Fundamental Limits of Communications in Interference Networks-Part I: Basic Structures

In these series of multi-part papers, a systematic study of fundamental limits of communications in interference networks is established. Here, interference network is referred to as a general single-hop communication scenario with arbitrary number of transmitters and receivers, and also arbitrary distribution of messages among transmitters and receivers. It is shown that the information flow in such networks follows similar derivations from many aspects. This systematic study is launched by considering the basic building blocks in Part I. The Multiple Access Channel (MAC), the Broadcast Channel (BC), the Classical Interference Channel (CIC) and the Cognitive Radio Channel (CRC) are proposed as the main building blocks for all interference networks. First, a brief review of existing results regarding these basic structures is presented. New observations are also presented in this regard. Specifically, it is shown that the well-known strong interference conditions for the two-user CIC do not change if the inputs are dependent. Next, new capacity outer bounds are established for the basic structures with two receivers. These outer bounds are all derived based on a unified framework. By using the derived outer bounds, some new capacity results are proved for the CIC and the CRC; a mixed interference regime is identified for the two-user CIC where the sum-rate capacity is established. This result contains the previously obtained result regarding the Gaussian mixed interference channel as a special case. Also, a noisy interference regime is derived for the one-sided CIC in which treating interference as noise is sum-rate optimal. For the CRC, a full characterization of the capacity region for a class of more-capable channels is obtained. Moreover, it is shown that the derived outer bounds are useful to study the channels with one-sided receiver side information wherein one of the receivers has access to the non-intended message; capacity bounds are also discussed in details for such scenarios. Our results lead to new insights regarding the nature of information flow in these basic interference networks.