複数の情報源出力を伴うシャノン暗号システムに対する符号化定理に関する研究

1.我们可以consider new coding problems for the new coding problems for thefollowing cases when we transmit a correlated source outputs (X)via Shannon's cipher system. The coding theorems for such cases cannot be derived from The known我们已经完全支持编码theorems by using the codes that can attain the commonSecret information is both X and Y, only X, which is described in 2Transmitted information is both X and Y, only Xor 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.我们可以define common information for correlated source outputs (X，Y). In this research， we give the following two new definitions of common信息，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 informationtheoretically, and we show that c_1 (X； Y)=I(X； Y) and c_2 (X； Y)=max{H(X)， H(Y)} hold。

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.