Information Complexity and the Quest for Interactive Compression (A Survey)

Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open problems in communication complexity and circuit complexity. A notable achievement of information complexity is the breakthrough in understanding of the fundamental direct sum and direct product conjectures, which aim to quantify the power of parallel computation. This survey provides a brief introduction to information complexity, and overviews some of the recent progress on these conjectures and their tight relationship with the fascinating problem of compressing interactive protocols

Communication for Generating Correlation: A Unifying Survey

The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of communication, into perfectly shared uniform random variables. Such perfect shared randomness, in turn, enables the solutions of many tasks. Even the reverse conversion of perfectly shared uniform randomness into variables with a desired form of correlation turns out to be insightful and technically useful. In this survey article, we describe progress-to-date on such problems and lay out pertinent measures, achievability results, limits of performance, and point to new directions.Comment: A review article to appear in IEEE Transactions on Information Theor