codes which allow different receivers to have different error-correcting capabilities are also studied. Note that the delta-error-correcting code is a special case of a differential error-correcting index code. Error correction at a subset of receivers is another special case which is discussed.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON COMMUNICATIONS
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	copyright for this article belongs to IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Keywords:	Index coding; error correction; matroids; polymatroids
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	03 Sep 2019 09:22
Last Modified:	03 Sep 2019 09:22
URI:	http://eprints.iisc.ac.in/id/eprint/63429

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