How did C. E. Shannon quantify information on his communication theory and cryptography theory?

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  • C. E.シャノンによる情報量概念の導入について : 通信理論と暗号理論の分析を通じて
  • C E シャノン ニ ヨル ジョウホウリョウ ガイネン ノ ドウニュウ ニ ツイテ ツウシン リロン ト アンゴウ リロン ノ ブンセキ オ ツウジテ

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C. E. Shannon formalized the concept of "the amount of information " and presented its formula H=-Σ^n_<i=1> p_i log p_i in 1940s, mainly in his paper "A Mathematical Theory of Communication ". His way of study had two progressive characteristics. Firstly, Shannon applied probability theory into his measure of information, which is more mathematically abstract and fruitful than those formalized by his precedent engineers, H.Nyquist and R.V.L.Hartley. By Shannon's expression it has been possible to measure "redundancy " and even "equivocation " which is the amount of lost information on the channel by using Bayesian probability. Secondly, Shannon regarded the discrete channel as the fundamental case and the continuous channel as its application, in spite of the fact that a continuous type was usually dealt as a basis at that time. In this point, his study of the cryptography affected his communication theory. In 1940s Shannon conducted researches on the communication theory as well as the cryptography simultaneously. Indeed "A Mathematical Theory of Communication " (1948) and his unpublished paper "The Mathematical Theory of Cryptography " (1945) have a lot of similar descriptions about the amount of information. Namely, Shannon's concept of information was influenced by both the preceding results on the communication theory and his own research on the cryptography. Boltzman's H formula seems to bear a close resemblance to Shannon's one, but any descriptions showing some direct relations between them have not been found.

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