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In this paper we investigate the performance of incremental redundancy hybrid automatic repeat request (HARQ) schemes based on low-density parity-check (LDPC) codes. We highlight some important issues and tradeoffs that arise when designing HARQ protocols that make use of these powerful codes. Our analysis is carried out under the assumption of maximum-likelihood (ML) decoding and frequency flat block fading channel. ML decoding, although not practical, provides the LDPC code performance limit. The HARQ protocol is modeled with a semi-Markov process, where the states represent the redundancy transmissions. Different HARQ schemes and mother-code rates are compared and discussed.