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Graph theory: Adjacency reducing mapping

In $G(V,E)$, an adjacency-reducing mapping is a mapping from $V$ to $V$ such that if $u,v\in V$ not adjacency in $G$, then $p(v),p(u)$ not adjacent, where $p(\cdot)$ is the mapping. Assume $V'$ is ...
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35 views

How to calculate the probabilty of symbol in huffman code?

I have a question that I tried to solve but I always get stuck.. The following Huffman code for an alphabet consisting of five symbols A to E ...
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33 views

Mutual information of discrete and continous stochastic variable

As part of a homework, I have a "quantizer" consisting of variables $X_{1}$ and $X_{2}$ which have the following joint distribution. $X_2$ is discrete and I can assume that all probabilities are ...
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49 views

Encoding a channel with Huffman Code

I have a random source which is with no memory and have this alphabet (A,B,C). Each symbol in the alphabet has a probability ( A = 0.5, B= 0.25, C = 0.25) It's given that each message including ...
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44 views

decreasing capacity of channel

I have a question regarding the capacity of a channel Consider a channel given by the transition probabilities $p(y|x)$ with capacity $C$. Now a friendly statistician offers to preprocess the output ...
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1answer
98 views

Help deciphering Levenshtein formula

I am trying to completely understand the Levenschtein formula, and I have been reading the Wikipedia article on this. However, the description of the mathematical formula confuses me: ...
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171 views

Entropy Problem: mutual information

I have a problem about entropy and mutual information that I have attempted, but would like feedback on. 30% Boas 20% Anaconda 50% Cobra Half of the Cobras were medium sized, and the other half were ...
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175 views

Simple trace distance problem

I am self studying a course on information theory and came with the following question: $A$ and $B$ represent two possibly different probability distributions representing two different independent ...
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55 views

Mutual information, handling start and end

In my homework, I am supposed to use Brown algorithm to compute word classes. I need to compute mutual information for some data and looking in my results and official results, I am probably making ...
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150 views

Cover & Thomas textbook notation

Exercise 2.27 in Elements of Information Theory (2nd ed.) reads: Let $\mathbf{p} = (p_{1}, p_{2}, \ldots, p_{m})$ be a probability distribution on $m$ elements (i.e., $p_{i} \geq 0$ and ...