Differentially Encoded LDPC Codes - Part II: General Case and Code Optimization

This two-part series of papers studies the theory and practice of differentially encoded low-density parity-check (DE-LDPC) codes, especially in the context of noncoherent detection. Part I showed that a special class of DE-LDPC codes, product accumulate codes, perform very well with both coherent and noncoherent detections. The analysis here reveals that a conventional LDPC code, however, is not fitful for differential coding and does not, in general, deliver a desirable performance when detected noncoherently. Through extrinsic information transfer (EXIT) analysis and a modified “convergence-constraint” density evolution (DE) method developed here, we provide a characterization of the type of LDPC degree profiles that work in harmony with differential detection (or a recursive inner code in general), and demonstrate how to optimize these LDPC codes. The convergence-constraint method provides a useful extension to the conventional “threshold-constraint” method, and can match an outer LDPC code to any given inner code with the imperfectness of the inner decoder taken into consideration.