TAILIEUCHUNG - Introducing Low-Density Parity-Check Codes

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. | Introducing Low-Density Parity-Check Codes Sarah J. Johnson School of Electrical Engineering and Computer Science The University of Newcastle Australia email Topic 1 Low-Density Parity-Check Codes Introduction 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. The relative quiescence of the coding field was utterly transformed by the introduction of turbo codes proposed by Berrou Glavieux and Thitimajshima in 1993 wherein all the key ingredients of successful error correction codes were replaced turbo codes involve very little algebra employ iterative distributed algorithms focus on average rather than worst-case performance and rely on soft or probabilistic information extracted from the channel. Overnight the gap to the Shannon limit was all but eliminated using decoders with manageable complexity. As researchers struggled through the 1990s to understand just why turbo codes worked as well as they did two researchers McKay and Neal introduced a new class of block codes designed to posses many of the features of the new turbo codes. It was soon recognized that these block codes were in fact a rediscovery of the LDPC codes developed years earlier by Gallager. Indeed the algorithm used

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