Outage probability bounds for integer-forcing source coding

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 the 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 rate allocated in excess of the Berger-Tung benchmark, where the probability is with respect to a random orthogonal 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 orthogonal transformation can be viewed as if it is performed by nature. Hence, the results provide performance guarantees for distributed source coding via integer forcing in this scenario.