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Creative fuel. Show What You Know. Plan Your Free Online Education at Lifehacker U: Spring Semester 2012. Theory of Data Compression. Theory of Data Compression Contents I. Introduction and Background In his 1948 paper, ``A Mathematical Theory of Communication,'' Claude E.
Shannon formulated the theory of data compression. Shannon established that there is a fundamental limit to lossless data compression. Shannon also developed the theory of lossy data compression. When the compression is lossless (i.e., no distortion or D=0), the best possible compression rate is R(0)=H (for a finite alphabet source). Lossless data compression theory and rate-distortion theory are known collectively as source coding theory. II. Imagine that you go to the library. Mathematically, the book you select is denoted by where represents the whole book, represents the first character in the book, represents the second character, and so on. , is defined to be the set of all 27 possible values of the characters: Now put yourself in the shoes of the engineer who designs the compression algorithm. Are random variables which take values on the alphabet.