Source and channel coding algorithms using rabbit (Golden) sequence terms

Abstract

Several source coding techniques are already available in the ever increasing field of coding theory for the symbols of discrete information sources. The most commonly used and optimum technique is the Huffman coding scheme since the codes derived from this algorithm are of minimum redundancy and hence gives the optimum average code length. But the scheme gives codes which are not formula based. The probabilities of the symbols are to be repeatedly arranged in several stages. Huffman scheme does not take care of the special features exhibited by the codes of Type I sources of m number of symbols for which Pi = and#931; pj lt pi-1 for every i in the j=i+1 range 2 and#8804; i and#8804; (m-2). In this thesis work an algorithm is developed and presented which gives codes for the messages of sources of Type I. Another novelty of this scheme is that it uses the terminating bits of internal sub division terms of the Golden sequence terms. Since the above algorithm fails to give the codes of Type II sources for which at least for one value of i, Pi and#8805; pi-1, a second algorithm is proposed which can cater to the symbols of Type II as well as Type I sources. The probabilities of the symbols are represented by Fibonacci numbers called F numbers, and the sum of least two probabilities in every stage is represented by the non-Fibonacci numbers between two contiguous Fibonacci numbers called G numbers. This results in much simpler tracking of individual probabilities during the final reading of the codes. The much observedinconvenience of repeated listing of probabilities of odd decimal values and their tracking at the end is eliminated in the proposed method. The total number of entries to be made is also far less. newlineThe widely used Hamming codes are the class of linear block codes in systematic form with minimum distance 3 which can correct efficiently single bit errors. The first step in the design of any (n, k) linear block channel code is to find the code length n for the fixed data block of length k bits.