TY - JOUR

T1 - Achievability Performance Bounds for Integer-Forcing Source Coding

AU - Domanovitz, Elad

AU - Erez, Uri

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

KW - Distributed compression

KW - integer forcing

KW - unitary precoding

UR - http://www.scopus.com/inward/record.url?scp=85081047361&partnerID=8YFLogxK

U2 - 10.1109/TIT.2019.2950931

DO - 10.1109/TIT.2019.2950931

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AN - SCOPUS:85081047361

SN - 0018-9448

VL - 66

SP - 1482

EP - 1496

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

M1 - 8889700

ER -