Ruchen Duan

Bounds and Capacity Theorems for Cognitive Interference Channels With State

A class of cognitive interference channels with state are investigated, in which a primary transmitter sends a message to two receivers (receivers 1 and 2) with assistance of a cognitive transmitter (that knows the primary transmitters message), and the cognitive transmitter also sends a separate message to receiver 2. The channel is corrupted by an independent and identically distributed state sequence. The scenario, in which the state sequence is noncausally known at both the cognitive transmitter and receiver 2, is first studied. The capacity region is obtained for both the discrete memoryless and Gaussian channels. The second scenario, in which the state sequence is noncausally known only at the cognitive transmitter, is further studied. Inner and outer bounds on the capacity region are obtained for the discrete memoryless channel and its degraded version. The capacity region is characterized for the degraded semideterministic channel and for 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 boundaries of the capacity region are characterized. The full capacity region is also characterized for channels that satisfy certain conditions. It is shown that certain Gaussian channels achieve the capacity of the same channels with state noncausally known at both the cognitive transmitter and receiver 2.

On the capacity region of Gaussian interference channels with state

The Gaussian interference channel with additive state at two receivers is investigated, in which the state information is noncausally known at both transmitters but not known at either receiver. For the very strong Gaussian interference channel with state, the capacity region is obtained under certain conditions on channel parameters. For the strong (but not very strong) Gaussian interference channel with state, points on the boundary of the capacity region are characterized under corresponding conditions on channel parameters. Finally, for the weak Gaussian interference channel with state, the sum capacity is obtained for certain channel parameters. All the above capacity-achieving rate points achieve the capacity for the corresponding channel without state.

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

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 1s 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.

Gaussian cognitive interference channels with state

A Gaussian cognitive interference channel model with state is investigated, in which transmitters 1 and 2 communicate with receivers 1 and 2 via an interference channel. The two transmitters jointly send one message to receivers 1 and 2, and transmitter 2 also sends a separate message to receiver 2. The channel outputs at the two receivers are corrupted by an independent and identically distributed (i.i.d.) Gaussian state sequences and Gaussian noise variables. The state sequence is noncausally known at transmitter 2 only. The Gaussian channels are partitioned into two classes based on channel parameters. For each class, inner and outer bounds on the capacity region are derived, and either the partial boundary of the capacity region or capacity region is characterized for all Gaussian channels. The cognitive interference channel with state known at both transmitter 2 and receiver 2 is further studied, and the capacity region is established for a class of such channels. It is also shown that this capacity can be achieved by certain Gaussian channels with state noncausally known only at transmitter 2.

Capacity bounds for a class of cognitive interference channels with state

A class of cognitive interference channels with non-causal state information is investigated, in which two transmitters (i.e., transmitters 1 and 2) communicate with two receivers (i.e., receivers 1 and 2) via an interference channel. The two transmitters jointly send one message to receivers 1 and 2, 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, which is noncausally known at transmitter 2 only. For the general discrete memoryless channel, inner and outer bounds on the capacity region are obtained. Bounds on degraded channels are also derived. In particular, the capacity region is established for the semideterministic degraded channel. Furthermore, for the case when the state information is also known at receiver 2, inner and outer bounds on the capacity region are obtained, and the capacity region is established for the degraded channel of this case.

Capacity Characterization for State-Dependent Gaussian Channel With a Helper

The state-dependent point-to-point Gaussian channel with a helper is first studied, in which a transmitter communicates with a receiver via a state-corrupted channel. The state is not known to the transmitter nor to the receiver, but known to a helper noncausally, which then wishes to assist the receiver to cancel the state. Differently from the previous work that characterized the capacity only in the infinite state power regime, this paper explores the general case with arbitrary state power. A lower bound on the capacity is derived based on an achievable scheme that integrates direct state subtraction and single-bin dirty paper coding. By analyzing this lower bound and further comparing it with the existing upper bounds, the capacity of the channel is characterized for a wide range of channel parameters. Such an idea of characterizing the capacity is further extended to study the two-user state-dependent multiple access channel with a helper. By comparing the derived inner and outer bounds, the channel parameters are partitioned into appropriate cases, and for each case, either segments on the capacity region boundary or the full capacity region are characterized.

