Capacity bounds for the Gaussian Interference Channel

Abstract

The capacity region of the two-user Gaussian Interference Channel (IC) is studied. Three classes of channels are considered: weak, one-sided, and mixed Gaussian ICs. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The channel sum capacity for some certain range of the channel parameters is derived. It is shown that when Gaussian codebooks are used, the full Han-Kobayashi achievable rate region can be obtained by using the naive Han-Kobayashi achievable scheme over three frequency bands (equivalently, three subspaces). For the one-sided Gaussian IC, a new proof for Sato's outer bound is presented. We derive the full Han-Kobayashi achievable rate region when Gaussian code books are utilized. For the mixed Gaussian IC, a new outer bound is obtained that again outperforms previously known outer bounds. For this case, the channel sum capacity for all ranges of parameters is derived. It is proved that the full Han-Kobayashi achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of the channel gains.

A View of Information-Estimation Relations in Gaussian Networks

“…Treating interference as noise with Gaussian codebooks has been shown to be sum-capacity optimal in the so called very-weak interference regime [71][72][73]. 2.…”

“…Unfortunately, the capacity expression in (49) is considered "uncomputable" in the sense that we do not know how to explicitly characterize the input distributions that attain its convex closure. Moreover, it is not clear whether there exists an equivalent single-letter form for (49) Because of "uncomputability" the capacity expression in (49) has received little attention, except for the following: in [79] the limiting expression was used to show that limiting to jointly Gaussian distributions in suboptimal; in [72] the limiting expression was used to derive the sum-capacity in the very weak interference regime; and in [90] it was shown that in the high-power regime the limiting expression normalized by the point-to-point capacity (i.e., the degrees of freedom (DoF)) can be single letterized.…”

“…In [71][72][73] it was shown that i.i.d. Gaussian inputs maximize the sum-capacity in (49) for inr snr (1 + inr) ≤ 1 2 in the symmetric case.…”

“…The extremal entropy inequality of [106], inspired by the channel enhancement method [107], was instrumental in showing several information theoretic converses in problems such as the MIMO wiretap channel [108], two-user Gaussian interference channel [71][72][73], and cognitive interference channel [109] to name a few. In view of the successful applications of the I-MMSE relationship to prove EPI type inequalities (e.g., [35,36,38,102]), it would be interesting to see if the extremal inequality presented in [106] can be shown via estimation theoretic arguments.…”

Efficient computation of the pareto boundary for the two-user MISO interference channel with multi-user decoding capable receivers

“…The maximum achievable rate R dn 2 (w 1 , w 2 ) is the minimum of the right-hand sides of (5) and (6). For link 2, we note that the maximum achievable rate does not necessarily exploit the signal-to-interference-plus-noise (SINR) ratio at RX 2 to the full extent.…”