  We study the advantages to be gained in quantum key distribution (QKD)
protocols by combining the techniques of local randomization, or noisy
preprocessing, and structured (nonrandom) block codes. Extending the results of
[Smith, Renes, and Smolin, quant-ph/0607018] pertaining to BB84, we improve the
best-known lower bound on the error rate for the 6-state protocol from 14.11%
for local randomization alone to at least 14.59%. Additionally, we also study
the effects of iterating the combined preprocessing scheme and find further
improvements to the BB84 protocol already at small block lengths.
