Virtual Signaling of CSIT via Non-Signaling Assistance

Non-signaling correlations, which (strictly) include quantum correlations, provide a tractable path to explore the potential impact of quantum nonlocality on the capacity of classical communication networks.Motivated by a recent discovery that certain wireless network settings benefit significantly from non-signaling (NS) correlations, various generalizations are considered.First, it is shown that for a point to point discrete memoryless channel N Y |XS with input X, output Y , channel state S, and non-causal channel state information at the transmitter (CSIT), the NS-assisted Shannon capacity is max P X|S I(X; Y |S), matching the classical (without NS assistance) capacity of the channel for the setting where S is also made available to the receiver.For any finite blocklength, the NS-assisted optimal probability of successful decoding over N Y |XS is shown to remain unchanged if in addition S is made available to the receiver.The key insight is summarized as 'virtual signaling of CSIT via NS-assistance' and is supported by further results as follows.For a discrete memoryless 2-user broadcast channel (BC), the Shannon capacity region with NS-assistance available only between the transmitter and User 1, is found next.Consistent with the aforementioned key insight, the result matches the classical capacity region for the setting where the desired message of User 2 is made available in advance as side-information to User 1.The latter capacity region is known from a result of Kramer and Shamai.Next, for a semi-deterministic BC, the Shannon capacity region with full (tripartite) NS-assistance is shown to be the same as if only bipartite NS-assistance was available between the transmitter and the non-deterministic user.Bipartite NS-assistance between the transmitter and only the deterministic user, does not improve the capacity region relative to the corresponding classical setting.The capacity region is also found for the BC obtained by passing the outputs of a semi-deterministic BC through separate erasure channels, provided that the deterministic output does not experience the worse erasure channel.The result matches Sato's converse bound.Finally, the analysis is extended to a K-user BC with full NS-assistance among all parties.It is shown that the optimal probability of successful decoding for any finite blocklength does not change if each User k, k ∈ [K] is provided in advance the desired messages of Users k + 1, k + 2, • • • , K.1