For tree-based protocols, bit-by-bit synchronization on tag response is desired such that the reader can detect the colliding bit positions of re-ceived tag responses.
For three different thresholds (0.5, 0.6 and 0.7) the informational significant bit positions of PubChem, 198, 180, and 159 respectively, were selected using Differential Shannon Entropy implemented in IMMAN package software.
Since the focus of this work was the generation of a novel fingerprint representation that includes the main features (bit positions) of the compounds in a molecular library, the following approach, inspired on the concept and applications of SE [10, 11] was followed: Firstly, for each binary digit position of the features encoded in the MACCS keys the frequencies and probabilities were recorded.
The different categories in the database are codified in bit positions of a fingerprint as explained previously.
It is not necessary to find the bit position for the insertion of 1 s as we do for inversion of bits to get the correct sum bit (S).
The majority decoder computes the vector V ec(V) = (V1, V2,..., V n ) for a n-bit code vector, denoted by V ec(v i ) = (v i,1,v i,2,..., v i,n), where V j = majority v1, j, v2, j,..., v M,j) is the majority of 0's and 1's at each bit position j of M vectors.
In the keystream recovery, an adversary has a freedom to choose the value of J and the J-bit positions of a keystream to be restored at the ith detection.
Thus the conditional BER for the horizontal part for a particular bit position b k of M-QAM for a given imaginary part of the desired symbol xi+and the image signal x−is P ~ H ( b k ∣ x i +, x − ) = P ~ Δ ̄ < B k ∣ x i +, x −, x r + > B k P ~ Δ ̄ > B k ∣ x i +, x −, x r + < B k.
Moreover, for the succeeding values of i that is up to N/4, the inversion bit position is the sum of previous iteration value and 2. For N = 8, the values of X 1 = 5 and X 2 = 7, so the fifth and seventh bit has to be inverted in the first and second row as implemented in Figure 9.
