Threshold Saturation for LDPC Convolutional Code Ensembles

Low-density parity-check (LDPC) codes, originally invented by Gallager in 1963, are now well-known for their good performances. Their convolutional counterpart was introduced by Felström and Zigangirov in 1999 and have already been shown to be able to achieve the Shannon capacity under low-complexity iterative decoding algorithms. In principle, the belief-propagation (BP) threshold of the convolutional or spatially-coupled LDPC code ensemble can be increased up to the maximum a posteriori (MAP) threshold of the underlying uncoupled ensemble. In this write-up, we will focus on explaining this “threshold saturation” phenomenon for the binary erasure channel (BEC) in detail, and propose some future research plans.