This paper studies the second-order asymptotics of the Gaussian multiple-access channel with degraded message sets. For a fixed average error probability ε ∈ (0, 1) and an arbitrary point on the boundary of the capacity region, we characterize the speed of convergence of rate pairs that converge to that boundary point for codes that have asymptotic error probability no larger than ε. We do so by elucidating clear relationships between the rate pairs achievable at large blocklengths and the local second-order asymptotics, i.e. the second-order behavior of these rate pairs in the neighborhood of a boundary point. We provide a numerical example to illustrate how the angle of approach to a boundary point affects the second-order coding rate. This is the first conclusive characterization of the second-order asymptotics of a network information theory problem in which the capacity region is not a polygon.
For the Gaussian MAC with degraded message sets, the complete second-order asymptotics was derived by Scarlett and Tan REF .
Second-Order Asymptotics for the Gaussian MAC with Degraded Message Sets
ArXiv
ArXiv
Mathematics Computer Science