This section presents the simulation results along with discussions for the proposed method on a MATLAB environment. The derived upper bound on Pb is sketched in Fig. 2, for 2000 samples and for various Hamming codes by assuming Pb;thr = 10^5, SNR = 15 (dB).
It is observed that the upper bound becomes tighter and rises by increasing the m for Hamming codes.
Accordingly, because of the simplicity and low complexity, the bound is not tight for small Hamming codes. Nevertheless, in dense networks where pre-selection is more important, the bound provides sufficient accuracy.
The satisfactory performance of the bound can also be justified by comparing the curves for different codes values. This upper can be obtained from (2).
Given the upper bound on Pb we may proceed to find the upper bound of Hamming codes. Table 1 shows the exact values of Pb for different required Hamming codes. It is clear that the upper bound bids realistic values for these predetermined Hamming codes. As shown in Fig. 3, we can see the probability of selection of the Hamming codes inside the WSNs.
According to (3) and these probabilities, R = 0.78 has been obtained. On the other hand, the calculation of P has been set to 0.007. Since in the case of static code, (15; 11) of Hamming codes should be selected and R0 = 11/15 = 0:73. So, we have \eta = 1.06 using Eq. (5), which means that 6% improvement has been seen by the proposed algorithm using Hamming codes.
As shown in Fig. 3, the probability of selection for Hamming (63,57) is set to 0 and has not been chosen by this scope.