  Spatially coupled codes have been of interest recently owing to their
superior performance over memoryless binary-input channels. The performance is
good both asymptotically, since the belief propagation thresholds approach
capacity, as well as for finite lengths, since degree-2 variables that result
in high error floors can be completely avoided. However, to realize the
promised good performance, one needs large blocklengths. This in turn implies a
large latency and decoding complexity. For the memoryless binary erasure
channel, we consider the decoding of spatially coupled codes through a windowed
decoder that aims to retain many of the attractive features of belief
propagation, while trying to reduce complexity further. We characterize the
performance of this scheme by defining thresholds on channel erasure rates that
guarantee a target erasure rate. We give analytical lower bounds on these
thresholds and show that the performance approaches that of belief propagation
exponentially fast in the window size. We give numerical results including the
thresholds computed using density evolution and the erasure rate curves for
finite-length spatially coupled codes.
