Shannon-Fano coding


Shannon Fano Coding  Techniques

In the field of data compression, Shannon-Fano coding is a suboptimal technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured).
In Shannon-Fano coding, the symbols are arranged in order from most probable to least probable, and then divided into two sets whose total probabilities are as close as possible to being equal.All symbols then have the first digits of their codes assigned; symbols in the first set receive "0" and symbols in the second set receive "1". As long as any sets with more than one member remain, the same process is repeated on those sets, to determine successive digits of their codes. When a set has been reduced to one symbol, of course, this means the symbol's code is complete and will not form the prefix of any other symbol's code.

The algorithm works, and it produces fairly efficient variable-length encodings; when the two smaller sets produced by a partitioning are in fact of equal probability, the one bit of information used to distinguish them is used most efficiently. Unfortunately, Shannon-Fano does not always produce optimal prefix codes; the set of probabilities {0.35, 0.17, 0.17, 0.16, 0.15} is an example of one that will be assigned

Shannon-Fano Algorithm
A Shannon-Fano tree is built according to a specification designed to define an effective code table. The actual algorithm is simple:
1.  For a given list of symbols, develop a corresponding list of probabilities or frequency counts so that each symbol’s relative frequency of occurrence is known.
2.  Sort the lists of symbols according to frequency, with the most frequently occurring symbols at the left and the least common at the right.
3.  Divide the list into two parts, with the total frequency counts of the left half being as close to the total of the right as possible.
4.  The left half of the list is assigned the binary digit 0, and the right half is assigned the digit 1. This means that the codes for the symbols in the first half will all start with 0, and the codes in the second half will all start with 1.
5.  Recursively apply the steps 3 and 4 to each of the two halves, subdividing groups and adding bits to the codes until each symbol has become a corresponding code leaf on the tree.

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