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The quantity is called the relative redundancy and gives the maximum possible data compression ratio, when expressed as the percentage by which a file size can be decreased. (When expressed as a ratio of original file size to compressed file size, the quantity R : r {\displaystyle R:r} gives the maximum compression ratio that can be achieved.)
[4] [5] The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors. Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth.
There is no redundancy, however, in the following code: #define max(A,B) ((A)>(B)?(A):(B)) int random ( int cutoff , int range ) { return max ( cutoff , rand () % range ); } If the initial call to rand(), modulo range, is greater than or equal to cutoff, rand() will be called a second time for a second computation of rand()%range, which may ...
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method.
The converse of the capacity theorem essentially states that () is the best rate one can achieve over a binary symmetric channel. Formally the theorem states: Formally the theorem states:
There are many names for interaction information, including amount of information, [1] information correlation, [2] co-information, [3] and simply mutual information. [4] Interaction information expresses the amount of information (redundancy or synergy) bound up in a set of variables, beyond that which is present in any subset of those variables.
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...