An Ordered-Statistics-Based Approximation of the Sum-Product Algorithm

"A complexity- and delay-efficient simplification of the sum-product algorithm (SPA) for decoding low-density parity-check (LDPC) codes is presented. The key feature of the new algorithm consists of a modification of the complexity-intensive and delay-causing update equations at the check nodes of the factor graph of the LDPC code. The modified update equations at a check node are based on ordering the reliability values of the incoming messages and on using a balanced tree topology to achieve optimum parallel processing. Furthermore, the complexity of the new algorithm can be adjusted: the least complex version of the algorithm corresponds to the so-called min-sum approximation, and the most complex version gives the full SPA."