ETH Series in
Information Theory and its Applications, Vol. 6
edited by Amos Lapidoth
Information-Theoretic Aspects of Optical Communications.
1st edition 2011. X,102 pages, € 64,00.
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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