Fountain codes are a class of rateless codes well-suited for communication over erasure channels with unknown erasure parameter. We analyze the decoding of LT codes, the first instance of practical, universal Fountain codes. A set of interest during LT decoding is the set of output symbols of reduced degree one (the “ripple”). The evolution of the ripple size throughout the decoding process is ...

The rationale of product platform-based product development has been well recognized for the implementation of mass customization. A product platform refers to the conceptual structure and logical organization of product families from both customer and technical viewpoints. This paper introduces graph grammar formalisms to the representation of product platform. The concepts of multi-pointed hy...

The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP converges to a suboptimal fixed point (Kulesza & Pereira, 2008). In this work, we s...

A large family of graph-based semi-supervised algorithms have been developed intuitively and pragmatically for the multi-label learning problem. These methods, however, only implicitly exploited the label correlation, as either part of graph weight or an additional constraint, to improve overall classification performance. Despite their seemingly quite different formulations, we show that all e...

Random structures often present a trade-off between realism and tractability, the latter predominantly enabled by independence. In pioneering random graph theory, Erdős and Rényi originally studied the set of all graphs with a given number of edges, seeking to identify its typical properties under the uniform measure, i.e., the G(n,m) model of random graphs. However, this approach quickly prese...

The rationale of platform-based product configuration has been well recognized for the implementation of mass customization. A product platform refers to the conceptual structure and logical organization of product families from both customer and technical viewpoints. This provides a generic umbrella under which product configuration manifests itself through variant derivation within common pro...

This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local approach that covers a graph by small subgraphs, so-called partial star products, and then utilizes this information to derive the global factors and an embeddin...

Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments designing an experiment permit effective statistical analysis results, they encode incidence structure finite geometries, encapsulate groups and more general algebraic objects known as quasigroups, produce optimal density error-correcting codes. This paper gives some new results on graph squares...