Construction of New Finite Geometry Non-Binary LDPC Codes With Reduced Alphabets

The finite Euclidean and Projective geometry codes are the most known among One-Step Majority-Logic Decodable codes that are Low-Density Parity-Check codes as well. Unfortunately, these codes are rare, and we do not have a great diversity when designing communication systems with a fixed code-length and code rate. Regarding the non-binary Euclidian and projective geometric Codes, each code is restricted to a unique alphabet. To offer a bigger range of possible alphabets for each code, we propose new construction by redefining the incidence vector of the lines of Euclidean and projective geometries over finite fields. This approach leads to an enrichment of the class of EG and PG codes. An error performance study of some new codes has been carried out and shows good results.