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arXiv:1208.1070

Timing Channels with Multiple Identical Quanta

Christopher Rose, Shahzad I. Mian, Ruochen Song

Published Aug 6, 2012• 10 citations
arXivHTMLPDF

Abstract

We consider mutual information between release times and capture times for a set of M identical quanta traveling independently from a source to a target. The quanta are immediately captured upon arrival, first-passage times are assumed independent and identically distributed and the quantum emission times are constrained by a deadline. The primary application area is intended to be inter/intracellular molecular signaling in biological systems whereby an organelle, cell or group of cells must deliver some message (such as transcription or developmental instructions) over distance with reasonable certainty to another organelles, cells or group of cells. However, the model can also be applied to communications systems wherein indistinguishable signals have random transit latencies.

DOI
10.48550/arxiv.1208.1070

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We consider mutual information between release times and capture times for a set of M identical quanta traveling independently from a source to a target. The quanta are immediately captured upon arrival, first-passage times are assumed independent and identically distributed and the quantum emission times are constrained by a deadline. The primary application area is intended to be inter/intracellular molecular signaling in biological systems whereby an organelle, cell or group of cells must deliver some message (such as transcription or developmental instructions) over distance with reasonable certainty to another organelles, cells or group of cells. However, the model can also be applied to communications systems wherein indistinguishable signals have random transit latencies.
In this paper, we consider the transmission of confidential message through non-identically and identically independent Nakagami-m fading single-input multiple-output (SIMO) channel in the presence of an eavesdropper. We are interested in protecting this message against eavesdropping i.e. the information is secure if it cannot be eavesdropped by any eavesdropper. Based on the problem of secure communications between transmitter and intended receiver over Nakagami-m fading channel where an eavesdropper observes their transmissions through another Nakagami-m fading channel, we derive the analytical expressions for the probability of non-zero secrecy mutual information, secure outage probability and ergodic secrecy mutual information of SIMO wireless communication systems over non-identically and identically independent Nakagami-m fading subchannels. Numerical results are presented and verified via Monte-Carlo simulation.
In this paper, we consider an independent and identically distributed Nakagami-q fading single-input multiple-output (SIMO) channel, where the transmitter sends some confidential message to the legitimate receiver in the presence of an eavesdropper. Both the receiver and the eavesdropper have multiple antennas. We formulated the probability of non-zero secrecy mutual information, secure outage probability, and ergodic secrecy mutual information for the SIMO wireless communication system. The calculations have been carried out using small limit argument approximation on zeroth-order modified Bessel function of first kind. This approximation provides decent results in the low signal-to-noise-ratio (SNR) regime. In the low-SNR regime, either the transmission power is small or the bandwidth is large. In either case, it is difficult for an eavesdropper to detect the signals in this regime. We present that in the presence of fading, positive secrecy mutual information is achievable even when the eavesdropper has better SNR than the main channel. We also found in our work that at low-SNR regime, the effect of number of eavesdropper's channel on average secrecy mutual information is almost negligible.
The problems studied in this thesis fall within two different topics in network information theory. The first part of this dissertation will be about information theoretic security and the second about distributed source coding. In the following a brief description of these problems will be given. In information theoretic security, we look at two different types of timing channels and we quantify the maximum rate at which a transmitter can communicate information reliably to a legitimate receiver while keeping an eavesdropper in the dark. The first timing channel that we study is the Poisson channel which is used to model certain direct detection optical communication systems. To transmit a message on this channel, the transmitter encodes information by modulating the intensity of an optical signal while the legitimate receiver and the eavesdropper use the arrival moments of the individual photons to decide which message was transmitted. The second timing channel studied is the exponential server queue. Here the transmitter encodes a message using a chosen sequence of packets inter-arrival times and both the legitimate receiver and the eavesdropper use the corresponding inter-departures from their respective exponential server queues to decode the transmitted message. In distributed source coding, we consider a rate-distortion problem in which a decoder is interested in estimating two correlated Gaussian random variables with mean-square error distortion constraints on each of the reproductions. The variables to be estimated are the roots of a given Gauss-Markov tree and each encoder observes one of the leaves of that tree. We show that a simple compression architecture that performs separate lossy quantization followed by SlepianWolf binning is sum-rate optimal for this problem.