  In this paper, we study a class of spatially coupled turbo codes, namely
partially information- and partially parity-coupled turbo codes. This class of
codes enjoy several advantages such as flexible code rate adjustment by varying
the coupling ratio and the encoding and decoding architectures of the
underlying component codes can remain unchanged. For this work, we first
provide the construction methods for partially coupled turbo codes with
coupling memory $m$ and study the corresponding graph models. We then derive
the density evolution equations for the corresponding ensembles on the binary
erasure channel to precisely compute their iterative decoding thresholds.
Rate-compatible designs and their decoding thresholds are also provided, where
the coupling and puncturing ratios are jointly optimized to achieve the largest
decoding threshold for a given target code rate. Our results show that for a
wide range of code rates, the proposed codes attain close-to-capacity
performance and the decoding performance improves with increasing the coupling
memory. In particular, the proposed partially parity-coupled turbo codes have
thresholds within 0.0002 of the BEC capacity for rates ranging from $1/3$ to
$9/10$, yielding an attractive way for constructing rate-compatible
capacity-approaching channel codes.
