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An Improved Decoding Method for Sipser-Spielman's Expander Codes

好一 坂庭, KOHICHI SAKANIWA

Published Jan 1, 2003• 0 citations
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Recently, G. Zemor (see IEEE Trans. Inf. Theory, vol.47, p.835-7, 2001) proposed an improvement on the Sipser-Spielman analysis of expander codes (Sipser, M. and Spielman, D.A., IEEE Trans. Inf. Theory, vol.42 , p.1710-22, 1996) and presented a linear-time iterative decoder that can correct a number of errors up to approximately 1/4 the known lower bound on the minimum distance of the code. We propose an improvement on Zemor's decoder for F=GF(2), with the number of correctable errors becoming close to half the lower bound on the minimum distance. The improvement is obtained by inserting into the decoding algorithm features akin to generalized minimum distance decoding of concatenated codes.
We present a simple soft-decision decoding algorithm that modifies Sipser and Spielman's (see IEEE Trans, Inform. Theory, vol.42, p.1710-22, Nov. 1996) hard-decision sequential "bit-flipping" algorithm for decoding expander codes. The algorithm incorporates symbol reliability information and a simple "taboo" function that avoids repeated flipping of the same bit. The two algorithms have comparable simplicity, but simulations show that the soft-decision algorithm results in both improved performance and-because fewer decoding iterations are necessary-improved speed.
Since Gallager introduced Bit-Flipping (BF ) decoding with hard-decision for Low-Density Parity-Check Codes (LDP C), other two variants were proposed by Sipser and Spielman for expander codes.Later, a soft-decision version of BF decoding, known as Modified Weighted BF (MW BF ) decoding, was investigated.This thesis proposes modified versions of Sipser and Spielman algorithms.Simulation results for long systematic Low-Density Generator Matrix (LDGM) codes show a better performance of the proposed versions.Moreover, for moderate length systematic LDGM codes, simulation results show performance similar to that of MWBF decoding with the advantage of not requiring floating-point operations.