Strong Converse Theorems for Multimessage Networks with Tight Cut-Set Bound

Strong Converse Theorems for Multimessage Networks with Tight Cut-Set Bound

This paper proves the strong converse for any discrete memoryless network (DMN) with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any DMN with tight cut-set bound and any fixed rate tuple that resides outside the capacity region, the average error probabilities of any sequence of length-n codes operated at the rate tuple must tend to 1 as n grows. Th...

Strong Converse for Discrete Memoryless Networks with Tight Cut-Set Bounds

This paper proves the strong converse for any discrete memoryless network (DMN) with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any DMN with tight cut-set bound and any fixed rate tuple that resides outside the capacity region, the average error probabilities of any sequence of length-n codes operated at the rate tuple must tend to 1 as n grows. Th...

Cut-set Theorems for Multi-state Networks

We derive new cut-set bounds on the achievable rates in a general multi-terminal network with finite number of states. Multiple states are common in communication networks in the form of multiple channel and nodes’ states. Our results are broadly applicable and provide much tighter upper bounds than the known single state min-cut max-flow theorem, and hence form an important new tool to bound t...

Strong converse theorems using Rényi entropies

On Two Strong Converse Theorems for Stationary Discrete Memoryless Channels

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subse...