<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 non-binary low-density parity-check (NB-LDPC) codes can offer promising performance advantages but suffer from high decoding complexity. To tackle this challenge, in this paper, we consider NB-LDPC codes over finite fields as codes over subfields as a means of reducing decoding complexity. In particular, our approach is based on a novel method of expanding a non-binary Tanner graph over a finite field into a graph over a subfield. This approach offers several decoding strategies for a single NB-LDPC code, with varying levels of performancecomplexity trade-offs. Simulation results demonstrate that in a majority of cases, performance loss is minimal when compared with the complexity gains.