Digital communication theory

During an observation period, Hg will be true with some probability Pg and Hi will be true with probability Pi, and 1 = Pq -f Pi. In single-molecule experiments. Pi corresponds to the fraction of time that a molecule is present in the probe volume in other words. Pi is the fractional occupancy of the probe volume. In general, this probability is imknown at the start of the experiment and is often the quantity sought. 

During the experiment, the signal is sampled at one or more points, creating a data vector N, which consists of the number of photocounts observed during each point in the acquisition window. Based on the vector, a decision must be made between Hg and Hi. The data points are conditionally distributed according to some law. If Hg is true, then the conditional probability is P(NlHg). If Hi is true, the conditional probability is given by P(W Ffi). 

Due to a lack of space, we describe a very simple data treatment. The photocounts contained in the sample vector are summed to yield one datum, N. We also assume that the signals are Poisson-distributed, so that the probability of observing N photocounts given that no molecule is present is given by 

There are several approaches to setting the threshold. In the Bayes approach, a threshold is chosen to minimize the total probability of an error, given by Pe = Po X fa -I- Pi X Pm. In general, Pq and Pi are unknown at the start of the experiment, but may be estimated from preliminary experiments. Pe is minimized by the following detection strategy. The processor will declare Hi is true if 

Since the logarithm is monotonic for positive numbers, the probabihties can be replaced by their logarithms, and H is declared if 

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In 2003, Dr. Hasna joined the Department of Electrical Engineering at Qatar University as an assistant professor. Currently, he serves as the vice president and chief academic ofScer of Qatar University. His research interests span the general area of digital communication theory and its application to performance evaluation of wireless communication systems over fading channels. His current specific research interests include cooperative communications, ad hoc networks, cognitive radio, and network coding. 

Shannon s theories, although difficult to master, are very easy to describe in terms of the less than obvious answers to two basic questions about the limits of digital communication. The first question, compression or source coding, asks how few bits per second are required for the faithful reproduction of a source (voice, video, or text). The second, transmission or channel coding, asks how many bits per second can be accurately transmitted over a noisy and otherwise impaired medium. The two papers published by Shannon in 1948 fully answered both questions It took nearly half a century, however, to develop communication systems that have almost reached the performance predicted by Shannon. 

Because of its severe approximations, in using the Huckel method (1932) one ignores most of the real problems of molecular orbital theory. This is not because Huckel, a first-rate mathematician, did not see them clearly they were simply beyond the power of primitive mechanical calculators of his day. Huckel theory provided the foundation and stimulus for a generation s research, most notably in organic chemistry. Then, about 1960, digital computers became widely available to the scientific community. 

Another breakthrough paper appeared twelve years afterwards, in 1948, again by Claude Shannon A mathematical theory of communication [2]. On this paper. Shannon defined the unit of information, the binary digit, or bit, and established the theory which tells us the amount of information (i.e., the number of bits) which can be sent per unit time through a communication channel, and how this information can be fully recovered, even in the presence of noise in the channel. This work founded the Theory of Information. 

This volume provides over 2,200 authoritative entries on terms used in media and communication, from concepts and theories to technical terms, across subject areas that inciude advertising, digital culture, journalism, new media, radio studies, and telecommunications. 

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