On deterministic linear network coded broadcast and its relation to matroid theory

Deterministic linear network coding (DLNC) is an important family of network coding techniques for wireless packet broadcast. In this paper, we show that DLNC is strongly related to and can be effectively studied using matroid theory without bridging index coding. We prove the equivalence between th...

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Bibliographic Details
Published in:2014 IEEE Information Theory Workshop (ITW 2014) pp. 536 - 540
Main Authors: Mingchao Yu, Sadeghi, Parastoo, Aboutorab, Neda
Format: Conference Proceeding
Language:English
Published: IEEE 01.11.2014
Subjects:
Decoding
Encoding
Graphics
Indexes
matroid representability
Network coding
Receivers
throughput
wireless broadcast
Wireless communication
ISSN:1662-9019
Online Access:Get full text
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Summary:Deterministic linear network coding (DLNC) is an important family of network coding techniques for wireless packet broadcast. In this paper, we show that DLNC is strongly related to and can be effectively studied using matroid theory without bridging index coding. We prove the equivalence between the DLNC solution and matrix matroid. We use this equivalence to study the performance limits of DLNC in terms of the number of transmissions and its dependence on the finite field size. Specifically, we derive the sufficient and necessary condition for the existence of perfect DLNC solutions and prove that such solutions may not exist over certain finite fields. We then show that identifying perfect solutions over any finite field is still an open problem in general. To fill this gap, we develop a heuristic algorithm which employs graphic matroids to find perfect DLNC solutions over any finite field. Numerical results show that its performance in terms of minimum number of transmissions is close to the lower bound, and is better than random linear network coding when the field size is not so large.
ISSN:1662-9019
DOI:10.1109/ITW.2014.6970889