Predicting Finite-length Performance of Multi-edge Type LDPC Ensembles

Design of moderate-length low-density parity check (LDPC) codes has been an ad hoc procedure. Early analysis focused on asymptotic (infinite block length) performance of groups of LDPC codes called ensembles. Results include a concentration theorem stating that the performance of individual codes in the ensemble converges (in probability) to the ensemble average with increasing block length. This asymptotic analysis provides useful insight into the potential of a set of codes, but the block lengths required to approach the asymptotic performance are impractical for most applications.;Recent results include significant advances in predicting finite-length performance. Researchers in this area show that LDPC ensemble average error performance follows a single curve where the argument depends only on threshold, block length, and two scaling parameters. Simulation results for regular and irregular ensembles show excellent agreement with the theoretical predictions even for moderate block lengths. Furthermore, stopping set enumeration methods provide accurate estimates of ensemble average error floors for the erasure channel. However, the complexity necessary for high-performance irregular ensembles is not ideal for implementation.;Multi-edge type (MET) ensembles generalize irregular ensembles by specifying graph connectivity. The extra degrees of freedom available in MET specifications often allow superior thresholds given implementation constraints such as maximum and average node degree. We extend the finite- length scaling and error floor research for analyzing MET ensembles. This work is the next step toward optimization of MET ensembles for finite-length performance specifications.