Lattice Index Codes From Algebraic Number Fields

Yu-Chih Huang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Broadcasting K independent messages to multiple users where each user demands all the messages and already has a subset of the messages as side information is studied. Recently, Natarajan et al. proposed a novel broadcasting strategy called lattice index coding, which adopts lattices constructed over some principal ideal domains (PID) for transmission. Using the structure of lattices over PID, they showed that this scheme provides uniform side information gain for any side information configuration, a desired property which essentially guarantees a fair signal-to-noise ratio gain when normalized by the amount of information contained in side information. In this paper, we generalize this strategy to a general ring of algebraic integers, which may not be a PID. Upper and lower bounds on the side information gains for the proposed scheme constructed over some interesting classes of number fields are provided and are shown to coincide asymptotically in message rate. This generalization substantially enlarges the design space and partially includes the scheme by Natarajan et al. as a special case. Perhaps more importantly, in addition to side information gains, the proposed lattice index codes benefit from diversity gains inherent in constellations carved from number fields when used over Rayleigh fading channel. Some interesting examples are provided for which the proposed scheme allows the messages to be from the same field.

Original languageEnglish
Pages (from-to)2098-2112
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2017
EventIEEE International Symposium on Information Theory (ISIT) - , Hong Kong
Duration: 14 Jun 201519 Jun 2015


  • Lattice codes
  • index coding
  • broadcast channels
  • side information

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