ACE Spectrum of LDPC Codes and Generalized ACE Design

The construction of good, finite-length, LDPC codes is currently an attractive research area. Reducing attention to the binary erasure channel (BEC), this problem translates into the problem of finding elements of selected (irregular) LDPC code ensemble with the size of the minimal stopping set being maximized. Faced with the lack of analytical solution to this problem, simple but powerful heuristic design algorithm, an ACE constrained design algorithm, was recently introduced. Building upon the ACE metric associated with every cycle in the code graph, we introduce the ACE spectrum of LDPC code as a useful measure of success in selection of the LDPC code from selected ensemble. Using ACE spectrum, we farther generalize ACE constrained design, making it more flexible and efficient.