Outage Behavior of Integer Forcing with Random Unitary Pre-Processing

Elad Domanovitz, Uri Erez

Research output: Contribution to journalArticlepeer-review


Integer forcing is an equalization scheme for the multiple-input multiple-output communication channel that has been demonstrated to allow operating close to capacity for 'most' channels. In this paper, the measure of 'bad' channels is quantified by considering a compound channel setting, where the transmitter communicates over a fixed channel but knows only its mutual information. The transmitter encodes the data into independent streams, all taken from the same linear code. The coded streams are transmitted after applying a unitary transformation. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. Considering pre-processing matrices drawn from a random ensemble, outage corresponds to the event that the target rate exceeds the achievable rate of integer forcing for a given channel matrix. For the case of the circular unitary ensemble, an explicit universal bound on the outage probability for a given target rate is derived that holds for any channel in the compound class. The derived bound depends only on the gap-to-capacity and the number of transmit antennas. The results are also applied to obtain universal bounds on the gap-to-capacity of multiple-antenna closed-loop multicast, achievable via linear pre-processed integer forcing.

Original languageEnglish
Pages (from-to)2774-2790
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2018


  • Integer forcing
  • MIMO communication
  • unitary precoding

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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