Variable-length feedback coding error-exponent lower-bound conjecture

Consider a variable-length feedback code with $M=2^K$ messages, target error probability $P_e$, expected decoding time $\mathbb{E}[T]$, rate $\overline{R}$, channel capacity $C$, first-stage reliability quantity $\tilde{C}_1$, and bounded one-step log-likelihood drift constant $C_2$. For any $\epsilon>0$, the error-exponent lower-bound conjecture.

$$-\frac{\log P_e}{\mathbb{E}[T]} \geq \tilde{C}_1\left(1-\frac{\overline{R}}{C}\right)+U(\epsilon,K,P_e,C,\tilde{C}_1,C_2),$$

where

$$\lim_{K\rightarrow\infty}U(\epsilon,K,P_e,C,\tilde{C}_1,C_2)=o_\epsilon(1).$$

The bound is intended to follow by combining the likelihood-ratio drift estimates for the two coding stages with the relation between drift and stopping time. The source presents it as a conjectural result because of issues raised after the one-step drift lemma; the supplied text does not establish whether the conjecture has since been resolved.