An Introduction to Low-Density Parity-Check Codes

Abstract

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 struc- tured 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 theorypractice gap.