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In this paper, we investigate the attainable performance of quasi-cyclic (QC) protograph low-density parity-check (LDPC) codes for transmission over both additive white Gaussian noise and uncorrelated Rayleigh channels. The presented codes are constructed using the Vandermonde matrix and thus have a girth of at least six in their corresponding Tanner graph. Furthermore, they also benefit from both low-complexity encoding and decoding, low memory requirements, as well as hardware-friendly implementations. Our simulation results demonstrate that the advantages offered by this family of QC protograph LDPC codes accrue with no compromise in the attainable bit error ratio (BER) and block error ratio (BLER) performances. In fact, it is also shown that despite their implementational benefits, the proposed codes exhibit slight BER/BLER gains when compared to some of their more complex counterparts of the same length.