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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:45:49 +0000General coding theorems for turbo-like codes
https://resolver.caltech.edu/CaltechAUTHORS:20111130-082915053
Authors: {'items': [{'id': 'Jin-H', 'name': {'family': 'Jin', 'given': 'Hui'}}, {'id': 'McEliece-R-J', 'name': {'family': 'McEliece', 'given': 'Robert J.'}}]}
Year: 2000
DOI: 10.1109/ISIT.2000.866412
In this paper we prove that for general memoryless binary input channels, most ensembles of parallel and serial turbo codes, with fixed component codes, are "good" in the sense that with maximum likelihood decoding, their word (or bit) error probability decreases to zero as the block length increases, provided the noise is below a finite threshold. Our proof uses the classical union bound, which shows that under very general conditions, if the noise is below a certain threshold, the word (or bit) error probability is controlled by the low-weight codewords as the block length approaches infinity. Our main coding theorems then follow from a study of the low weight terms in the ensemble weight enumerator. Using this methodology, we can prove that the threshold is finite for most ensembles of parallel and serial turbo codes.https://authors.library.caltech.edu/records/1ryk8-4fk51AWGN Coding Theorems from Ensemble Weight Enumerators
https://resolver.caltech.edu/CaltechAUTHORS:20111128-074933357
Authors: {'items': [{'id': 'Divsala-D', 'name': {'family': 'Divsalar', 'given': 'D.'}}, {'id': 'Dolinar-S', 'name': {'family': 'Dolinar', 'given': 'S.'}}, {'id': 'Jin-H', 'name': {'family': 'Jin', 'given': 'H.'}}, {'id': 'McEliece-R-J', 'name': {'family': 'McEliece', 'given': 'R.'}}]}
Year: 2000
DOI: 10.1109/ISIT.2000.866757
We develop AWGN coding theorems for ensembles of codes for which we can calculate, or at least closely estimate, the ensemble weight enumerator. As a rule, for such an ensemble we can find a threshold c such that if E_b/N_0>c, then the ensemble maximum-likelihood error probability approaches zero. This threshold is always better, and usually much better, than can be obtained from the union bound. The role of low-weight code words is the key.https://authors.library.caltech.edu/records/rxn81-qz180