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Fig. 16 The results of randomness measurement using the perfectly scrambled LDPC and the proposed JID scheme at 0 and 2 dB region.
Therefore, ({P_{m}^{i}}) is the bit error probability for each position when e≠0. Figure 16 shows the results of randomness measurement (the entire distribution of errors) of the final decoded message (hat {U}_{E}) with errors for the perfectly scrambled LDPC and the proposed JID scheme.
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Furthermore, given the sufficient randomness of the Gaussian random measurement matrix elements, the reconstruction performance of the five reconstruction algorithms under the Gaussian random measurement matrix are better than those under the Bernoulli random measurement matrix.
Gaussian random measurement matrix is the most commonly used measurement matrix, and its elements have enough randomness to satisfy the design requirement of measurement matrix in CS.
In the following Bernoulli random measurement matrix, if the elements are simple and few elements are generated by Eq. (1) at low compression ratios; therefore, the elements have enough randomness.
The randomness measures are 250 p-values.
Due to the randomness of measurement matrix Φ, all the experiment results are the mean value of ten times computations.
Each such observed value is determined by a mixture of different factors, including the previous expression level of the gene, the activity of its regulators, decay of mRNA transcripts, randomness, and measurement errors.
The key point here, then, is that the randomness between measurements across nodes is based on the localization of the source, which is precisely what we wish to observe.
(We also tested the ML approach on a different data set of 4 measurements which was created without randomness in the measurement times: the ML approach performed much better in this case since the estimated parameters varied around the true values; data not shown).
Randomness resulting from measurement errors and fuzziness resulting from system fuzziness are two different kinds of uncertainty.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com