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Bounds on the thresholds of non-binary LDPC codes

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2 Author(s)
Oron Levi ; School of Electrical Engineering, Tel Aviv University, 69978, Israel ; David Burshtein

LDPC codes over non-binary Galois fields were proposed for reliable transmission over arbitrary discrete memoryless channels and in particular for transmission in the bandwidth efficient regime. It was shown that some properties, originally derived for binary LDPC codes, extend to the appropriately defined non-binary ensemble. However, the extension of density evolution to this ensemble results in a prohibitive computational complexity. In this paper we analyze the performance by tracking the evolution of the Bhattacharya noise parameter associated with the decoding messages, and derive upper and lower bounds on its evolution. These bounds are then used to obtain upper and lower bounds on the asymptotic threshold required for reliable communication.

Published in:

Electrical and Electronics Engineers in Israel, 2008. IEEEI 2008. IEEE 25th Convention of

Date of Conference:

3-5 Dec. 2008