Abstract
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources as well. Under the general assumption of discrete statistical signal sources, we propose a practical problem of sampling incomplete noisy signals for which we do not know a priori and the sampling size is bounded. We approach this sampling problem by Shannon’s channel coding theorem. Our main results demonstrate that it is the large Walsh coefficient(s) that characterize(s) discrete statistical signals, regardless of the signal sources. By the connection of Shannon’s theorem, we establish the necessary and sufficient condition for our generic sampling problem for the first time. Our generic sampling results find practical and powerful applications in not only statistical cryptanalysis, but software system performance optimization.
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Notes
- 1.
Throughout the paper, we refer to the large transform-domain coefficient d as the one with a large absolute value.
- 2.
Sometimes it’s called Shannon’s Second Theorem.
- 3.
That is, it is possible that not all the outputs are generated by sampling.
- 4.
With \(n=1\), this appears as an informal result in symmetric cryptanalysis, which is used as a black-box analysis tool in several crypto-systems.
- 5.
See [14] for most recent results on the conjecture.
- 6.
Note that current computing technology [16] can afford exascale WHT (i.e., on the order of \(2^{60}\)) within 2 years, which uses \(2^{15}\) modern PCs.
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Lu, Y.J. (2019). Walsh Sampling with Incomplete Noisy Signals. In: Arai, K., Kapoor, S., Bhatia, R. (eds) Advances in Information and Communication Networks. FICC 2018. Advances in Intelligent Systems and Computing, vol 887. Springer, Cham. https://doi.org/10.1007/978-3-030-03405-4_9
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