The study of data representations that enable error detection, error correction and/or compression.

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Lexicographical position of a string in its type class

I have the following problem: Given a string $x\in\{1,...,M\}^+$ of length $n$. Let $S$ be the set of all words with exactly the same numbers of occurences of smybols as in $x$. In fact, $S$ consists ...
4
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1answer
94 views

Are Lie theoretic codes impractical?

I have been recently studying Lie theory. I discovered that there is a family of Lie theoretic error correcting codes. I did not find any information except this paper: “Representations of Lie ...
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2answers
51 views

How to determine letter boundaries in Huffman encoded strings?

I'm trying to understand the Huffman compression algorithm. Lets assume the word : YESSSS According to Huffman tree we will get : S : 4 times -> Code : 0 Y : once -> Code : 01 E : once -> ...
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0answers
124 views

Huffman tree and maximum depth

Knowing the frequencies of each symbol, is it possible to determine the maximum height of the tree without applying the Huffman algorithm? Is there a formula that gives this tree height?
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57 views

Error detection/correction algorithm

We have 2 stations that communicate with each other, but we need to detect (or even correct) when something is wrong. We use 8 binary words: each consisting of 3 bits and to send it we code it as ...
4
votes
1answer
38 views

How many sequences in a prefix code can be compressed by m bits?

I have a little understanding problem with Appendix A ("Universal Codes") in the paper "Shannon Information and Kolmogorov complexity" by Gründwald and Vitanyi (Link). At the end of page 50, they ...
2
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1answer
80 views

Compute minimum hamming distance of a code

How do you find the minimum hamming distance of a code? A naive way is computing the distance of each pair of codewords in our code. It becomes hard when the code is sufficiently large. Is there a ...
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1answer
70 views

Information of a stream of bits

Here is my problem. I have to compute the amount of information that is possible to encode in a string of bits. This string of bits represent a stream. Let us call such stream as ...
6
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2answers
88 views

Efficiently map different codes to rotation-different codes

Let $\mathbb{F}^n_2$ denote the set of $n$-bit 0-1 strings. How to construct an efficiently computable function $f:\mathbb{F}^n_2\to \mathbb{F}^m_2 (m>n)$ satisfying that $\forall u\neq ...
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2answers
450 views

Network modem question

How would I solve the following can anyone help me.I know MIPS is basically how many instruction the processor can do per second but what should I do? Assume that we are receiving a message across a ...
3
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1answer
234 views

Algorithm for determining minimal set of covering prefixes

I have a set of strings. My goal is to find a minimal set of longest prefixes which will match most of that set. For instance, if my set is: ...
5
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1answer
94 views

Application of Expander Codes

I need to give a talk about expander codes at university (I'm a student of computer science). Since they have been introduced to show a family of codes looking good when thinking of the Shannon ...
5
votes
3answers
324 views

No compression algorithm can compress all input messages?

I just started reading a book called Introduction to Data Compression, by Guy E. Blelloch. On page one, he states: The truth is that if any one message is shortened by an algorithm, then some ...
5
votes
2answers
324 views

What is a good binary encoding for $\phi$-based balanced ternary arithmetic algorithms?

I've been looking for a way to represent the golden ratio ($\phi$) base more efficiently in binary. The standard binary golden ratio notation works but is horribly space inefficient. The Balanced ...
7
votes
1answer
122 views

Prove fingerprinting

Let $a \neq b$ be two integers from the interval $[1, 2^n].$ Let $p$ be a random prime with $ 1 \le p \le n^c.$ Prove that $$\text{Pr}_{p \in \mathsf{Primes}}\{a \equiv b \pmod{p}\} \le c ...
3
votes
1answer
396 views

Encoding the sequence 0110 and determining parity, data bit and value

I've been struggling with several Hamming code/error detection questions because the logic behind it doesn't seem to make sense. eg.1 eg.2 I don't really understand the above two examples and ...
8
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1answer
145 views

Error-correcting rate is misleading

In coding theory, 'how good a code is' means how many channel errors can be corrected, or better put, the maximal noise level that the code can deal with. In order to get better codes, the codes are ...