Distributed structure: Joint expurgation for the multiple-access channel

Eli Haim*, Yuval Kochman, Uri Erez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper, we obtain an improved lower bound on the error exponent of the memoryless multiple-access channel via the use of linear codes, thus demonstrating that structure can be beneficial even when capacity may be achieved via random codes. We show that if the multiple-access channel is additive over a finite field, then any error probability, and hence any error exponent, achievable by a linear code for the associated single-user channel, is also achievable for the multiple-access channel. In particular, linear codes allow to attain joint expurgation, and hence, attain the single-user expurgated exponent of the single-user channel, whenever the latter is achieved by a uniform distribution. Thus, for additive channels, at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used for at most one of the users. Even when the multiple-access channel is not additive, it may be transformed into such a channel. While the transformation is information-lossy, we show that the distributed structure gain in some 'nearly additive' cases outweighs the loss. Finally, we apply a similar approach to the Gaussian multiple-access channel. While we believe that due to the power constraints, it is impossible to attain the single-user error exponent, we do obtain an improvement over the best known achievable error exponent, given by Gallager, for certain parameters. This is accomplished using a nested lattice triplet with judiciously chosen parameters.

Original languageAmerican English
Article number7374734
Pages (from-to)5-20
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2017

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Error exponents
  • expurgation
  • linear codes
  • multiple access channels
  • structured codes


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