Error Exponents of Parallel Two-way Discrete Memoryless Channels using Variable Length Coding

Achievable error exponents for two-way parallel discrete memoryless channels (DMC) using variable block length coding (VLC) are presented. First, Forney's erasure decoding error exponent is shown to be achievable for both directions simultaneously. Next, for some rate-pairs, it is shown that the error exponent of the direction with a smaller capacity may be further increased by allocating feedback resources to it in the other direction, at the price of a decreased error exponent for the other terminal. The presented two-way communication scheme builds upon Draper-Sahai's one-way DMC achievability scheme with noisy feedback under VLC. Both achievable error exponent regions demonstrate that the use of VLC and interaction between the terminals may benefit both directions' error exponents over fixed block length and feedback free transmission.¹.