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Recent advances in modern coding theory resulted in a number of different ensembles of error-correcting codes with capacity-approaching performance and linear encoding/decoding complexity. Codes designed on sparse graphs and decoded using the iterative Belief-Propagation (BP) algorithm, such as Low-Density Parity-Check (LDPC) codes or recently proposed rateless codes (LT codes or Raptor codes), are on the forefront of these exciting new developments. These codes are studied in a traditional coding-theoretic setup where the message to be transmitted is entirely available at the transmitting node responsible for the encoding process.
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