Chapter Questions
How many bits/character are generally required for simple text files?
Why are there so many extensions of the 7-bit ASCII character set?
A book has 900 pages. Assume that each page contains on average 40 lines, and each line contains 75 characters. What would be the file size if the book is stored in digital form?
What are the main principles of the text compression techniques?
Justify the inverse logarithmic relationship between the information contained in a symbol and its probability of occurrence.
Why is entropy a key concept in coding theory? What is the significance of Shannon's noiseless coding theorem?
Calculate the entropy of a 5-symbol source with symbol probabilities $\{0.25,0.2$, $0.35,0.12,0.08\}$.
Show that the first order entropy of a source with alphabet-size $K$ is equal to $\log _2 K$ only when all the symbols are equi-probable.
Design a Huffman table for the information source given in Example 6.2. Show that the average bit-rate is $1.41 \mathrm{bits} / \mathrm{symbol}$.
How many unique sets of Huffman codes are possible for a three-symbol source? Construct them.
An information source has generated a string "AbGOODbDOG" where the symbol "b" corresponds to a blank space. Determine the symbols you need to represent the string. Calculate the entropy of the information source (with the limited information given by the string). Design a Huffman code to encode the symbols. How many bits does the Huffman coder need on average to encode a symbol?
How many distinct text files are possible that contain 2000 English letters? Assume an alphabet size of 26.
Consider the information source given in Example 6.2. Determine the sub-interval for arithmetic coding of the string "abbbc".
Repeat the above experiment with an arithmetic coder.
Why do we need a special EOF symbol in arithmetic coding? Do we need one such symbol in Huffman coding?
Show that Huffman coding performs optimally (i.e., it provides the bit-rate identical to entropy of the source) only if all the symbol probabilities are integral powers of $1 / 2$.
Explain the principle of dictionary-based compression. What are the different approaches in this compression method?
Explain sliding window-based compression technique. Consider the text string "PJRKTYLLLMNPPRKLLLMRYKMNPPRLMRY". Compress the file using the sliding window of length 16 and a look-ahead window of length 5.
Explain the LZ78 compression method. Encode the sentence "DOG EAT DOGS".
Compare the LZ77 and LZ78 compression technique?