Petak, 6.02.2015. u 14:00h, sala 301f, MI SANU
Dr. Bane Vasic, Univerzitet u Arizoni, Katedra za elektroniku i racunarstvo, Katedra za matematiku, Tuson, Arizona, SAD
GOOD DEEDS DUE TO FAULTS: FAULT-RESILIENT DECODERS AND MEMORIES MADE OF UNRELIABLE COMPONENTS

Abstract: In this talk we present our recent results in iterative decoders of low-density parity check codes made of unreliable logic gates. Such codes ensure reliable transmission and storage of information in computer chips made in nano-technologies, but unlike von Neumann approach, they guarantee an arbitrarily low probability of bit error while with only finite redundancy. We show evidences that probabilistic behavior of a decoder due to unreliable components can be exploited to our advantage and lead to an improved performance and reduced hardware redundancy. We provide examples of such decoding algorithms and give an explanation of this seemingly counter-intuitive behavior following from our insights in iterative decoding dynamics. Iterative decoding can be viewed as a recursive procedure for Bethe free energy function minimization, and the randomness in a message update may help the decoder to escape from the local minima. The decoder operates in a stochastic gradient descent fashion, but the random perturbations do not require any additional hardware as they are built-in the faulty hardware itself. Thus the decoder harvests good deeds of logic gate faults.

KORIST USLED KVARA: DEKODERI I MEMORIJE OTPORNI NA OTKAZE KOMPONENTI

Rezime: U ovom predavanju, predstavicemo nove rezultate u oblasti iterativnog dekodera low-density parity check codes sacinjenih od nepouzdanih logickih kola. Ovakvi kodovi obezbedjuju pouzdani prenos i memorisanje informacije u racunarskim cipovima napravljenim u nanotehnologijama, ali za razliku od von Neumann-ovog pristupa, oni garantuju proizvoljno malu verovatnocu greske po bitu zahtevajuci samo konacnu redundansu. Prikazacemo nove dokaze da se stohasticka priroda dekodera usled nepouzdanosti njegovih komponenti moze iskoristiti za poboljsanje rada dekodera uz smanjenu hardversku kompleksnost. U radu cemo dati primere algoritama dekodovanja sa ovakvim kontraintuitivnim ponasanjem koji su izvedeni iz uvida u dinamiku procesa iterativnog dekodovanja. Naime, iterativno dekodovanje se moze posmatrati kao minimizacija funkcije Bethe slobodne energije, a stohastika u formiranju poruka moze pomoci dekoderu da izadje iz lokalnog minimuma. Dekoder radi kao stohasticki gradientni algoritam, ali slucajne perturbacije ne zahtevaju nikakav dodatni hardver zato sto vec postoje u samom hardveru. Na taj nacin dekoder ubira plodove kvarova u svojim komponentama.

Petak, 20.02.2015. u 14:00h, 301f MI SANU
Professor Todor Gramchev, University of Cagliari
ISOTROPIC AND ANISOTROPIC SHUBIN TYPE OPERATORS OVER GELFAND SHILOV SPACES AND THE WEYL FORMULA

Abstract: Old an new classes of Gelfand Shilov spaces (isotropic and anisotropic) will be presented as a basis for bisingular type pseudodifferential operators. The counting function for the elliptic positive Shubin type bisingular operators will be explained.

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