In information theory, turbo codes are a class of high-performance forward error correction (FEC) codes developed around 1990–91, but first published in 1993. They were the first practical codes to closely approach the maximum channel capacity or Shannon limit, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level. Turbo codes are used in 3G/4G mobile communications and in satellite communications as well as other applications where designers seek to achieve reliable information transfer over bandwidth- or latency-constrained communication links in the presence of data-corrupting noise. Turbo codes compete with low-density parity-check (LDPC) codes, which provide similar performance. Until the patent for turbo codes expired, the patent-free status of LDPC codes was an important factor in LDPC's continued relevance.