The higher level requests for retransmission would be TCP. I don't think there is any retransmission without G.INP, otherwise they wouldn't have needed to do G.INP separately (G.INP does exist for ADSL2 and ADSL2+, but not on any BT equipment, although the newest 21CN exchanges appear to get Broadcom equipment so probably would be capable of doing it).
Also, regarding HEC errors, it actually states in the ITU-T technical recommendations that no error correction is performed (G.992.1 7.2.3.6 and G.992.3 K.2.8.5). In general ATM networks, yes the HEC could correct a single bit error, but apparently that ability is not used on ADSL.
AFAIK, if part of your ICMP ping packet gets corrupted and fails the CRC check, there's no "ARQ", and the packet is lost.