Paulo Elias

Elias George Hall

3 Elias-bassalygo Theorem

Problem Set 1 is due next Wednesday. 2 Overview Today we will do the following. • Prove the Elias-Bassalygo-Johnson Bound introduced in the previous lecture. Recall that the proof consists of the two lemmas described roughly below – List decodable codes have poor rate. – Good error correcting codes are nicely decodable. • Introduce some algebraic codes along with some helpful idea from algebra....

Dynamic Elias-Fano Representation

We show that it is possible to store a dynamic ordered set S(n, u) of n integers drawn from a bounded universe of size u in space close to the information-theoretic lower bound and yet preserve the asymptotic time optimality of the operations. Our results leverage on the EliasFano representation of S(n, u) which takes EF(S(n, u)) = ndlog u ne+ 2n bits of space and can be shown to be less than h...

Elias Phocas MD (1930-2012)

We recently said our last goodbye to Elias Phocas, a distinguished gastroenterologist, teacher and friend. He faithfully and selflessly served Hellenic Gastroenterology for decades in a wide array of positions, including the Presidency of the Hellenic Society of Gastroenterology, and Presidency of the Panhellenic Gastroenterology Congress. The manner in which Elias practiced gastroenterology se...

Lecture 6 : The Elias - Bassalygo Bound

We currently know the following four bounds on rate as a function of relative distance, three of them upper bounds (which tell us what rate-distance combinations are impossible), and one lower bound (which tells us what rate-distance combinations we can achieve). In the following, R is the rate and δ the relative distance of a code. For example, a (n, k, d) code has R = k/n and δ = d/n. Hq(x) i...