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| ==== abstract ==== | ==== abstract ==== | ||
| Error-correcting codes which employ iterative decoding algorithms are now | Error-correcting codes which employ iterative decoding algorithms are now | ||
| + | considered state of the art in communications. There is now a large | ||
| + | collection of code families which achieve a small gap to capacity with | ||
| + | feasible decoding complexity. Examples are low-density parity-check (LDPC) | ||
| + | codes, irregular repeat-accumulate (IRA) codes, and Raptor codes. For each | ||
| + | of these code families, one can construct code sequences which provably | ||
| + | achieve capacity on the binary erasure channel (BEC). In each case, | ||
| + | however, the decoding complexity becomes unbounded as the gap to capacity | ||
| + | vanishes. This talk will focus on recently constructed code families whose | ||
| + | complexity remains bounded as the gap to capacity vanishes. Assuming only | ||
| + | basic knowledge of LDPC codes, three closely related ensembles will be | ||
| + | described: IRA codes, accumulate-repeat-accumulate (ARA) codes, and | ||
| + | accumulate-LDPC (ALDPC) codes. Using the duality between these ensembles | ||
| + | and simplified approach to density evolution, we will construct a variety | ||
| + | of codes which achieve capacity with bounded complexity. This is joint work | ||
| + | with Igal Sason and Ruediger Urbanke. | ||