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r) LDPC: a piece of 21st-century coding in the 20th century

r) LDPC: a piece of 21st-century coding in the 20th century

25.03.2019

 

In 1958, Robert Gallager, a Ph.D. student at MIT, had already created a class of capacity-approaching codes. Gallager's simulations showed that, indeed, his LDPC codes came very close to Shannon's capacity. However, they presented a computational challenge far too complex for the computers of the day. Most coding theorists seemed to regard LDPC codes as intriguing but quixotic and promptly forgot about them. How is that possible? Well, in 1968, Robert Gallager wrote his classic textbook "Information Theory and Reliable Communication," where he explained most of the coding theory known at the time but neglected to mention LDPC codes! Perhaps he thought he had already covered the material in a 1963 monograph that was made from his thesis, or maybe he also did not regard LDPC codes as practical. In the late 1990s, with the coding world buzzing about turbo codes, several researchers independently rediscovered Gallager's work and LDPC codes rapidly became the state of the art. Amazingly, most important concepts about LDPC codes were already in Gallager's 1960 thesis. In the words of Prof. David Forney:

"LDPC codes are a piece of 21st-century coding that happened to fall in the 20th century".

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