This paper investigates the potential of non-binary LDPC codes to replace widely used Reed-Solomon (RS) codes for applications in communication and storage systems for combating mixed types of noise and interferences. The investigation begins with presentation of four algebraic constructions of RS-based non-binary quasi-cyclic (QC)-LDPC codes. Then, the performances of some codes constructed based on the proposed methods with iterative decoding are compared with those of RS codes of the same len