Low-complexity error correction of Hamming-code-based LDPC codes

Authors:
V. A. Zyablov;R. Johannesson;M. Lončar
Affiliations:
Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia;Dept. of Electrical and Information Technology (EIT), Lund University, Lund, Sweden;Nokia, Devices R&D, Modem Algorithm Design, Copenhagen, Denmark
Venue:
Problems of Information Transmission
Year:
2009

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Abstract

Ensembles of binary random LDPC block codes constructed using Hamming codes as constituent codes are studied for communicating over the binary symmetric channel. These ensembles are known to contain codes that asymptotically almost meet the Gilbert-Varshamov bound. It is shown that in these ensembles there exist codes which can correct a number of errors that grows linearly with the code length, when decoded with a low-complexity iterative decoder, which requires a number of iterations that is a logarithmic function of the code length. The results are supported by numerical examples, for various choices of the code parameters.