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Low-density parity-check code
In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel.〔David J.C. MacKay (2003) Information theory, Inference and Learning Algorithms, CUP, ISBN 0-521-64298-1, (also (available online ))〕〔Todd K. Moon (2005) Error Correction Coding, Mathematical Methods and Algorithms. Wiley, ISBN 0-471-64800-0 (Includes code)〕 An LDPC is constructed using a sparse bipartite graph.〔Amin Shokrollahi (2003) LDPC Codes: An Introduction〕 LDPC codes are , which means that practical constructions exist that allow the noise threshold to be set very close (or even ''arbitrarily'' close on the BEC) to the theoretical maximum (the Shannon limit) for a symmetric memoryless channel. The noise threshold defines an upper bound for the channel noise, up to which the probability of lost information can be made as small as desired. Using iterative belief propagation techniques, LDPC codes can be decoded in time linear to their block length.
LDPC codes are finding increasing use in applications requiring reliable and highly efficient information transfer over bandwidth or return channel-constrained links in the presence of corrupting noise. Implementation of LDPC codes has lagged behind that of other codes, notably turbo codes. The fundamental patent for Turbo Codes expired on August 29, 2013.〔NewScientist, ''Communication speed nears terminal velocity'', by Dana Mackenzie, 9 July 2005〕
LDPC codes are also known as Gallager codes, in honor of Robert G. Gallager, who developed the LDPC concept in his doctoral dissertation at the Massachusetts Institute of Technology in 1960.
==History==
Impractical to implement when first developed by Gallager in 1963, LDPC codes were forgotten until his work was rediscovered in 1996.〔David J.C. MacKay and Radford M. Neal, "Near Shannon Limit Performance of Low Density Parity Check Codes," Electronics Letters, July 1996〕 Turbo codes, another class of capacity-approaching codes discovered in 1993, became the coding scheme of choice in the late 1990s, used for applications such as the Deep Space Network and satellite communications. However, in the last few years, the advances in low-density parity-check codes have seen them surpass turbo codes in terms of error floor and performance in the higher code rate range, leaving turbo codes better suited for the lower code rates only.〔(Telemetry Data Decoding, Design Handbook )〕
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