Multiple access computational offloading

Uplink resource allocation for multiple access computational offloading

“…In specifying that constraint for a particular multiple access scheme, we will assume that the data blocks are long enough for the asymptotic characterization to be valid. Under the asymptotic assumption, the achievable rate region of a FullMA scheme is the capacity region (see (10) below), and for the TDMA scheme, since each user transmits in a different interval, the rate R k at which it can reliably communicate during that interval is upper-bounded by the classical single-user capacity expression, e.g., [23]. 1 If B k denotes the total number of bits describing the task of user k, then let γ k B k define the number of bits offloaded by the k th user, where γ k ∈ {0, 1} for the binary offloading case, and γ k ∈ [0, 1] for the partial offloading case.…”

“…For a FullMA scheme, the achievable rate region is the capacity region of the multiple access channel. Since there are K ′ users in S ′ , that region can be described by the K ′ constraints of the form 0 ≤ R k and the (2 K ′ − 1) constraints of the form [23], [24] i∈N R i ≤ log 1 + i∈N α i P i , (10) in which α i = |h i | 2 σ 2 and N ⊆ S ′ . Furthermore, in a FullMA scheme the available channel is simultaneously assigned to all users, and hence t w k = 0, ∀k.…”

“…Our strategy for solving the resource allocation problem for systems with a FullMA scheme is based on the insights developed in our previous work on the two-user case [10], [14], which suggests algebraic decompositions of the problem. We will exploit the polymatroid structure of the capacity region of the multiple access channel (see [25]) in both the complete offloading and partial offloading cases.…”

Multiple Access Computational Offloading: Communication Resource Allocation in the Two-User Case (Extended Version)

“…When only one user is offloading, the duration of the first time slot is zero, (i.e., τ 1 = 0), and the solution to the minimal transmission energy problem has a simple closed-form expression [18]. If we consider the case in which user 1 is offloading, then the problem in (1) can be written as min…”

“…Our approach to solving the problem in (7), and indeed the other problems that we will consider in this manuscript, will be to (i) (precisely) decompose the problem into inner and outer problems, (ii) determine a closed-form or quasi-closed-form expression for the optimal solution of the inner problem in terms of the variables of the outer problem, and (iii) solve the outer problem and subsequently obtain optimal values for the inner problem, e.g., [18]. In the first step, we decompose the problem in (7) in such a way that the transmission rate and transmission power of the time slot in which user 2 transmits alone can be obtained in terms of the rates and powers of the first time slot, namely, Since the first part of the objective function in ( 7) is independent of P 23 and R 23 , the inner optimization in ( 8) is min…”