Introduction

    If you don't know or don't remember what are the fibonacci numbers i will  briefly summarize their definitions.    Fibonacci numbers create sequence called... the Fibonnaci sequence. In the fibonnaci sequence every number expect the first two is the sum of the two preceding numbers.  As you can see in the illustration with the spiral we start with two ones  Then we have 2 (1+1), 3 (2+1), 5 (2+3), 8 (3+5) and so on.

Fibonacci coding

    Fibonacci coding is not as popular as other codings methods such as huffman coding or arithmetic coding. According to the Zeckendorf's theorem every integer can be written uniquely as sum of  nonconsecutive fibonacci numbers.  By adding a 1 and reversing the resulting sequence we form a prefix code. Thanks to the properties of fibonacci numbers we can be sure that token "11" indicates the end of code word.  the In the prefix code, none of the code words are prefixes of another word, this makes the prefix code  unambiguously decodable. 

 Sample encoding looks like this. 

for n = 1 fibonacci code is 11 as we add 1 at the end

for n = 2 fibonacci code is 011

for n = 11 fibonacci code is 001011 because 11 = 8 + 3 

Field of application

     At first glance it may seem that the use of fibonacci coding does not make sense. However, they are applicable for compressing a set of small integers also decoding is very fast.  Fibonacci coding can be used in communication channels where high noise levels because they are resistant to insertions and deletions. More informations abour fibonacci codes robustness you can find here > http://www.sciencedirect.com/science/article/pii/0166218X9300116H

Dont forget fibonacci is everywhere!