# Shannon-Fano coding calculator

This online calculator generates Shannon-Fano coding based on a set of symbols and their probabilities

### This page exists due to the efforts of the following people:

#### Karen Luckhurst

Created: 2019-04-01 09:29:46, Last updated: 2020-12-03 12:02:34

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8168/. Also, please do not modify any references to the original work (if any) contained in this content.

This online calculator produces Shannon-Fano coding for a set of symbols given their probabilities. A bit of theory can be found below the calculator.

#### Symbols probability table

NameValue
Items per page:

Digits after the decimal point: 2
Weighted path length

Shannon entropy

The file is very large. Browser slowdown may occur during loading and creation.

## Shannon-Fano coding

In the field of data compression, Shannon–Fano coding, named after Claude Shannon and Robert Fano, is a technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding.

In Shannon–Fano coding, the symbols are arranged in order from the most probable to the 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 this means the symbol's code is complete and will not form the prefix of any other symbol's code.

The algorithm 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 non-optimal codes by Shannon–Fano coding.

For this reason, Shannon–Fano is almost never used; Huffman coding is almost as computationally simple and produces prefix codes that always achieve the lowest expected code word length, under the constraints that each symbol is represented by a code formed of an integral number of bits.1

URL copied to clipboard

#### Similar calculators

PLANETCALC, Shannon-Fano coding calculator