Decoding of NB-LDPC codes over Subfields

<div>In this paper, we present a novel method to expand a graph over a finite field into a larger one over one of </div><div>the original field’s subfields. This allows a number of different graph expansions for any given graph. </div><div>These expansions can be used in various applications, and we focus specifically on the case of decoding </div><div>NB-LDPC codes. Using the novel expanded graphs, it is possible to reduce decoding complexity of NB-</div><div>LDPC codes significantly with minimal performance losses.</div>

Decoding of NB-LDPC codes over Subfields

<div>In this paper, we present a novel method to expand a graph over a finite field into a larger one over one of </div><div>the original field’s subfields. This allows a number of different graph expansions for any given graph. </div><div>These expansions can be used in various applications, and we focus specifically on the case of decoding </div><div>NB-LDPC codes. Using the novel expanded graphs, it is possible to reduce decoding complexity of NB-</div><div>LDPC codes significantly with minimal performance losses.</div>

The Graph Expansion of an Ordered Groupoid

We generalise the Margolis-Meakin graph expansion of a group to a construction for ordered groupoids, and show that the graph expansion of an ordered groupoid enjoys structural properties analogous to those for graph expansions of groups. We also use the Cayley graph of an ordered groupoid to prove a version of McAlister's P-theorem for incompressible ordered groupoids.

PERFECT STOCHASTIC SUMMATION IN HIGH ORDER FEYNMAN GRAPH EXPANSIONS

We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.