Low-density parity-check (LDPC) codes are forward error-correction codes,

first proposed in the 1962 PhD thesis of Gallager at MIT. At the time, their

incredible potential remained undiscovered due to the computational demands

of simulation in an era when vacumm tubes were only just being replaced by

the first transistors. They remained largely neglected for over 35 years. In the

mean time the field of forward error correction was dominated by highly structured

algebraic block and convolutional codes. Despite the enormous practical

success of these codes, their performance fell well short of the theoretically

achievable limits set down by Shannon in his seminal 1948 paper. By the late

1980s, despite decades of attempts, researchers were largely resigned to this

seemingly insurmountable theory–practice gap.