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Lattices and Index Coding

This chapter was written in collaboration with Lakshmi Natarajan (IIT Hyderabad, India) and Yi Hong (Monash University, Australia)

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Lattices Applied to Coding for Reliable and Secure Communications

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

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Abstract

A wireless channel is characterized by its broadcast nature: a signal transmitted by a source is received not only by the intended recipient but also by all the terminals within the transmission range. This can create a scenario where a passive listener becomes aware of the message originally intended for another node in the broadcast network, while the intended recipient himself is yet to receive the message packet successfully. This might occur, for example, if the main recipient is out of transmission range or if the packet is lost due to fading or channel noise, while the channel gain at the passive listener is strong enough for decoding to be successful. As a result, we have a broadcast channel where the source is required to transmit a finite set of messages intended to be delivered to finitely many receivers, each receiver desires to decode a subset of the transmitted messages while having prior knowledge of the values of a different subset of messages. This prior knowledge at the receivers, called side information , can arise when receivers overhear the previous transmissions as information propagates through a communication network in multiple hops or through multiple rounds of transmission.

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Authors and Affiliations

  1. Institute of Mathematics, Statistics and Computer Science, University of Campinas, Campinas, São Paulo, Brazil

    Sueli I. R. Costa

  2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Frédérique Oggier

  3. Department of Electrical and Electronic Engineering, Imperial College London, London, UK

    Antonio Campello

  4. Communications and Electronics Department, Télécom ParisTech, Paris, France

    Jean-Claude Belfiore

  5. Department of Electrical and Computer Systems Engineering, Monash University, Clayton, VIC, Australia

    Emanuele Viterbo

Authors
  1. Sueli I. R. Costa
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  2. Frédérique Oggier
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  3. Antonio Campello
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  4. Jean-Claude Belfiore
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  5. Emanuele Viterbo
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Costa, S.I.R., Oggier, F., Campello, A., Belfiore, JC., Viterbo, E. (2017). Lattices and Index Coding. In: Lattices Applied to Coding for Reliable and Secure Communications. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67882-5_6

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