7,666 research outputs found
Network Information Flow with Correlated Sources
In this paper, we consider a network communications problem in which multiple
correlated sources must be delivered to a single data collector node, over a
network of noisy independent point-to-point channels. We prove that perfect
reconstruction of all the sources at the sink is possible if and only if, for
all partitions of the network nodes into two subsets S and S^c such that the
sink is always in S^c, we have that H(U_S|U_{S^c}) < \sum_{i\in S,j\in S^c}
C_{ij}. Our main finding is that in this setup a general source/channel
separation theorem holds, and that Shannon information behaves as a classical
network flow, identical in nature to the flow of water in pipes. At first
glance, it might seem surprising that separation holds in a fairly general
network situation like the one we study. A closer look, however, reveals that
the reason for this is that our model allows only for independent
point-to-point channels between pairs of nodes, and not multiple-access and/or
broadcast channels, for which separation is well known not to hold. This
``information as flow'' view provides an algorithmic interpretation for our
results, among which perhaps the most important one is the optimality of
implementing codes using a layered protocol stack.Comment: Final version, to appear in the IEEE Transactions on Information
Theory -- contains (very) minor changes based on the last round of review
Power and Channel Allocation for Non-orthogonal Multiple Access in 5G Systems: Tractability and Computation
Network capacity calls for significant increase for 5G cellular systems. A
promising multi-user access scheme, non-orthogonal multiple access (NOMA) with
successive interference cancellation (SIC), is currently under consideration.
In NOMA, spectrum efficiency is improved by allowing more than one user to
simultaneously access the same frequency-time resource and separating
multi-user signals by SIC at the receiver. These render resource allocation and
optimization in NOMA different from orthogonal multiple access in 4G. In this
paper, we provide theoretical insights and algorithmic solutions to jointly
optimize power and channel allocation in NOMA. For utility maximization, we
mathematically formulate NOMA resource allocation problems. We characterize and
analyze the problems' tractability under a range of constraints and utility
functions. For tractable cases, we provide polynomial-time solutions for global
optimality. For intractable cases, we prove the NP-hardness and propose an
algorithmic framework combining Lagrangian duality and dynamic programming
(LDDP) to deliver near-optimal solutions. To gauge the performance of the
obtained solutions, we also provide optimality bounds on the global optimum.
Numerical results demonstrate that the proposed algorithmic solution can
significantly improve the system performance in both throughput and fairness
over orthogonal multiple access as well as over a previous NOMA resource
allocation scheme.Comment: IEEE Transactions on Wireless Communications, revisio
Decoding by Embedding: Correct Decoding Radius and DMT Optimality
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP)
are the core algorithmic problems on Euclidean lattices. They are central to
the applications of lattices in many problems of communications and
cryptography. Kannan's \emph{embedding technique} is a powerful technique for
solving the approximate CVP, yet its remarkable practical performance is not
well understood. In this paper, the embedding technique is analyzed from a
\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary
analyses of the embedding technique: We establish a reduction from BDD to
Hermite SVP (via unique SVP), which can be used along with any Hermite SVP
solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL)
algorithm), and show that, in the special case of LLL, it performs at least as
well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis
helps to explain the folklore practical observation that unique SVP is easier
than standard approximate SVP. It is proven that when the LLL algorithm is
employed, the embedding technique can solve the CVP provided that the noise
norm is smaller than a decoding radius , where
is the minimum distance of the lattice, and . This
substantially improves the previously best known correct decoding bound . Focusing on the applications of BDD to decoding of
multiple-input multiple-output (MIMO) systems, we also prove that BDD of the
regularized lattice is optimal in terms of the diversity-multiplexing gain
tradeoff (DMT), and propose practical variants of embedding decoding which
require no knowledge of the minimum distance of the lattice and/or further
improve the error performance.Comment: To appear in IEEE Transactions on Information Theor
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