Quasi-cyclic low-density parity-check (QC-LDPC) codes are a 0cm 0cm 0pt; LINE-HEIGHT: 115%; TEXT-ALIGN: justify" are based on constructing parity-check matrices that are arrays of circulant permutation matrices . We show that finite fields can be used effectively to construct of arrays of circulant permutation matrices and zero matrices as parity-check matrices of QC-LDPC codes . The construction methods give codes without cycles of length four in their Tanner graphs . The fact that these cycles are naturally eliminated in the constructions allows the code designer to concentrate more on improving the performance and lowering the error floor of the constructed codes . The thesis is organized as fallows : Chapter 1 gives a brief introduction of QC-LDPC codes , including the definitions of parity-check and generator matrices in circulant forms and basic structure . Chapter 2 contains several structured QC-LDPC codes; a construction is presented by multiplicative group of finite field F q Corresponding to the cyclic subgroup of greatest prime factor of q-1 in F q , a method constructing a QC-LDPC code is given , and also for prime field F q a method is given to construct binary LDPC codes . In all these constructions , it is shown that the base matrices satisfy the four-cycle free property know as (RC)-constraint . We also introduce a method known as Masking method . The Masking operation can be mathematically formulated as a special case of matrix product operation . By Masking , we present a This construction gives base matrices satisfying the (RC)-constraint . The elements in these matrices are then replaced by binary or non-binary circulant to form parity-check matrices of binary or non-binary QC-LDPC codes , respectively . This construction generate binary and q-ary QC-LDPC codes with high rates. Experimental results show that the constructed codes perform very well over the additive white Gaussian noise channel when decoded with iterative decoding based on sum-product algorithm .