2003 · 184 citations · 8 references
EngineeringComputer EngineeringComputer ScienceDigital CommunicationFault-tolerant ComputingInformation TheoryChannel CapacityChannel CodingCoding TheoryError Control CodingError CorrectionError-correcting CodesBlock CodesBlock CodingCode ConstructionsCode DesignDecoder DesignDistance CriterionLdpc CodesMinimum Distance
GLD codes extend Tanner codes and Gallager’s LDPC codes, offering flexible parameters that suit both small and large block‑length forward error‑correcting schemes. The authors aim to construct generalized low‑density codes by intersecting two interleaved block codes. They build these pseudo‑random error‑correcting codes through the intersection of two interleaved block codes, enabling a simple and fast SISO decoder. GLD codes approach channel capacity with a fast SISO decoder, and ensemble analysis proves they are asymptotically good under the minimum‑distance criterion.
We build a class of pseudo-random error correcting codes, called generalized low density codes (GLD), from the intersection of two interleaved block codes. GLD code performance approaches the channel capacity limit and the GLD decoder is based on simple and fast SISO (soft input-soft output) decoders of smaller block codes. GLD codes are a special case of Tanner codes and a generalization of Gallager's LDPC codes. It is also proved by an ensemble performance argument that these codes are asymptotically good in the sense of the minimum distance criterion. The flexibility in selecting the parameters of GLD codes makes them suitable for small and large block length forward error correcting schemes.
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Low-density parity-check codes
Robert G. Gallager · IEEE Transactions on Information Theory · 1962 · 10.6K citations · Full text