Man has grappled with the meaning and utility of randomnessfor millennia. Randomness is paramount to many fields of sci-ence, and in particular plays a key role in information theory andcoding theory. Here we explore some key aspects of the meaningand utility of randomness in computation.

Source coding is accomplished via the mapping of consecutive source symbols (blocks) into code blocks of fixed or variable length. The fundamental limits in source coding introduces a tradeoff between the rate of compression and the fidelity of the recovery. However, in practical communication systems many issues such as computational complexity, memory capacity, and memory access requirements ...

The material covered in this thesis falls mainly in two parts. In the first part, which is found in chapter II, the foundations of source coding are considered. A careful introduction to the notion of codes for symbols, blocks and infinite sequences is given. The classical notion of a stationary ergodic source is then introduced as a natural concept arising when assuming limiting statistical co...

In this paper the quantum version of the source coding theorem is obtained for a completely ergodic source. This result extends Schumacher’s quantum noiseless coding theorem for memoryless sources. The control of the memory effects requires some earlier results of Hiai and Petz on high probability subspaces. Our result is equivalently considered as a compression theorem for noiseless stationary...

Motivated by the design of low-complexity distributed quantizers and iterative decoding algorithms that leverage the correlation in the data picked up by a large-scale sensor network, we address the problem of finding correlation preserving clusters. To construct a factor graph describing the statistical dependencies between sensor measurements, we develop a hierarchical clustering algorithm th...