Re: Compressed/Encrypted Voice using Modems
Shannon didn't consider intersymbol interference.
Sure he did. That's why the bandwidth term appears in his channel capacity equation. Shannon built on and generalized Nyquist's earlier work. Shannon's law says only that it is theoretically *possible* to signal over a bandlimited AGWN channel with specific bandwidth and S/N ratio with arbitrarily low error as long as the signalling speed is less than the channel capacity as given by his formula. What it doesn't show is *how* to do it. In this respect, Shannon's law is much like the 2nd law of thermodynamics; it tells you how efficient you can make a heat engine in theory, but it doesn't tell a turbine designer how to shape his blades. By the way, just to bring this back to crypto, everyone should be aware that not only did Claude Shannon establish modern information theory, he also wrote a seminal paper that established much of modern cryptography. It was originally written during WWII and classified at that time, but it was declassified soon after the war and appeared in the BSTJ in 1948, I believe. Probably the most well known aspect of this paper is his discussion of "product ciphers", whereby you can combine different ciphers that are by themselves relatively weak (substitution and permutation, which he calls "confusion" and "diffusion") and produce a far more powerful cipher. DES is based on this principle, as are other modern ciphers. I bet this is one paper that the NSA wishes had never been declassified. Far more important, in my opinion, than anything by Friedman. Phil
Shannon didn't consider intersymbol interference.
Sure he did. That's why the bandwidth term appears in his channel capacity equation.
(stuff deleted) I was probably being unclear. According to my text, Shannon's capacity formula does not account for intersymbol interference. My text also states that Nyquist used intersymbol interference as a limit in his 2-bit rule. I'm considering my text to be correct, because the capacity formula doesn't account for the imperfections (like intersymbol interference) and other problems encountered in practice (envelope delay distortion, the need for echo cancell- ation, etc.). And in your words, it says that you can, but it doesn't say how. For those who just tuned in, intersymbol interference refers to when the residual tail or bounce of a dying pulse interferes with a subsequent pulse.
By the way, just to bring this back to crypto, everyone should be aware that not only did Claude Shannon establish modern information theory, he also wrote a seminal paper that established much of modern cryptography.
Not only that, he was single handedly responsible for the 15 minute delay rule in reporting stock market transactions. Evidently he applied information-theoretic techniques to the data and was able to make a load of money at it. I have no references on this, and would love to see some. Eric
participants (3)
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Eric Hughes
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Phiber Optik
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Phil Karn