AFAIK, in practice it’s actually the sub-deacon who reads the Epistle. Albeit that it’s not formally proper, I’ve seen the deacon read the Gospel in translation, but it’s the celebrant who normally sings it in Chaldean.
The celebrant in the West Syriac & Armenian Churches usually does the Gospel as well. Of course the Maronites, (in yet another clear Novus Ordo-inspired neo-latinization), have adopted the current Roman fashion where a deacon, if present, does it. The epistle is normally read by a lay person, again according to current Roman fashion.
In the West Syriac Churches, a deacon is subtitled “mshamshono d’egartho” (deacon of the epistle), and I think (but wil not swear) that the same applies to the East Syriac Churches.
True archdeacons (as opposed to proto-deacons) are a rarity, to the point that I don’t believe even one exists in the Maronite Church. Whether or not the SCC has them I’m not sure, but they’re not all that common even in the SOC. I have no knowledge about archdeacons in the East Syriac or Armenian Churches or, for that matter, among the Alexandrenes either.