By Peter Seibt
Algorithmic details conception treats the math of many vital components in electronic info processing. it's been written as a read-and-learn publication on concrete arithmetic, for lecturers, scholars and practitioners in digital engineering, machine technological know-how and arithmetic. The presentation is dense, and the examples and workouts are a number of. it really is in keeping with lectures on info expertise (Data Compaction, Cryptography, Polynomial Coding) for engineers.
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Extra info for Algorithmic Information Theory: Mathematics of Digital Information Processing (Signals and Communication Technology)
04+6+8 = 20. So, the arithmetic code word of daaabaaacaaabaaa is shorter than the (concatenated) Shannon code word. This is a general fact: whenever the probabilities are not powers of 12 , arithmetic coding is better than any block coding (of ﬁxed block length). Exercises (1) The memoryless source which produces the four letters a, b, c, d, according to the probability distribution given by p(a) = 34 , p(b) = 18 , p(c) = p(d) = 1 16 . Compute the arithmetic code word of daaabaaacaaabaaa (thus completing the example above).
Our source will still produce the four letters a, b, c, d, but now according to 1 . 42, I(b) = 3, I(c) = I(d) = 4. The Shannon code: a b c d • − − − − − − − − − − −− • −− • − • − • 3 7 15 1 0 4 8 16 a −→ 0 b −→ 110 c −→ 1110 d −→ 1111 Let us choose a source word in conformity with the statistics: daaabaaacaaabaaa. The associated Shannon code word is 11110001100001110000110000 and has 26 bits. 04+6+8 = 20. So, the arithmetic code word of daaabaaacaaabaaa is shorter than the (concatenated) Shannon code word.
We shall restrict ourselves to the presentation of a single version which is seductively clear and simple. 1 LZW Coding Situation A source produces a stream of letters, taken from a ﬁnite alphabet. The encoder will establish a dictionary of strings of characters (of motives) which are characteristic for the source stream (and it will create this way implicit statistics of the source production). The compressed message is given by the stream of pointers (≡ the numbers attributed to the strings in the dictionary).
Algorithmic Information Theory: Mathematics of Digital Information Processing (Signals and Communication Technology) by Peter Seibt