Universal rate-compatible LDPC code families for any increment ordering

Rate-compatible (RC) codes are at the core of systems with incremental redundancy. Usually, an RC code family supports successively lower code rates by sending specific increments of additional redundancy at each rate. That is, the order of the increments is fixed. However, in some multi-hop communication systems and also in recently proposed inter-frame coding, the order in which the decoder of the RC code receives the increments is not predetermined. A different ordering of the increments at the decoder may change the codes of various rates. This paper seeks RC codes that are universally good over all increment orderings. We call RC codes satisfying this requirement universal for any increment ordering (UIO) codes. We design protograph-based Raptor-like (PBRL) low-density parity-check (LDPC) code ensembles for UIO codes using protograph thresholds as components of two design metrics. One metric seeks codes that, at each code rate, have exactly the same frame error rate for all increment orderings. The other metric sacrifices strictly identical performance for every ordering to seek codes that achieve the best possible throughput in a variable-length setting with random increment ordering, as would occur with inter-frame coding. Simulation results of UIO-PBRL codes from the new ensembles show that our designs satisfy the two metrics.