Cognitive Interference Channels with Confidential Messages

The cognitive interference channel with confidential messages is studied. Similarly to the classical two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at the two receivers. It is assumed that there is a common message source (message 1) known to both transmitters, and an additional independent message source (message 2) known only to the cognitive transmitter (transmitter 2). The cognitive receiver (receiver 2) needs to decode both messages, while the non-cognitive receiver (receiver 1) should decode only the common message. Furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. The level of secrecy is measured by the equivocation rate. A single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is established and is further explicitly derived for the Gaussian case. Moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, establishes a new capacity theorem for a class of interference channels, by providing a converse theorem.

💡 Research Summary

This paper studies a cognitive interference channel (CIC) in which two transmitters interfere at two receivers, but the information structure is enriched by a common message and a confidential message. Both transmitters know a common message (W_{1}) that must be decoded by both receivers. In addition, only the cognitive transmitter (transmitter 2) knows an independent confidential message (W_{2}). Receiver 2 (the cognitive receiver) must decode both (W_{1}) and (W_{2}), while receiver 1 (the non‑cognitive receiver) is required to decode only (W_{1}). The confidentiality of (W_{2}) is measured by the equivocation rate (R_{e}= \frac{1}{n}H(W_{2}|Y_{1}^{n})); perfect secrecy corresponds to (R_{e}=R_{2}), where (R_{2}) is the transmission rate of the confidential message.

The authors first derive a single‑letter characterization of the capacity‑equivocation region (\mathcal{C}) for the discrete memoryless version of this channel. The region is expressed as a union over auxiliary random variables (U) and (V) that represent, respectively, the code layer for the common message and the code layer for the confidential message. The constraints are: \