Multiple-access channel

In information theory, the multiple-access channel (MAC) is a model for communication scenarios where several transmitters wish to communicate to a common receiver. Sometimes these channels are also called multiaccess channels. Among multiterminal networks, multiple-access channels are those for which the strongest results are known, including an exact capacity result for the discrete memoryless setting with an arbitrary number of senders.

= Discrete memoryless multiple-access channels = Theorem The capacity for a $k$-sender discrete memoryless MAC is the set of $(R_1,R_2,\ldots,R_k)$-tuples satisfying $$ \sum_{j\in\mathcal{J}}R_j \leq I(X(\mathcal{J});Y|X(\mathcal{J}^c),Q)  \text{ for all } \mathcal{J}\subset[1:K]$$ for some joint pmf $p(q)p(x_1|q)p(x_2|q)\cdots p(x_k|q)$ with $Q\in\mathcal{Q}$ and $|\mathcal{Q}|\leq k$. In the above, $X(\mathcal{J}) = \{X_j|j\in\mathcal{J}\}$.

= Gaussian multiple-access channels = Theorem The capacity region for the $k$-sender additive white Gaussian noise (AWGN) multiple-access channel is the set of $(R_1,R_2,\ldots,R_k)$-tuples satisfying $$ \sum_{j\in\mathcal{J}}R_j \leq C\left(\sum_{j}S_j\right)  \text{ for all } \mathcal{J}\subset[1:K]$$ where $S_j$ is the signal-to-noise ratio (SNR) for the $j$th transmitter.

= Fading multiple-access channels =

= Collision channels =