Related papers: A note on outer bounds for broadcast channel
This paper provides an explicit expression for the capacity region of the two-user broadcast Z channel and proves that the optimal boundary can be achieved by independent encoding of each user. Specifically, the information messages…
In this paper, we investigate the half-duplex cooperative communication scheme of a two user Gaussian interference channel. We develop achievable region and outer bound for the case when the system allow either transmitter or receiver…
This paper studies the problem of secure communication over the broadcast channel with receiver side information under the lens of individual secrecy constraints. That is, the transmitter wants to send two independent messages to two…
Achievable rate regions and outer bounds are derived for three-user interference channels where the transmitters cooperate in a unidirectional manner via a noncausal message-sharing mechanism. The three-user channel facilitates different…
We derive the capacity region of the degraded broadcast channel (DBC) subject to the constraint that the communication is not detected by an adversary, the Warden. Our capacity result is in a computable form and numerical results show that…
A channel is degradable if there exists a second channel that maps the output state of the channel to the environment state. These channels satisfy the property that the output state contains more information about the input than the…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
We define the notions of outer medians and outer median triangles. We show that outer median triangles enjoy similar properties to that of the median triangle.
In this short note, we show that the inradius of a convex body is comparable to its volume divided by its surface area. We also give a simple formula, in terms of its volume and inradius, that is comparable to the volume of its intersection…
This paper is concerned with general interference channels characterized by a sequence of transition (conditional) probabilities. We present a general formula for the capacity region of the interference channel with two pairs of users. The…
When experimentally learning the action of a continuous variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is using low…
In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.
We consider a state-dependent multiaccess channel (MAC) with state non-causally known to some encoders. We derive an inner bound for the capacity region in the general discrete memoryless case and specialize to a binary noiseless case. In…
Seymour's Second-Neighborhood Conjecture states that every directed graph whose underlying graph is simple has at least one vertex $v$ such that the number of vertices of out-distance $2$ from $v$ is at least as large as the number of…
This paper investigates the joint source-channel coding problem of sending two correlated memoryless sources with common part over a memoryless multiple access channel (MAC). An inner bound and two outer bounds on the achievable distortion…
We consider the discrete memoryless degraded broadcast channels. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent function.…
We identify the common underlying form of the capacity expression that is applicable to both cases where causal or non-causal side information is made available to the transmitter. Using this common form we find that for the single user…
We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the $N$-dimensional Euclidean space with nonempty boundary. We give a lower bound for the corresponding best Hardy constant for a domain…
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…
We extend Shannon's result on the capacity of channels with state information to multiple user channels. More specifically, we characterize the capacity (region) of degraded broadcast channels and physically degraded relay channels where…