Abstract
In this thesis, we investigate and analyze the performance of two algebraic constructions of low-density parity-check codes. They are Margulis codes [18] and Ramanujan-Margulis codes [19], [9], [29]. By a random search method, we obtain Margulis codes with larger girths. We also describe a method to construct irregular codes based on these two algebraically constructed codes. They have better performance than randomly constructed codes. They also outperform PEG codes in low SNR region.