On the achievable rates of sources having a group alphabet in a distributed source coding setting

We consider the problem of compression via homomorphic encoding of a source having a group alphabet. This is motivated by the problem of distributed function computation, where it is known that if one is only interested in computing a function of several sources, then one can at times improve upon the compression rate required by the Slepian-Wolf bound. The functions of interest are those which could be represented by the binary operation in the group. We first consider the case when the source alphabet is the cyclic Abelian group, Zpr. In this scenario, we show that the set of achievable rates provided by Krithivasan and Pradhan [1], is indeed the best possible. In addition to that, we provide a simpler proof of their achievability result. In the case of a general Abelian group, an improved achievable rate region is presented than what was obtained by Krithivasan and Pradhan. We then consider the case when the source alphabet is a non-Abelian group. We show that if all the source symbols have non-zero probability and the center of the group is trivial, then it is impossible to compress such a source if one employs a homomorphic encoder. Finally, we present certain non-homomorphic encoders, which also are suitable in the context of function computation over non-Abelian group sources and provide rate regions achieved by these encoders.

On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.

Setting up Multilingual Information Repository: A case Study with EPrints.org Software

Today 80 % of the content on the Web is in English, which is spoken by only 8% of the World population and 5% of Indian population. There is wealth of useful content in the various languages of the world other than English, which can be made available on the Internet. But, to date, for various reasons most of it is not yet available on the Internet. India itself has 18 officially recognized languages and scores of dialects. Although the medium of instruction for most of the higher education and research in India is English, substantial amount of literature by way of novels, textbooks, scholarly information are being generated in the other languages in the country. Many of the e-governance initiatives are in the respective state languages. In the past, support for different languages by the operating systems and the software packages were not very encouraging. However, with the advent of Unicode technology, operating systems and software packages are supporting almost all the major languages of the world that have scripts. In the work reported in this paper, we have explained the configuration changes that are needed for Eprints.org software to store multilingual content and to create a multilingual user interface.

Multiple garnet growth in garnet-kyanite-staurolite gneiss, Pangong metamorphic complex, Ladakh Himalaya: New constraints on tectonic setting

Garnet-kyanite-staurolite gneiss in the Pangong complex, Ladakh Himalaya, contains porphyroblastic euhedral garnets, blades of kyanite and resorbed staurolite surrounded by a fine-grained muscovite-biotite matrix associated with a leucogranite layer. Sillimanite is absent. The gneiss contains two generations of garnet in cores and rims that represent two stages of metamorphism. Garnet cores are extremely rich in Mn (X(Sps) = 0.35-038) and poor in Fe (X(Alm) = 0.40-0.45), whereas rims are relatively Mn-poor (X(Sps) =0.07-0.08), and rich in Fe (X(Alm), = 0.75-0.77). We suggest that garnet cores formed during prograde metamorphism in a subduction zone followed by abrupt exhumation, during early collision of the Ladakh arc and Karakoram block. The subsequent India-Asia continental collision subducted the metamorphic rocks to a mid-crustal level, where the garnet rims overgrew the Mn-rich cores at ca. 680 degrees C and ca. 8.5 kbar. PT calculations were estimated from phase diagrams calculated using a calculated bulk chemical composition in the Mn-NCKFMASHT system for the garnet-kyanite-staurolite-bearing assemblage. Muscovites from the metamorphic rocks and associated leucogranites have consistent K-Ar ages (ca. 10 Ma), closely related to activation of the Karakoram fault in the Pangong metamorphic complex. These ages indicate the contemporaneity of the exhumation of the metamorphic rocks and the cooling of the leucogranites. (C) 2011 Elsevier B.V. All rights reserved.