| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Research Abstract |
We obtained the following results for this research.
1. We can consider new coding problems for the following cases when we transmit a correlated source outputs (X, Y) via Shannon's cipher system. The coding theorems for such cases cannot be derived from the known results. We have perfectly proved the coding theorems by using the codes that can attain the common information, which is described in 2.
・ Secret information is both X and Y, only X, or only Y.
・ Transmitted information is both X and Y, only X, or only Y.
・ Security of the system is measured by 1/H(X^KY^<K >|W)or(1/H(X^K|W), 1/H(Y^K|W)).
2. We can define common information for correlated source outputs (X, Y). In this research, we give the following two new definitions of common information, which are different from the known ones (i.e., Gacs-Korner's or Wyner's common information).
(a) C_1(X ; Y) : The rate of the attainable minimum core of (X^K, Y^K) by removing each private information from (X^K, Y^K) as much as possible.
(b) C_2(X ; Y) : The rate of the attainable maximum core of V_C such that if we lose V_C, then each uncertainty of X^K and Y^K becomes H(V_C).
We evaluate these two common information theoretically, and we show that C_1(X ; Y)=I(X ; Y) and C_2(X ; Y)=max{H(X), H(Y)} hold.
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