State-Dependent Parallel Gaussian Networks With a Common State-Cognitive Helper

State-dependent parallel networks with a common state-cognitive helper is studied, in which K transmitters wish to send K messages to their corresponding receivers over K state-corrupted parallel channels, and a helper who knows the state information noncausally wishes to assist these receivers to cancel state interference. Furthermore, the helper also has its own message to be sent simultaneously to its corresponding receiver. Since the state information is known only to the helper, but not to other transmitters, transmitter-side state cognition and receiver-side state interference are mismatched. Our focus is on the high state power regime, i.e., the state power goes to infinity. Three (sub)models are studied. Model I serves as a basic model, which consists of only one transmitter-receiver (with state corruption) pair in addition to a helper that assists the receiver to cancel state in addition to transmitting its own message. Model II consists of two transmitter-receiver pairs in addition to a helper, and only one receiver is interfered by a state sequence. Model III generalizes model I to include multiple transmitter- receiver pairs with each receiver corrupted by independent state. For all models, the inner and outer bounds on the capacity region are derived, and comparison of the two bounds yields characterization of either full or partial boundary of the capacity region under various channel parameters.

State-Dependent Gaussian Interference Channels: Can State Be Fully Canceled?

The state-dependent Gaussian interference channel (IC) and Z-IC are investigated, in which two receivers are corrupted by the same but differently scaled states. The state sequence is noncausally known at both transmitters, but not known at either receiver. Three interference regimes are studied, i.e., the very strong, strong, and weak regimes. In the very strong regime, the capacity region is characterized under certain channel parameters by designing a cooperative dirty paper coding between the two transmitters to fully cancel the state. In the strong regime, points on the capacity region boundary are characterized under certain channel parameters by designing an achievable scheme based on rate splitting, layered dirty paper coding, and successive state cancellation. In the weak regime, the sum capacity is obtained by independent dirty paper coding at two transmitters. For all the above regimes, the capacity achieves that of the IC/Z-IC without state. Comparison between the state-dependent regular IC and the Z-IC suggests that even with one interference-free link, the Z-IC does not necessarily perform better, because dirty paper coded interference in the regular IC facilitates to cancel the state through the cooperative dirty paper coding between the transmitters.

State-dependent parallel Gaussian channels with a common helper in high power regime

The state-dependent parallel Gaussian channel with a common helper is investigated, in which transmitters 1 and 2 transmit two messages respectively to receivers 1 and 2 over the parallel channel. Furthermore, both parallel subchannels can be corrupted by independent state sequences, respectively, which are unknown to both transmitters and receivers. There is a common helper that knows the states noncausally and assists communication between transmitters and receivers. Our focus is on the high state power regime, i.e., the state power goes to infinity. Two Gaussian models are studied with model I having only receiver 1 interfered by the state and with model II having both receivers interfered by independent states. Each model has its unique challenge to address. For both models, inner and outer bounds on the capacity region are derived, and comparison of the two bounds leads to capacity results under certain channel parameters.

Dirty interference cancellation for Gaussian broadcast channels.

The state-dependent broadcast channel with a helper is investigated, in which a transmitter wishes to send messages to two receivers via a broadcast channel. The channel is corrupted by an independent and identically distributed (i.i.d.) state sequence which is known to neither the transmitter nor the receivers. A helper that knows the state sequence noncausally assists the broadcast transmission to cancel state interference. Two scenarios are studied. In scenario 1, the transmitter sends one message to both receivers, and in scenario II, the transmitter sends two private messages respectively to two receivers. Our focus is on the Gaussian channel with additive state. Inner and outer bounds are derived for both scenarios. By comparing the inner and outer bounds, capacity/capacity region are characterized under various ranges of channel parameters. Practical impact of the model and results are discussed.