Convergence of the Min-Sum Decoding Scheme for LDPC Codes from a Dynamical Systems Perspective

LDPC codes represent a class of codes for a wide variety of modern day coding applications including wireless communications and also some aspects of Cryptography. The general decoder for these codes, the Sum-Product algorithm can be viewed as a nonlinear dynamical system and has been shown to exhibit bifurcations and chaotic phenomena in the low and waterfall SNR zone in an AWGN channel. It has been attempted to investigate whether the Min-Sum decoder, a major approximation of the Sum-Product decoder, exhibits similar phenomena in its corresponding waterfall SNR zone for a particular Gallager code in the AWGN Channel. The results obtained indicate that the decoder does not show bifurcations and chaos in the waterfall SNR zone. Nevertheless, the decoder converges smoothly when the SNR stays above the waterfall region. This work guides how to find the convergent SNR zone for decoding any particular LDPC code with the Min-Sum decoder.