  In streaming applications, doping improves the performance of
spatially-coupled low-density parity-check (SC-LDPC) codes by creating
reduced-degree check nodes in the coupled chain. We formulate a scaling law to
predict the bit and block error rate of periodically-doped semi-infinite
SC-LDPC code ensembles streamed over the binary erasure channel under sliding
window decoding for a given finite component block length. The scaling law
assumes that with some probability doping is equivalent to full termination and
triggers two decoding waves; otherwise, decoding performs as if the coupled
chain had not been doped at all. We approximate that probability and use the
derived scaling laws to predict the error rates of SC-LDPC code ensembles in
the presence of doping. The proposed scaling law provides accurate error rate
predictions. We further use it to show that in streaming applications periodic
doping can yield higher rates than periodic full termination for the same
error-correcting performance.
