Linear physical layer network coding for multihop wireless networks

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider linear network coding functions that can be employed at the relays in wireless physical layer network coding, applied to a general multi-hop network topology. We introduce a general model of such a network, and discuss the algebraic basis of linear functions, deriving conditions for unambiguous decodability of the source data at the destination. We consider the use of integer rings, integer fields, binary extension fields and the ring of binary matrices as potential algebraic constructs, and show that the ring constructs provide more flexibility. We use the two-way relay channel and a network containing two sources and two relays to illustrate the concept and to demonstrate the effect of fading of the wireless channels. We show the capacity benefits of the more flexible rings.

Original languageEnglish
Title of host publicationEuropean Signal Processing Conference
PublisherEuropean Signal Processing Conference, EUSIPCO
Number of pages5
ISBN (Print)9780992862619
Publication statusPublished - 2014
Event22nd European Signal Processing Conference, EUSIPCO 2014 - Lisbon, United Kingdom
Duration: 1 Sept 20145 Sept 2014


Conference22nd European Signal Processing Conference, EUSIPCO 2014
Country/TerritoryUnited Kingdom


  • linear algebra
  • Physical layer network coding (PNC)
  • rings

Cite this