Integer-Forcing Source Coding

Or Ordentlich*, Uri Erez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This paper applies the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure. All encoders use the same nested lattice codebook. Each encoder quantizes its observation using the fine lattice as a quantizer and reduces the result modulo the coarse lattice, which plays the role of binning. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. In general, the linear combinations have smaller average powers than the original signals. This allows to increase the density of the coarse lattice, which in turn translates to smaller compression rates. We also propose and analyze a one-shot version of IF source coding that is simple enough to potentially lead to a new design principle for analog-to-digital converters that can exploit spatial correlations between the sampled signals.

Original languageAmerican English
Article number7745894
Pages (from-to)1253-1269
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - Feb 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 IEEE.


  • Analog-to-Digital conversion
  • Distributed lossy compression
  • lattice codes
  • modulo-lattice additive noise channel
  • structured binning


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