State-dependent Gaussian Z-channel with mismatched side-information and interference

Abstract

A state-dependent Gaussian Z-interference channel model is investigated in the regime of high state power, in which transmitters 1 and 2 communicate with receivers 1 and 2, and only receiver 2 is interfered by transmitter 1's signal and a random state sequence. The state sequence is known noncausally only to transmitter 1, not to the corresponding transmitter 2. A layered coding scheme is designed for transmitter 1 to help interference cancelation at receiver 2 (using a cognitive dirty paper coding) and to transmit its own message to receiver 1. Inner and outer bounds are derived, and are further analyzed to characterize the boundary of the capacity region either fully or partially for all Gaussian channel parameters. Our results imply that the capacity region of such a channel with mismatched transmitter-side state cognition and receiver-side state interference is strictly less than that of the corresponding channel without state, which is in contrast to Costa type of dirty channels, for which dirty paper coding achieves the capacity of the corresponding channels without state.

Z-interference channel with side information at the transmitters

“…Here, (22) comes from (18) and the fact that X i , i = 1, 2, is a function of (S i , M i ) as well as the fact that {S 1 , S 2 , M 1 , M 2 } are mutually independent, (23) is due to the fact that the conditioning reduces entropy, (24) follows from (18) and these facts that the conditioning reduces entropy and X 2 = f 2 (S 2 , M 2 ), and finally (25) follows from the Cauchy-Schwarz inequality as well as the fact that the differential entropy is maximized by a Gaussian distribution for a fixed second moment. In addition, we can rewrite (22)-(25) as…”

“…Moreover, a state-dependent Gaussian ZIC with a mismatched receiver-side state interference and transmitter-side state cognition has been studied in Ref. [22], where a state that corrupts only the received signal at receiver 2 is known non-causally only at the transmitter 1 while the intended transmitter 2 is unaware of it, hence the problem investigated in the current work is completely different to the work done in Ref. [22].…”

On the capacity of state-dependent Gaussian cognitive interference channel

“…Therefore, by using time sharing between the two corner points, given in (14) and (27), we can achieve the following rate region:…”

“…For the very strong interference regime, as well as for the weak regime, the sum capacity is obtained under certain conditions on channel parameters [13]. In [14], a state-dependent Gaussian Z-interference channel model in the regime of high state power is investigated. By utilizing a layered coding scheme, inner and outer bounds on the capacity region are derived.…”

“…Similar to [14,36], we assume that the channel state has unbounded variance. This is referred to as a high state power regime.…”