Nonlinear Dynamics of the Message Passing Decoder of LDPC Codes

G.M. Maggio, F. Lehmann, L. Kocarev, and Z. Tasev (USA)


LDPC codes, Message passing decoding, Gaussian density, Nonlinear dynamics.


In this paper we investigate the nonlinear dynamics of the message passing decoding algorithm of low-density parity-check (LDPC) codes, based on Gaussian densities. Namely, we introduce a novel closed-form 1-D map whose iterates directly represent the error probability. This map allows a qualitative analysis of the nonlinear dynamics of the decoding algorithm. Moreover, it is shown that our approach leads to the correct stability condition and that the corresponding threshold values are in good agreement with density evolution.

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