13,765 research outputs found
Algorithmic Aspects of Optimal Channel Coding
A central question in information theory is to determine the maximum success
probability that can be achieved in sending a fixed number of messages over a
noisy channel. This was first studied in the pioneering work of Shannon who
established a simple expression characterizing this quantity in the limit of
multiple independent uses of the channel. Here we consider the general setting
with only one use of the channel. We observe that the maximum success
probability can be expressed as the maximum value of a submodular function.
Using this connection, we establish the following results:
1. There is a simple greedy polynomial-time algorithm that computes a code
achieving a (1-1/e)-approximation of the maximum success probability. Moreover,
for this problem it is NP-hard to obtain an approximation ratio strictly better
than (1-1/e).
2. Shared quantum entanglement between the sender and the receiver can
increase the success probability by a factor of at most 1/(1-1/e). In addition,
this factor is tight if one allows an arbitrary non-signaling box between the
sender and the receiver.
3. We give tight bounds on the one-shot performance of the meta-converse of
Polyanskiy-Poor-Verdu.Comment: v2: 16 pages. Added alternate proof of main result with random codin
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
Short Block-length Codes for Ultra-Reliable Low-Latency Communications
This paper reviews the state of the art channel coding techniques for
ultra-reliable low latency communication (URLLC). The stringent requirements of
URLLC services, such as ultra-high reliability and low latency, have made it
the most challenging feature of the fifth generation (5G) mobile systems. The
problem is even more challenging for the services beyond the 5G promise, such
as tele-surgery and factory automation, which require latencies less than 1ms
and failure rate as low as . The very low latency requirements of
URLLC do not allow traditional approaches such as re-transmission to be used to
increase the reliability. On the other hand, to guarantee the delay
requirements, the block length needs to be small, so conventional channel
codes, originally designed and optimised for moderate-to-long block-lengths,
show notable deficiencies for short blocks. This paper provides an overview on
channel coding techniques for short block lengths and compares them in terms of
performance and complexity. Several important research directions are
identified and discussed in more detail with several possible solutions.Comment: Accepted for publication in IEEE Communications Magazin
Feedback Allocation For OFDMA Systems With Slow Frequency-domain Scheduling
We study the problem of allocating limited feedback resources across multiple
users in an orthogonal-frequency-division-multiple-access downlink system with
slow frequency-domain scheduling. Many flavors of slow frequency-domain
scheduling (e.g., persistent scheduling, semi-persistent scheduling), that
adapt user-sub-band assignments on a slower time-scale, are being considered in
standards such as 3GPP Long-Term Evolution. In this paper, we develop a
feedback allocation algorithm that operates in conjunction with any arbitrary
slow frequency-domain scheduler with the goal of improving the throughput of
the system. Given a user-sub-band assignment chosen by the scheduler, the
feedback allocation algorithm involves solving a weighted sum-rate maximization
at each (slow) scheduling instant. We first develop an optimal
dynamic-programming-based algorithm to solve the feedback allocation problem
with pseudo-polynomial complexity in the number of users and in the total
feedback bit budget. We then propose two approximation algorithms with
complexity further reduced, for scenarios where the problem exhibits additional
structure.Comment: Accepted to IEEE Transactions on Signal Processin
Shannon Information and Kolmogorov Complexity
We compare the elementary theories of Shannon information and Kolmogorov
complexity, the extent to which they have a common purpose, and where they are
fundamentally different. We discuss and relate the basic notions of both
theories: Shannon entropy versus Kolmogorov complexity, the relation of both to
universal coding, Shannon mutual information versus Kolmogorov (`algorithmic')
mutual information, probabilistic sufficient statistic versus algorithmic
sufficient statistic (related to lossy compression in the Shannon theory versus
meaningful information in the Kolmogorov theory), and rate distortion theory
versus Kolmogorov's structure function. Part of the material has appeared in
print before, scattered through various publications, but this is the first
comprehensive systematic comparison. The last mentioned relations are new.Comment: Survey, LaTeX 54 pages, 3 figures, Submitted to IEEE Trans
Information Theor
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