Decoding of expander codes at rates close to capacity

Author

Ashikhmin, Alexei ; Skachek, Vitaly

Author_Institution

Dept. of Math. of Commun., Lucent Technol. Bell Labs., Murray Hill, NJ

fYear

2005

fDate

4-9 Sept. 2005

Firstpage

317

Lastpage

321

Abstract

The concatenation of nearly-MDS expander codes of Roth and Skachek, "On Nearly-MDS Expander Codes," Proc. IEEE ISIT\´04, with \´typical\´ LDPC codes is investigated. It is shown that for the rates R = (1 - epsi)C (C is the capacity of the binary symmetric channel (BSC)), under certain condition on the parameters of LDPC codes, these concatenated codes have decoding time linear in their length and polynomial in 1/epsi, and the decoding error probability decays exponentially. These codes are compared to the recently presented codes of Barg and Zemor, "Error Exponents of Expander Codes," IEEE Trans. Inform. Theory, 2002, and "Concatenated Codes: Serial and Parallel," IEEE Trans. Inform. Theory, 2005. It is shown that the latter families can not be tuned to have all the aforementioned properties

Keywords

channel coding; decoding; error statistics; parity check codes; set theory; binary symmetric channel; concatenated codes; decoding error probability; expander codes; low-density parity-check codes; Capacity planning; Communication channels; Computer science; Concatenated codes; Decoding; Error probability; Graph theory; Mathematics; Parity check codes; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on

Conference_Location

Adelaide, SA

Print_ISBN

0-7803-9151-9

Type

conf

DOI

10.1109/ISIT.2005.1523346

Filename

1523346