In this thesis we present a Due to the property of both QC LDPC codes and SC LDPC codes, in this thesis we addressed the construction of SC LDPC codes with a QC structure, over arbitrary finite fields; these codes are called SC QC LDPC codes. A natural method of constructing SC QC LDPC codes is to unwrap a QC LDPC block code. The unwrapping construction can preserve many structural properties of the underlying block code, such as the girth and the minimum distance; however unwrapped SC QC LDPC block codes could start to show error floors at a block error rate (BLER) of 10^{-2}, which is the operating LER of many wireless communication systems. So this is undesirable for practical applications since the throughput of many communication systems is determined by the BLER. For solving this problem the replicate and mask (R M) construction of finite length spatially coupled LDPC codes is proposed. The crux of the R M construction is replicating the parity check matrix of an LDPC block code and masking it with a designed masking matrix this construction generalizes the conventional matrix unwrapping construction and contains it as a special case and result in a much larger Compared to the conventional unwrapping approach, the proposed R M construction provides more flexibility in the selectio of the code parameters, such as the rate and degree distributions and the optimization of the constructed codes. The R M SC LDPC codes can also be guaranteed to have certain girth properties. We illustrate the R M construction of different SC QC LDPC codes by some examples. In addition belief propagation decoding algorithm for finite length LDPC codes over BEC channel and one algorithm for decoding infinite length LDPC convolutional codes, which is called window decoding, are studied in this thesis. Also the girth, rank and time varying periodicity of the proposed R M SC QC LDPC codes are analyzed. The error rate performance of finite length binary and nonbinary algebraic SC QC LDPC codes is investigated with window decoding. Spatially coupled construction reduces the rate of convolutional codes generated from base block code. It is shown that low complexity regular puncturing schemes can be deployed on these codes to construct families of rate compatible irregular SC QC LDPC codes with good performance.
