  Devising efficient communication in a network consisting of multiple
transmitters and receivers is a problem of immense importance in communication
theory. Interestingly, resources in the quantum world have been shown to be
very effective in enhancing the performance of communication networks. In this
work, we study entanglement-assisted communication over classical network
channels. When there is asymmetry such that noise introduced by the channel
depends on the input alphabets, non communicating senders may exploit shared
entangled states to overcome the noise. We consider multiple access channels,
an essential building block for many complex networks, and develop an extensive
framework for n-senders and 1-receiver multiple access channels based on
nonlocal games. We obtain generic results for computing correlation assisted
sum-capacities of these channels. The considered channels introduce less noise
on winning and more noise on losing the game, and the correlation assistance is
classified as local (L), quantum (Q), or no-signaling (NS). Furthermore, we
consider a broad class of multiple access channels such as depolarizing ones
that admix a uniform noise with some probability and prove general results on
their sum-capacities. Finally, we apply our analysis to three specific
depolarizing multiple access channels based on Clauser-Horne-Shimony-Holt,
magic square, and Mermin-GHZ nonlocal games. In all three cases we find
significant enhancements in sum-capacities on using nonlocal correlations. We
obtain either exact expressions for sum-capacities or suitable upper and lower
bounds on them. The general framework developed in this work has much wider
applicability and the specificity studied in details are some illustrative
examples to compare with recent studies in this direction.
