LDPC convolutional codes are defined by sparse parity check matrices, analogous to LDPC block codes, and they can be decoded by iterative message-passing algorithms. LDPC convolutional codes have the capability of attaining good efficiency. Two main methods have been introduced for making these codes. The first construction method has been introduced by Michael Tanner . This method is based on parity check matrix of a quasi cyclic LDPC block code. The second method has been introduced by Jimenez-Feltstorm and Zigangirov . This method is based on unwrapping of parity check matrices of LDPC block codes. In this thesis a code consruction method called graph-cover method is introduced and an algebraic representation of it is provided. Using graph-cover, we study the relationship between two basic construction methods for LDPC convolutional codes. Using the same approach a method based on graph-cover is presented for deriving time-varying LDPC convolutional codes from LDPC block codes. Some LDPC convolutional codes resulted in from this method have remarkable efficiency comparing to the underlying LDPC block codes. This efficiency improvement (LDPC convolutional codes compared to background LDPC block codes) is called “convolutional gain”. Some aspects of this gain are reviewed here.