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Quasi-cyclic (QC) codes are a wide class of error-correcting codes possessing nice theoretical properties and having many practical applications. This paper provides a new approach to the problem of efficient encoding of QC codes based on the Chinese remainder theorem (CRT). We present a number of fast systematic CRT-based encoding algorithms that have superior asymptotic complexity than the previous methods based on shift registers. We also consider the encoding problem for QC low-density parity-check (LDPC) codes. In the special case when the parity part of a sparse parity-check QC matrix has a QC generalized inverse we propose a systematic CRT-based encoding algorithm that can exploit the parity-check matrix sparseness. We also give necessary and sufficient conditions when a QC matrix over an arbitrary field has a QC generalized inverse of the same circulant size.
№ | Имя | Описание | Имя файла | Размер | Добавлен |
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1. | Презентация | ISIT2015.pdf | 904,3 КБ | 24 июня 2015 [panteleev] |