State-Dependent Gaussian Multiple Access Channels: New Outer Bounds and Capacity Results

Abstract

This paper studies a two-user state-dependent Gaussian multiple-access channel (MAC) with state noncausally known at one encoder. Two scenarios are considered: i) each user wishes to communicate an independent message to the common receiver, and ii) the two encoders send a common message to the receiver and the non-cognitive encoder (i.e., the encoder that does not know the state) sends an independent individual message (this model is also known as the MAC with degraded message sets).For both scenarios, new outer bounds on the capacity region are derived, which improve uniformly over the best known outer bounds. In the first scenario, the two corner points of the capacity region as well as the sum rate capacity are established, and it is shown that a single-letter solution is adequate to achieve both the corner points and the sum rate capacity. Furthermore, the full capacity region is characterized in situations in which the sum rate capacity is equal to the capacity of the helper problem. The proof exploits the optimal-transportation idea of Polyanskiy and Wu (which was used previously to establish an outer bound on the capacity region of the interference channel) and the worst-case Gaussian noise result for the case in which the input and the noise are dependent.

Outer bounds for Gaussian multiple access channels with state known at one encoder

“…where f (•) is defined in (16). Proof: The corner point (27) follows from (17) and (19) (with ρ = 0), and (28) follows from (13) by setting R 2 = C 2 , and by taking δ → 0.…”

“…Due to space constraints, we have omitted the proofs of most results. They can be found in [16]. Theorem 1: The capacity region C(P 1 , P 2 , Q) of the dirty MAC (1) is outer-bounded by the region with rate pairs…”

“…• The bottom corner point (C 1 , C 2 ) also follows from the (genie-aided) outer bound in (4) and (6). • The following three statements are equivalent [16]:…”

MIMO Gaussian State-Dependent Channels with a State-Cognitive Helper

“…The type of channels with mismatched property has been addressed in the past for various models, for example, in [21][22][23][24][25], the state-dependent multiple access channel (MAC) is studied with the state known at only one transmitter. The best outer bound for the Gaussian MAC setting was recently reported in [26]. The point-to-point helper channel studied in [27,28] can be considered as a special case of [25], where the cognitive transmitter does not send any message.…”

“…where in the last equality we used the definition of Σ X 0 S from (26). Consequently, we established an upper bound on I(S n ; Y n 1 |M 1 ):…”