In this work, we study network coding technique, its relation to random matrices, and their applications to communication systems. The dissertation consists of three main contributions. First, we propose efficient algorithms for data synchronization via a broadcast channel using random network coding. Second, we study the resiliency of network coding based large distributed systems via characterization of minimum rank recovery of random matrices over finite field. Third, we propose a novel Location Assisted Coding technique to manage interference and increase capacity in Free Space Communication (FSO) systems. In the data synchronization problem, we assume there is a sender who broadcasts a set of packets to a number of receivers. Each receiver is assumed to have a random partial set of the desired packets. The goal is to devise network coding algorithms to minimize the number of packets transmitted by the sender until all the receivers successfully receive the entire set of packets. We establish probabilistic bounds and asymptotic results on the minimum number of transmitted packets for three randomized algorithms. In the minimum rank decoding problem, the goal is to recover the network coded packets from a malicious attacker who randomly corrupts the header of the packets with limited magnitude errors. We cast this problem as the problem of rank recovery of random matrices over finite field in presence of noise. We present some initial asymptotic results on joint distribution of weight and rank of random matrices for simple models which are useful for the rank recovery problem. We show that limited magnitude noise is likely not to decrease the rank of low-rank matrices with uniformly distributed weights. Finally, we show that the proposed LAC technique can increase throughput and reduce interference for multiple users in a dense array of FSO femtocells. Our theoretical analysis and numerical experiments show orders of magnitude increase in throughput using LAC over traditional approaches.