Dependence balance outer bounds for the discrete memoryless two-way multiple access broadcast channel

We present an outer bound for the discrete memo-ryless two-way multiple access broadcast channel (TW-MAC/BC) using the dependence balance idea. The cut-set outer bound for multi-user channels allows arbitrarily correlated input distributions while the dependence balance idea limits the set of arbitrarily correlated input distributions to those satisfying a specific constraint known as dependence balance bound, which is particularly useful in channels with feedback or adaptation, as in two-way channels. We obtain a general dependence-balance-based outer bound for the discrete memoryless TW-MAC/BC, and a parallel channel extension for the single-output channel. We then show that for the single-output binary additive noisy TW-MAC/BC Y = X₁ + X₂ + X₃ + Z (Z Bernoulli(0.5)), an outer bound to the symmetric sum-rate of our outer bound is strictly smaller than that of the cut-set outer bound. This is shown using the composite function technique introduced by Willems and used by Tandon and Ulukus in the context of multiple-access channels with feedback.