Network coding and function computation: We investigate the maximum rate at which a given function of a set of source messages can be computed at a fusion node in an arbitrary acyclic, noiseless network. After appropriately defining the computing capacity, we obtained lower and upper bounds on the capacity for several classes of functions and compare the tightness of these bounds. We also investigated the performance of linear codes for computing different classes of functions. In an ongoing work, we consider computing linear functions of source messages. In an another independently line of work, we studied scaling laws for optimally computing symmetric functions over binary symmetric channels. Random matrices over finite fields: We investigate the necessary and sufficient size of a finite field F for a random matrix A over F to be such that every submatrix of A is full rank with probability approaching 1. Sequence generation for CDMA: We consider the problem of constructing generalized zero-correlation sequences for code division multiple access as well as generating complete Golay complementary sequences from Reed-Muller codes. |