Negligible Cooperation: Contrasting the Maximal- And Average-Error Cases

Parham Noorzad, Michael Langberg, Michelle Effros

Research output: Contribution to journalArticlepeer-review


In communication networks, cooperative strategies are coding schemes where network nodes work together to improve performance metrics such as the total rate delivered across the network. This work studies encoder cooperation in the setting of a discrete multiple access channel (MAC) with two encoders and a single decoder. A network node, here called the cooperation facilitator (CF), that is connected to both encoders via rate-limited links, enables the cooperation strategy. Previous work by the authors presents two classes of MACs: (i) one class where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero, and (ii) a second class of MACs where the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work contrasts the power of the CF in the maximal- and average-error cases, showing that a constant number of bits communicated over the CF output link can yield a positive gain in the maximal-error sum-capacity, while a far greater number of bits, even a number that grows sublinearly in the blocklength, can never yield a non-negligible gain in the average-error sum-capacity.

Original languageEnglish
Article number9469892
Pages (from-to)5885-5902
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - Sep 2021
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received November 23, 2019; revised June 5, 2021; accepted June 16, 2021. Date of publication July 1, 2021; date of current version August 25, 2021. This work was supported by the National Science Foundation under Grant 1527524 and Grant 1526771. This article was presented in part at the 2016 IEEE Globecom Workshops and the 2018 IEEE International Symposium Information Theory. (Corresponding author: Parham Noorzad.) Parham Noorzad was with the California Institute of Technology, Pasadena, CA 91125 USA. He is now with Qualcomm Technologies, Inc., San Diego, CA 92121 USA (e-mail:

Publisher Copyright:
© 1963-2012 IEEE.


  • Capacity region continuity
  • cooperation facilitator
  • edge removal problem
  • maximal-error capacity region
  • multiple access channel


Dive into the research topics of 'Negligible Cooperation: Contrasting the Maximal- And Average-Error Cases'. Together they form a unique fingerprint.

Cite this