Friday, October 29, 2010

The Ghost of Fractals Past

There I was minding my own business, which in this particular case happened to be a classic paper by Peter Elias (P. Elias, "Coding for two noisy channels", Proc. Third London Symposium on Information Theory, The Royal Institution, London, September 12-17, 1955), when one B. Mandelbrot made an unexpected appearance. It was in the "Discussion" section appended to the end of the paper:

B. MANDELBROT: Some of Dr. Elias' results can be deduced by continuing the argument of Feinstein (cf. Mandelbrot, Ann. Telecomm., June 1955). I should like to ask Dr. Elias if he can say more about the relationship between Feinstein's work and random coding.

P. ELIAS in reply: [...] Dr. Mandelbrot's question is difficult to answer briefly, but in general Feinstein's work may be considered as random coding operating under constraints. These constraints do not reduce channel capacity, nor do they alter the exponent in the exponentially decreasing error probability, so far as the leading term for rates very near channel capacity is concerned. However, they do increase the error probability for somewhat lower transmission rates compared with what unconstrained random coding can do.

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