# Tag Info

Accepted

### Calculate Huffman code length having probability?

The intended answer is probably that the length of the longest codeword is approximately $$-\log_2 10^{-6} = 20.$$ But this is wrong. The information given doesn't come close to specifying the length ...
Accepted

### How many different Huffman encoding for a given number of symbols

The answer is $C_{n-1} n!$ . That is, the $(n-1)$st Catalan number times $n$ factorial. There are $C_{n-1}$ ways of making a complete binary tree with $n$ leaves, and there are $n!$ ways of assigning ...

Accepted

### Is subtractive dithering the optimal algorithm for sending a real number using one bit?

Note: See the edit at the bottom for an argument showing that there is an unbiased algorithm which has variance strictly lower than $1/12$ for all $x \in [0,1]$. We can at least prove that if $x$ is ...

### Number of bits required for encoding variables with fixed sum?

Answer to question 1: $\left\lceil \log_2 \binom{M-1}{r-1} \right\rceil$ bits suffice to encode the variables. Proof: Count how many ways there are to choose $y_1,\ldots,y_r$ such that $y_i \ge 0$ ...

### Question about "typical set" in Shannon's source coding theorem

$S_δ$ is not a subset of the typical set. As you mentioned, the most probable element is a member of $S_δ$ but it is not necessarily a member of the typical set. The only reason to use the typical ...
Accepted

### Treewidth relations between Boolean formulas and Tseitin encodings

There is a relation between the treewidth of a circuit and the primal treewidth of its Tseitin transformation but you will have to take the fan-in of the circuit into account, which is large when ...
Accepted

### Why Asymptotic Equipartition Property theorem proofs assume the source is memoryless?

Before we try to get into ergodic or whatever else, let's try to understand what phenomenon a mathematician or scientist is trying to (or could be trying to) model with AEP. Well Asymptotic for ...
1 vote

### How many different Huffman encoding for a given number of symbols

The answer by Peter Shor is correct. But for an optimal case when the symbols can only be placed at unique leaf nodes the number of possible Huffman codes drops to $C_{n-1}2^{n-1}$.
1 vote
Accepted

### Entropy of a byte in a compression algorithm?

I define a random variable X which samples a bit uniformly at random from C∗. Should I expect Prob[X = 0] to be close to 1/2? Roughly, yes. The compression algorithm is lossless (bijective), so the ...
1 vote
Accepted

### Can we say that Church encoding is a form of Gödelization?

It's possible to do a Gödel numbering that assigns every term in System F to a unique natural number? The answer is yes, pick your favorite way of coding terms in F, simply because they are ...

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