Shannon and Poisson. sergio verdú
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1 Shannon and Poisson sergio verdú
2
3 P λ (k) = e λλk k! deaths from horse kicks in the Prussian cavalry. photons arriving at photodetector packets arriving at a router DNA mutations
4 Poisson entropy
5 law of small numbers Harremoes, Johnson and Kontoyiannis (2007) Thinning and the law of small numbers
6 Poisson as maximum entropy distribution Johnson (2008) Log-concavity and the maximum entropy property of the Poisson distribution
7 Poisson entropy
8 lossless compression of one Poisson sample Verdú and Han (1997) The role of the asymptotic equipartition property in noiseless source coding
9 lossy compression of Poisson processes COMPRESSOR DECOMPRESSOR
10 lossy compression of Poisson processes COMPRESSOR DECOMPRESSOR Rubin (1974) Information rates and datacompression schemes for Poisson processes Gallager (1976) Basic limits on protocol information in data communication networks Sato and Kawabata (1987) Information rates for Poisson point processes
11 lossy compression of Poisson processes COMPRESSOR DECOMPRESSOR Verdú (1996) The exponential distribution in information theory
12 lossy compression of Poisson processes COMPRESSOR DECOMPRESSOR R (d) = λ [ 1 log 2 λd ] + bits/arrival Verdú (1996) The exponential distribution in information theory
13 lossy compression of Poisson processes COMPRESSOR DECOMPRESSOR Bedekar (2001) On the Information about message arrival times required for in-order decoding Coleman, Kiyavash, Subramanian (2008) Rate distortion function of a Poisson process with a queueing distortion measure
14 lossy compression of Poisson processes COMPRESSOR DECOMPRESSOR R (d) = λ [ 1 log 2 λd ] + bits/arrival Bedekar (2001) On the Information about message arrival times required for in-order decoding Coleman, Kiyavash, Subramanian (2008) Rate distortion function of a Poisson process with a queueing distortion measure
15 Shannon capacity of a queue ENCODER QUEUE DECODER
16 Shannon capacity of a queue ENCODER QUEUE DECODER Anantharam and Verdú (1996) Bits through queues
17 Shannon capacity of a queue ENCODER QUEUE DECODER Anantharam and Verdú (1996) Bits through queues
18 Shannon capacity of a queue ENCODER QUEUE DECODER Anantharam and Verdú (1996) Bits through queues
19 Shannon capacity of a queue ENCODER QUEUE DECODER Anantharam and Verdú (1996) Bits through queues
20 error exponent of the exponential server Arikan (2002) On the reliability function of the exponential timing channel
21 Shannon capacity of a discrete-time geometric-server queue Wagner and Anantharam (2005) Zero-rate reliability of the exponential timing channel
22 Shannon capacity of a discrete-time geometric-server queue Thomas (1997) On the Shannon capacity of discrete-time queues Bedekar and Azizoglu (1998) The informationtheoretic capacity of discrete-time queues Prabhakar and Gallager (2005) Entropy and the timing capacity of discrete queues
23 Shannon capacity of the direct-detection Poisson photon-counting channel Kabanov (1978) Capacity of a channel of a Poisson type Davis (1980) Capacity and cutoff rate for Poisson-type channels Wyner (1988) Capacity and error exponent for the direct detection photon channel
24 error exponent of the direct-detection Poisson photon-counting channel Wyner (1988) Capacity and error exponent for the direct detection photon channel
25 error exponent of the direct-detection Poisson photon-counting channel with feedback Lapidoth (1993) On the reliability function of the ideal Poisson channel with noiseless feedback
26 capacity of the direct-detection Poisson photon-counting channel with fading Chakraborthy and Narayan (2007) The Poisson fading channel
27 pulse-amplitude modulation Poisson photon-counting channel Lapidoth and Moser (2003) Asymptotic capacity of the discrete-time Poisson channel
28 mutual information and estimation Guo, Shamai, Verdú (2008) Mutual information and conditional mean estimation in Poisson Channels
29 mutual information and estimation Guo, Shamai, Verdú (2008) Mutual information and conditional mean estimation in Poisson Channels
30 filtering with Poisson observations
31 mutual information and causal filtering Kabanov (1978) Capacity of a channel of a Poisson type Liptser and Shiryaev (1978) Statistics of Random Processes
32 causal and noncausal filtering Guo, Shamai, Verdú (2008) Mutual information and conditional mean estimation in Poisson Channels
33 Life is good for only two things: discovering mathematics and teaching mathematics Simeon Denis Poisson
34 Life is good for only two things: discovering mathematics and teaching mathematics Simeon Denis Poisson I can think of other things Anthony Ephremides
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