Analysis of Probability of Error and Layered Secrecy Sample Clauses

Analysis of Probability of Error and Layered Secrecy. By symmetry, we may assume without loss of generality that Xxxxx sends the messages M0 = M1 = M2 = 1 using L1 = L2 = 1. Consider the following probabilistic events, GA = {(Xn(1), Xn(1, 1), Xn(1, 1, 1)) ∈/ Aδ1 (pX ,X ,X )} (204) and DB,0 = {Mˆ0 ƒ= 1} (205) DE1,0 = {M˜0 ƒ= 1} (206) DE2,0 = {M˘0 1} (207) DB,1 = {Lˆ1 ƒ= 1} (208) ˜ DE1,1 = {L1 ƒ= L1} (209) DB,2 = {Lˆ2 ƒ= 1} (210) ≡ |X ||X | with δ1 δ/(2 1 2 ), where the notation Ds,j indicates the decoding error of Receiver s with respect to the layer-j message. We also consider the secrecy violation events, A1 (211) E 2 n 2 2 SE ,1 ={ σ − σ˘En > δ} A1,A2 A1 1 2 (212) EnE EnE SE E ,2 ={ σ n − σ˜ n > δ} where we have denoted the averaged output states by σ˘BnEnEn = 2ΣnR˜1 2ΣnR˜2 σ n n A1,A2 BnE E (213) and
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