Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fairness in Multiuser Systems with Polymatroid Capacity Region   For a wide class of multi-user systems, a subset of capacity region which
includes the corner points and the sum-capacity facet has a special structure
known as polymatroid. Multiaccess channels with fixed input distributions and
multiple-antenna broadcast channels are examples of such systems. Any interior
point of the sum-capacity facet can be achieved by time-sharing among corner
points or by an alternative method known as rate-splitting. The main purpose of
this paper is to find a point on the sum-capacity facet which satisfies a
notion of fairness among active users. This problem is addressed in two cases:
(i) where the complexity of achieving interior points is not feasible, and (ii)
where the complexity of achieving interior points is feasible. For the first
case, the corner point for which the minimum rate of the active users is
maximized (max-min corner point) is desired for signaling. A simple greedy
algorithm is introduced to find the optimum max-min corner point. For the
second case, the polymatroid properties are exploited to locate a rate-vector
on the sum-capacity facet which is optimally fair in the sense that the minimum
rate among all users is maximized (max-min rate). In the case that the rate of
some users can not increase further (attain the max-min value), the algorithm
recursively maximizes the minimum rate among the rest of the users. It is shown
that the problems of deriving the time-sharing coefficients or rate-spitting
scheme can be solved by decomposing the problem to some lower-dimensional
subproblems. In addition, a fast algorithm to compute the time-sharing
coefficients to attain a general point on the sum-capacity facet is proposed.

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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio