**ETH Series in
Information Theory and its Applications, Vol. 6
edited by Amos Lapidoth**

Ligong Wang,

**Information-Theoretic Aspects of Optical Communications.**

1st edition 2011. X,102 pages, € 64,00.

ISBN 978-3-86628-392-3

**Abstract**

This
dissertation studies several information-theoretic aspects of optical
communications.

The
first aspect it studies is the one-shot classical capacity of a quantum
communication channel. It proves new upper and lower bounds on the amount of
classical information that can be transmitted through a single use of a quantum
channel, under a constraint on the average error probability. The bounds are
expressed using a quantity defined via quantum hypothesis testing. Combined
with the Quantum Stein's Lemma, these bounds provide a conceptually simple
proof for the Holevo-Schumacher-Westmoreland Theorem
for the classical capacity of a memoryless quantum
channel. Further, they also give a general capacity formula that is valid for
any, not necessarily memoryless, quantum channel.

The
second topic studied in this dissertation is the capacity of a continuous-time
peak-limited Poisson channel with spurious counts in the output. It is shown
that, if the positions of the spurious counts are known noncausally
to the encoder but not to the decoder, then the capacity of this channel equals
the capacity of the same channel but with no spurious counts, regardless of
whether the spurious counts are random or are chosen by a malicious adversary.
On the other hand, if the positions of the spurious counts are known only
causally to the encoder but not to the decoder, then such information does not
help to increase the capacity of this channel.

Next,
a rate-distortion problem for point processes is considered. In this problem,
an encoder sees a point pattern on the interval [0,*T*] and describes it to a reconstructor using bits. Based on this description, the reconstructor produces a subset of [0,*T*] of Lebesgue
measure not exceeding *DT* for some *D>0* to cover all the points in the
pattern. It is shown that, if the point pattern is the outcome of a homogeneous
Poisson process of intensity *λ*,
then, as *T* tends to infinity, the
minimum number of bits per second needed for the encoder to describe the
pattern is -*λ* log *D*. Further, any point pattern containing
no more than *λ* points per second
can be successfully described in this sense using -* λ* log *D* bits per
second. A Wyner-Ziv version of this problem is also
studied where some points in the pattern are known to the reconstructor.

The
last problem considered in this dissertation is the asymptotic capacity at low
input powers of a discrete-time Poisson channel under average-power or average-
and peak-power constraints. For a Poisson channel whose dark current is zero or
decays to zero linearly with the allowed average input power E, capacity is
shown to scale like E log as E tends to zero. For a Poisson channel
whose dark current is a nonzero constant, capacity is shown to scale, to within
a constant, like

E
log log .

**Keywords**: Arbitrarily varying channel,
arbitrarily varying source, channel capacity, finite blocklength,
hypothesis testing, low signal-to-noise ratio, optical communication, Poisson
channel, Poisson process, quantum channel, rate-distortion theory, side-information.

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