Achievability Performance Bounds for Integer-Forcing Source Coding

Elad Domanovitz, Uri Erez

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result modulo a coarse lattice. 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. It has been observed that the method works very well for 'most' but not all source covariance matrices. The present work quantifies the measure of bad covariance matrices by studying the probability that integer-forcing source coding fails as a function of the allocated rate, where the probability is with respect to a random orthonormal transformation that is applied to the sources prior to quantization. For the important case where the signals to be compressed correspond to the antenna inputs of relays in an i.i.d. Rayleigh fading environment, this orthonormal transformation can be viewed as being performed by nature. The scheme is also studied in the context of a non-distributed system. Here, the goal is to arrive at a universal, yet practical, compression method using equal-rate quantizers with provable performance guarantees. The scheme is universal in the sense that the covariance matrix need only be learned at the decoder but not at the encoder. The goal is accomplished by replacing the random orthonormal transformation by transformations corresponding to number-Theoretic space-Time codes.

Original languageEnglish
Article number8889700
Pages (from-to)1482-1496
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - Mar 2020


FundersFunder number
Heron consortium
Israel Ministry of Economy and Industry
Israel Science Foundation1956/17


    • Distributed compression
    • integer forcing
    • unitary precoding


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