Coding Theorem for Secret Sharing Communication Systems with Two Noisy Channels
Hirosuke Yamamoto
IEEE Trans. on Information Theory, Vol. 35, No3, pp.572-578, MAY.1989
- The coding theorem is proved for the secret sharing communication system (SSCS) with two noisy channels, each of which is a broadcast channel characterized by $P(y_jz_j|x_j)$,$ j=1,2;$. It is assumed that the legitimate channel $(X_j \rightarrow Y_j)$ is less noisy than the wiretapped channel $(X_j \rightarrow Z_j)$. The code $(f,\phi)$ for the SSCS is defined by two mappings: $(X_1^{N_1},X_2^{N_2})=f(S^K, T)$ and $\hat{S}=\phi(Y_1^{N_1},Y_2^{N_2})$ where $T$ is an arbitrarily chosen random number and $S$ is an independent identically distributed source output that must be transmitted to the lejitimate receiver with an arbitrarily small error. The rate of each channel is given by $N_j/K$ while the security level for each wiretapper can be evaluated by $(1/K)H(S^K | Z_j^{N_j}). The admissible region of rates and security levels is given by a ''single-letter characterization.
- DOI:10.1109/18.30979