 Hello everyone. I am Mr Praveen Yalapa Kumbar. Today we want to see arithmetic coding. The learning outcome of this topic is at the end of the session, students will be able to explain the concept of arithmetic coding in multimedia communication techniques. The contents of this topic are introduction and arithmetic encoding procedure. The arithmetic code is an efficient code because when we increase the size of the message, the half-month code becomes inefficient at this case. In order to overcome this drawback, we are going for arithmetic coding. Arithmetic coding is a stream-based encoding. Arithmetic coding is used in the lossless data compression. Arithmetic coding is a non-block code means the arithmetic code does not generate individual codes for each character, but performs the arithmetic operation on block of data based on the probabilities of the next character. It works very well for the sequence with low entropy. Now arithmetic encoding procedure. Now we want to see the procedure steps. First step, divide the numeric range 0 to 1 into number of different symbols present in the message. Second, expand the first letter to be coded along with the range further subdivide this range into number of symbols. Now third step is repeat this procedure until the termination character is encoded. Now we want to see one example. Consider the transmission of a message PRPO comparing a string of character with probabilities P is equal to 0.5, R is equal to 0.25 and O is equal to 0.24. Now if you observe in this example here is a transmission characters as well as the probabilities of each character is present here. But in some cases they are provided only the transmission character. Now from that character you have to calculate the probabilities. Now how we calculate the probabilities? First we want to understand. Here if you observe these characters how many characters are present? 1, 2, 3, 4. Therefore total 4 characters are present. Now I want to calculate the probability of character P. So therefore how many character of P present? 2. Therefore the probability of P is equal to 2 by 4 that is 0.5. In the same way we want to calculate the probability of R as well as the probability for O. Now calculation of a probability of R is how many symbols are present of R in this character? There is only one symbol. Therefore the probability of R is 1 by 4 that is 0.25. Now for the same way we have to calculate the probability of O that is 1 by 4 is 0.25. Now from that previous example I made one table that is a symbol and their respective probabilities. Now for the P we have to calculate the probability 0.5. For the R we calculate 0.25 and for the O we calculate 0.25. Now everyone pause the video and recall what is the first step of arithmetic coding. Now first step is divide the numeric range 0 to 1 into the number of different symbol present in the message. Now why I want to divide this numeric range 0 to 1? Because if you observe in this table I want to calculate the probabilities. And the properties of probabilities that the probabilities always lies between 0 to 1. Therefore we divide this symbol into the 0 to 1. Now I want to show with the help of this diagrammatic representation the divide of these symbols as this is a 0 to 1 I want to divide. After that one the probability of P is 0.5 therefore P is present at here 0.5. The location of R is present after the P at 0.25. Therefore it becomes from 0 it becomes 0.5 plus 0.25 that is 0.75 that is R. And after that one O is present in between 0.75 to 1. In this way I divide 0 to 1 this symbols P is present at 0 to 0.5. R is present from 0.5 to 0.75 and O is present from 0.75 to 1. Now second rule expand the first letter to be coded along with the range further subdivide this range into the number of symbols. Now we want to do one by one. Now this one we calculated the previously. Now according to the second rule again I want to divide this subdivide this P symbol. Again I divide this P symbol before the divide of that P symbol there is some mathematical formulation we want to see. We want to calculate the first D. D is a difference that is upper band minus the lower band and for P the D calculation is 0.5 minus 0 that is 0.5. Now after that one I want to calculate range of symbol in terms of P that is formula is lower limit tends to lower limit plus D into probability of symbol. Now putting this values into the above equation we get range of symbol that is P is lower limit is 0 tends to lower limit 0 plus D is 0.5. Probability of symbol is 0.5 therefore it will become as 0 to 0.25. Again I want to calculate range of symbol of R in for the P subdivision. So therefore putting the values into the above formulas we get 0.25 is to 0.375. Now after putting the values of O we get range of the symbol O in terms of P subdivision we get 0.375 to 0.5. Now we want to show with the help of this diagrammatic representation subdivide of P. This is the overall subdivision of a P. Now we have to calculate the previous slide this is the value of D. Again I want to see the range for the symbol in this case for P is 0 to 0.25 that I want to show here. So P is 0 to 0.25. Then afterwards you have to calculate the range of symbol R that is 0.25 to 0.375 that is 0.2 to 0.375 is R. Then again I have to calculate the range of O that is 0.375 to 0.5 that is the O symbol. Now here I want to calculate for subdivide of R. Again use the same formula which has to use for division for P. Here again the D for upper band minus lower band in this case D is 0.375 minus 0.25 that is 0.125. Again I am using same formula range of symbol and the division of P RO I want to calculate for the range of E symbol. The range of symbol for the P is 0.25 to 0.25 plus 0.125 into 0.5. These values put into this above equation we get range of symbol P is 0.25 to 0.312. Again I want to calculate the range of symbol of R we get 0.3125 to 0.343. Again I want to calculate the range of symbol for O we get 0.343 to 0.375. Now if you observe the calculation of symbol R and symbol O here lower limit always taken as the higher of the previous one means what? Here the lower limit for the R is 0.3125 but it is the higher band of the P that is 0.312. Again for the range of symbol O the lower limit is 0.343 but it is the higher range of the R that is 0.343. Now I want to show with the diagrammatic representation of a subdivide of symbol R. So we have to calculate this one in the previous slide that is D is 0.125. It is a range of symbol for the P that we calculated 0.25 to 0.312 this one. The range of symbol of R is 0.3125 to 0.343 and again the symbol of range of symbol for the O is 0.343 to 0.375. Now further I want to again divide this one for P because in our question we want to divide P or PO now third bit is again P. Now again you have to calculate for D that is upper band minus lower band that is 0.062. After that one this is a range of symbol formulas put the values into this equation we get range of symbol for the P that is 0.25 to 0.28. Now range of symbol R that is 0.28 to 0.296. Again the range of symbol O after the calculation of this one we get 0.296 to 0.312. Now we want to show the subdivision of P symbol with the diagrammatic representation as the P is 0.25 to 0.28. R is 0.28 to 0.296 and O is 0.296 to 0.312. Now after that one the last symbol is O now I want to subdivide this is O. But if you observe in the question that is a P or PO the last word is O then you don't require again subdivide this O symbol. You simply calculate the tag for the tag you have to remember the range of the last symbol. Here last symbol is O the range of O is 0.296 to 0.312. Therefore O is range from 0.296 to 0.312. Therefore tag is the average of two numbers. Therefore the tag for the O is 0.312 plus 0.296 divided by 2 that is 0.304. The references for this topic is thank you.