For a given channel code ensemble, there are three fundamental limits on the channel parameter above which reliable communication is not possible; capacity threshold, maximum a posteriori (MAP) threshold, and belief propagation (BP) threshold. The capacity threshold correspond to the fundamental limit imposed by the underlying channel, and this limit is applicable for an arbitrary rate R code ensemble. The MAP threshold correspond to the given rate R ensemble and the BP threshold correspond to the limit that can be achieved in practice via BP decoding. For a practical capacity achieving code ensemble, these three thresholds should coincide. Recently it has been shown that, multiple copies of a given code ensemble can be appropriately coupled spatially such that the BP threshold of the spatially-coupled code approaches the MAP threshold of the uncoupled ensemble. To design a capacity achieving spatially-coupled code ensemble, it is thus desirable to first find the MAP threshold of the uncoupled code ensemble. However, finding the MAP threshold of a given uncoupled code ensemble is, in general, known to be computationally intractable. This work proposes a computationally tractable method to estimate the MAP thresholds for various families of sparse-graph codes when the noise is introduced by the additive white Gaussian noise (AWGN) channel.
Arti D. Yardi received her PhD degree from the Department of Electrical Engineering, Indian Institute of Technology Bombay in January 2017. She is currently a post-doctoral researcher in Informatics Research Institute of Toulouse, France and a recipient of the CIMI postdoctoral fellowship. She is also a recipient of the DST-INSPIRE Faculty Fellowship Award for the year 2018.