Capacity optimality of lattice codes in common message Gaussian broadcast channels with coded side information

Lakshmi Natarajan, Yi Hong, Emanuele Viterbo

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Lattices possess elegant mathematical properties which have been previously used in the literature to show that structured codes can be efficient in a variety of communication scenarios. We consider the family of single-transmitter multiple-receiver Gaussian channels where the source transmits a set of common messages to all the receivers (multicast scenario), and each receiver has coded side information, i.e., prior information in the form of linear combinations of the messages. This channel model is motivated by applications to multi-terminal networks where the nodes may have access to coded versions of the messages from previous signal hops or through orthogonal channels. The capacity of this channel is known and follows from the work of Tuncel (2006), which is based on random coding arguments. In this paper, following the approach introduced by Erez and Zamir, we show that lattice codes are capacity-optimal for this family of channels. The structured coding scheme proposed in this paper is derived from Construction A lattices designed over prime fields, and utilizes algebraic binning at the decoders to expurgate the channel code and obtain good lattice subcodes, for every possible set of linear combinations available as side information.
Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory (ISIT 2017)
EditorsMartin Bossert, Stephen Hanly, Stephan ten Brink, Sennur Ulukus
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages5
ISBN (Electronic)9781509040964
ISBN (Print)9781509040971
Publication statusPublished - 2017
EventIEEE International Symposium on Information Theory 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017 (Proceedings)


ConferenceIEEE International Symposium on Information Theory 2017
Abbreviated titleISIT 2017
Internet address


  • Lattices
  • Receivers
  • Linear codes
  • AWGN channels
  • Channel models
  • Decoding

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