Question

In this assignment the source Alphabet is A={a,b,c}. The symbol counts are ng=14, no=1, sequence ccba using incremental arithmetic coding algorithm. Show all the steps. If there indicate what type and why.

Answer 1

Step 1 : Obtain the probability value of each symbol from the value of symbol counts.

Probability of symbol a = 14 / 16 = 0.875

Probability of symbol b = 1 / 16 = 0.0625

Probability of symbol c = 1 / 16 = 0.0625

Given sequence is ccba

The probability always ranges between 0 and 1.

The upper limit at a particular stage is equal to lowe limit value of the previous stage + ( difference of upper limit and lowe limit of the previous stage ) * ( probability of the symbol )

The interval diagram is as follows :  

Step 1 Step 2 Step 3 Step 4 0.9991211 1 0.9375 0.9925 0.9991211 + 0.99911427 \b 0.875 0.9921 0.9990625 0.99911377 + Codeword 0.9375 0.9925 0.9990625

The codeword ranges in between 0.9990625 and 0.9991137.

Symbol scanned	Interval period
c	[0.9375 - 1]
c	[0.9925 - 1]
b	[0.9990625 - 0.9991211]
a	[0.9990625 - 0.99911377]

The final low value of the above figure the above table, that is for symbol a,will give the encoded value for the sequence ccba

and hence, the answer is 0.9990625.