1,275 research outputs found
A General Formula for the Mismatch Capacity
The fundamental limits of channels with mismatched decoding are addressed. A
general formula is established for the mismatch capacity of a general channel,
defined as a sequence of conditional distributions with a general decoding
metrics sequence. We deduce an identity between the Verd\'{u}-Han general
channel capacity formula, and the mismatch capacity formula applied to Maximum
Likelihood decoding metric. Further, several upper bounds on the capacity are
provided, and a simpler expression for a lower bound is derived for the case of
a non-negative decoding metric. The general formula is specialized to the case
of finite input and output alphabet channels with a type-dependent metric. The
closely related problem of threshold mismatched decoding is also studied, and a
general expression for the threshold mismatch capacity is obtained. As an
example of threshold mismatch capacity, we state a general expression for the
erasures-only capacity of the finite input and output alphabet channel. We
observe that for every channel there exists a (matched) threshold decoder which
is capacity achieving. Additionally, necessary and sufficient conditions are
stated for a channel to have a strong converse. Csisz\'{a}r and Narayan's
conjecture is proved for bounded metrics, providing a positive answer to the
open problem introduced in [1], i.e., that the "product-space" improvement of
the lower random coding bound, , is indeed the mismatch
capacity of the discrete memoryless channel . We conclude by presenting an
identity between the threshold capacity and in the DMC
case
Interference Mitigation in Large Random Wireless Networks
A central problem in the operation of large wireless networks is how to deal
with interference -- the unwanted signals being sent by transmitters that a
receiver is not interested in. This thesis looks at ways of combating such
interference.
In Chapters 1 and 2, we outline the necessary information and communication
theory background, including the concept of capacity. We also include an
overview of a new set of schemes for dealing with interference known as
interference alignment, paying special attention to a channel-state-based
strategy called ergodic interference alignment.
In Chapter 3, we consider the operation of large regular and random networks
by treating interference as background noise. We consider the local performance
of a single node, and the global performance of a very large network.
In Chapter 4, we use ergodic interference alignment to derive the asymptotic
sum-capacity of large random dense networks. These networks are derived from a
physical model of node placement where signal strength decays over the distance
between transmitters and receivers. (See also arXiv:1002.0235 and
arXiv:0907.5165.)
In Chapter 5, we look at methods of reducing the long time delays incurred by
ergodic interference alignment. We analyse the tradeoff between reducing delay
and lowering the communication rate. (See also arXiv:1004.0208.)
In Chapter 6, we outline a problem that is equivalent to the problem of
pooled group testing for defective items. We then present some new work that
uses information theoretic techniques to attack group testing. We introduce for
the first time the concept of the group testing channel, which allows for
modelling of a wide range of statistical error models for testing. We derive
new results on the number of tests required to accurately detect defective
items, including when using sequential `adaptive' tests.Comment: PhD thesis, University of Bristol, 201
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