Interference channel

The mathematical model for this channel is the following:

Interference channel model

where, for ${\displaystyle i\in \{1,2\}}$:

• ${\displaystyle W_{i}}$ is the message to be transmitted by user ${\displaystyle i}$;
• ${\displaystyle X_{i}}$ is the channel input symbol (${\displaystyle X_{i}^{n}}$ is a sequence of ${\displaystyle n}$ symbols) of user ${\displaystyle i}$;
• ${\displaystyle Y_{i}}$ is the channel output symbol (${\displaystyle Y_{i}^{n}}$ is a sequence of ${\displaystyle n}$ symbols) of user ${\displaystyle i}$;
• ${\displaystyle {\hat {W}}_{i}}$ is the estimate of the transmitted message by user ${\displaystyle i}$; and
• ${\displaystyle p(y_{1},y_{2}|x_{1},x_{2})}$ is the noisy memoryless channel, which is modeled by a conditional probability distribution.

The capacity of this channel model is not known in general; only for special cases of ${\displaystyle p(y_{1},y_{2}|x_{1},x_{2})}$ the capacity has been calculated, e.g., in the case of strong interference or deterministic channels.[1]