Bounds and Capacity Theorems for Cognitive Interference Channels With State

Abstract

A class of cognitive interference channel with state is investigated, in which two transmitters (transmitters 1 and 2) communicate with two receivers (receivers 1 and 2) over an interference channel. The two transmitters jointly transmit a common message to the two receivers, and transmitter 2 also sends a separate message to receiver 2. The channel is corrupted by an independent and identically distributed (i.i.d.) state sequence. The scenario in which the state sequence is noncausally known only at transmitter 2 is first studied. For the discrete memoryless channel and its degraded version, inner and outer bounds on the capacity region are obtained. The capacity region is characterized for the degraded semideterministic channel and channels that satisfy a less noisy condition. The Gaussian channels are further studied, which are partitioned into two cases based on how the interference compares with the signal at receiver 1. For each case, inner and outer bounds on the capacity region are derived, and partial boundary of the capacity region is characterized. The full capacity region is characterized for channels that satisfy certain conditions. The second scenario in which the state sequence is noncausally known at both transmitter 2 and receiver 2 is further studied. The capacity region is obtained for both the discrete memoryless and Gaussian channels. It is also shown that this capacity is achieved by certain Gaussian channels with state noncausally known only at transmitter 2.

On the capacity of state-dependent Gaussian cognitive interference channel

“…state sequence. We investigate the asymmetric cognitive scenario, as [15,16], where the state is non-causally known at transmitter 2 and is unknown at transmitter 1 and at the receivers. The system model is depicted in Figure 1.…”

“…In [16], by using random coding, two inner bounds for the G-CICS are provided when |a| ≤ 1. By evaluating the inner bound 1 of Proposition 3 in [16] and replacing S → aS, b → a, c → 1 a , we can see that this inner bound when the channel gain tends to zero vanishes, and thus, we cannot achieve any positive rate region by such scheme. The following theorem presents the second inner bound.…”

“…The common message known to both transmitters, i.e., message 1, needs to be decoded at both receivers instead of at receiver 1 only. This model is investigated in [16], in which by using superposition coding, rate splitting, and Gelfand-Pinsker binning scheme, inner bounds are established. It is shown that the inner bounds are coincided with the outer bounds for a degraded semi-deterministic channel and channels that satisfy a less noisy condition.…”

“…All achievable rate regions in [16] are based on random coding. In this paper, we use the lattice-based coding scheme (especially lattice alignment) to establish capacity regions for this channel.…”

Nested lattice codes for the state-dependent Gaussian interference channel with a common message

“…In [3], [4], a model of cognitive state-dependent interference channels is studied, in which one of the transmitters, knows both messages and also the states of the channel in a non-causal manner while the other transmitter knows only one of the messages and does not know the channel states. In the considered model in [4], the common message known to both transmitters needs to be decoded at both receivers while at the considered model in [3], each receiver only decodes the desired message.…”