We study adaptive prefix-length selection for reliability-ordered coded transmission over $N$ coordinates, using only the $K$ most reliable, to balance age of information (AoI) against throughput. An additive-increase/decrease (AID) prefix-walk controller updates the prefix length from the last decoding outcome alone, at $O(1)$ per-slot cost with no channel estimation, inducing an irreducible birth--death chain whose mean drift fixes a unique balance point $K^\dagger$ (largest $K$ with success probability $\ge\tfrac12$), around which the stationary distribution concentrates geometrically. We derive this distribution in closed form via detailed balance and obtain exact steady-state AoI and goodput via renewal-reward analysis. Simulations on a $64$-coordinate polar code over a binary symmetric channel (BSC) confirm these predictions to within $0.3\%$. Relative to a genie-aided upper bound with perfect channel knowledge, we further quantify the goodput cost of adapting from a single feedback bit alone.

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