Capacity bounds for the Gaussian X channel

Prasad, R. ; Chockalingam, A. (2013) Capacity bounds for the Gaussian X channel In: 2013 Information Theory and Applications Workshop (ITA), 10-15 February 2013, San Diego, USA.

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Official URL: http://ieeexplore.ieee.org/document/6502928/

Related URL: http://dx.doi.org/10.1109/ITA.2013.6502928

Abstract

We consider bounds for the capacity region of the Gaussian X channel (XC), a system consisting of two transmit-receive pairs, where each transmitter communicates with both the receivers. We first classify the XC into two classes, the strong XC and the mixed XC. In the strong XC, either the direct channels are stronger than the cross channels or vice-versa, whereas in the mixed XC, one of the direct channels is stronger than the corresponding cross channel and vice-versa. After this classification, we give outer bounds on the capacity region for each of the two classes. This is based on the idea that when one of the messages is eliminated from the XC, the rate region of the remaining three messages are enlarged. We make use of the Z channel, a system obtained by eliminating one message and its corresponding channel from the X channel, to bound the rate region of the remaining messages. The outer bound to the rate region of the remaining messages defines a subspace in R4+ and forms an outer bound to the capacity region of the XC. Thus, the outer bound to the capacity region of the XC is obtained as the intersection of the outer bounds to the four combinations of the rate triplets of the XC. Using these outer bounds on the capacity region of the XC, we derive new sum-rate outer bounds for both strong and mixed Gaussian XCs and compare them with those existing in literature. We show that the sum-rate outer bound for strong XC gives the sum-rate capacity in three out of the four sub-regions of the strong Gaussian XC capacity region. In case of mixed Gaussian XC, we recover the recent results in [11] which showed that the sum-rate capacity is achieved in two out of the three sub-regions of the mixed XC capacity region and give a simple alternate proof of the same.

Item Type:Conference or Workshop Item (Paper)
Source:Copyright of this article belongs to Institute of Electrical and Electronics Engineers.
Keywords:Sum Capacity; Capacity Region; X Channel; Interference Channel
ID Code:102201
Deposited On:24 Mar 2017 11:10
Last Modified:24 Mar 2017 11:10

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