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LDPC codes were invented in 1960 by R. Gallager. They were largely ignored until the discovery of turbo codes in 1993. Since then, LDPC codes have experienced a renaissance and are now one of the most intensely studied areas in coding. In this article we review the basic structure of LDPC codes and the iterative algorithms that are used to decode them. We also briefly consider the state of the art of LDPC design.