The Avaya 1600 Series use the HIS-1 cord, not the HIC-1 cord.
Also, do NOT get the cheap HIS-1s available on the internet. We have a site with 1608s and they bought cheap HIS-1 cables via Google. On every call, for all 250 agents, their speech was repeated back to them about 0.5 second after they spoke. Swapping out for authentic HIS-1s solved the problem.
HIS-1s should be about £18 not £12.