  In this paper, we investigate the performance of a class of spatially coupled
codes, namely partially information coupled turbo codes (PIC-TCs) over the
binary erasure channel (BEC). This class of codes enjoy flexible code rate
adjustment by varying the coupling ratio. Moreover, the coupling method can be
directly applied to any component codes without changing the encoding and
decoding architectures of the underlying component codes. However, the
theoretical performance of PIC-TCs has not been fully investigated. For this
work, we consider the codes that have coupling memory $m$ and study the
corresponding graph model. We then derive the exact density evolution equations
for these code ensembles with any given coupling ratio and coupling memory $m$
to precisely compute their belief propagation decoding thresholds for the BEC.
Our simulation results verify the correctness of our theoretical analysis and
also show better error performance over uncoupled turbo codes with a variety of
code rates on the BEC.
