arithmetic and adaptive arithmetic coding

arithmetic and adaptive arithmetic coding

• 1.
  ARITHMETIC AND ADAPTIVE ARITHMETICCODING. By-Ayush Gupta
• 2.
  CONTENT  INTRODUCTION  TAGGENRATION METHODS  ADAPTIVE ARITHMETIC CODING  COMPARISION WITH OTHER COMPRESSION TECHNIQUES
• 3.
  Introduction  Arithmetic codingis a form of entropy encoding used in lossless data compression .  It is a method of generating variable length code.  Arithmetic coding is useful when we are dealing with source with small alphabet ar binary sources.  In arithmetic coding a unique identifier used for distinguish a sequence of symbol from another sequence of symbol ,called “TAG”.  Tag value always lies between [0,1]
• 4.
  Tag Generation Methods Taggeneration in terms of binary fraction value  In this method tag value lies between [0,1] . where 0-lower limit 1- upper limit Tag generation with scaling method  In this method [0,1] divides in two parts…  [0 ,1] lower half upper half [0,0.5] [0.5,1] send-0 send-1 E1(x)=2x E2(x)=2(x-0.5)
• 5.
  Formula  Let thesequence x={x1, x2, x3, ………, xn}  Then  ln = ln-1 +(un-1 – ln-1) * fx(xn-1)  un = ln-1 +(un-1 – ln-1) * fx(xn) where n is the length of sequence xnis the nth element of sequence FinalTag value— Tx(x)=( un + ln)/2
• 6.
  Question based onfirst method..  Q. Encode the sequence “1321”/ “a1,a3,a2,a1” where Fx(1)=0.8, Fx(2)= 0.82, Fx(3)=1 Solution… “ By Marker on Board ” You’ll see it batter
• 7.
  Adaptive Arithmetic coding One an other advantages of arithmetic coding over other similar methods of data compression is the convenience of adaption.  Adaption is the changing of frequency table while processing the data.  The decoded data matches the original data as long as the frequency table is replaced in the same way and in the same step as in encoding.
• 8.
  Comparison with other compressiontechniques  Arithmetic Coding surpasses the Huffman technique in its compression ability.  The Huffman method assigns an integral number of bits to each symbol , while Arithmetic Coding assigns one long code to the entire input string.  Arithmetic coding consists of few arithmetic operations due to which its complexity is less…  O(Nlog(n)). N represents the length of the input while n represents the number of intervals present in[0, 1).