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In this paper, we deal with practical implementation issues of the max* operation in generalized form used for decoding of both turbo and low-density-parity-check (LDPC) codes. In particular, first, a unified framework for the so-called generalized max* operation is established, which includes most of the previously published algorithms already known for turbo decoding. Next, the hardware architectures used for the practical implementation of the generalized max* operation, which is derived from this novel framework, are revealed for the first time and further analyzed, in terms of hardware complexity reduction. It is also shown how this generalized max8 operation can be adopted in LDPC decoding, achieving essentially optimal bit error rate performance with small computational complexity against other algorithms in joint turbo-LDPC architectures. This solution is useful in applications where joint decoding architectures are deployed to decode both turbo and LDPC codes. An important example of such application is in software radio receivers of 4G wireless communication systems, such as those proposed in conjunction with the WiMAX standard.