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In this paper the low density party check (LDPC) codes used in the IEEE 802.16 standard physical layer are studied, and two novel techniques to enhance the performance of such codes are introduced. In the first technique, a novel parity check matrix for LDPC codes over GF(4) with the non-zero entries chosen to maximize the entropy is proposed, the parity check matrix is based on the binary parity check matrix used in the IEEE 802.16 standard. The proposed code is proven to outperform the binary code used in the IEEE 802.16 standard over both additive white Gaussian noise (AWGN) and Stanford University Interim (SUI-3) channel models. In the second technique, a high rate LDPC code is used in a concatenated coding structure as an outer code with a convolutional code as an inner code. The Convolutional codes are decode using two techniques bit-based maximum a posteriori probability (Log-MAP) decoder with its soft outputs feed into a binary LDPC decoder, and a symbol-based Log-MAP decoder with its soft outputs feed into a non-binary Galois Field LDPC decoder. The performance of such LDPC-CC concatenated codes is compared with the commonly used concatenated convolutional Reed-Solomon codes over the standard SUI-3 channel model, and the LDPC-CC codes showed better performance.