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Which message will the decoder choose?
Watch the decoder score each possible message as symbols arrive.
Uses preset lab settings
n = 0
Message scores
Sent message
Best competing score
Stop threshold
Same codebook and noise, with matching axes. Each trace ends when its decoder stops.
Ready to transmit
Watch which score reaches the stop threshold first.
Codebook vs. channel output
Does the sent message pull ahead?
Compare the information-density walks of the sent message and a competing one.
Estimating how the scores change…
True codeword: drift +C
Wrong codeword: drift −L
Ville: P[supn S̄n ≥ g] ≤ 2−g
The martingale 2S̄n: mean 1, median → 0
When does the decoder have enough evidence to stop?
Follow the possible received prefixes for one codebook. Colored branches mark where the decoder stops.
Computing the stopping time…
Atoms of 𝓕n, widths P(yn | W = 1)
Codebook (first symbols)
Hover an atom to see its prefix yn, every Sn(m), and what the decoder does there.
P(τ > n | W = w): the live mass of each row
P(error | W = m) for this codebook
How often does the decoder make a mistake?
Estimate error across transmissions with fresh codebooks and noise.
Waiting for simulation results…
Run the Monte Carlo to see E[τ] and Pe against the bounds.
Distribution of τ at the current γ
E[τ] against γ, with Wald's bounds
Pe against γ, with the union bound
Rate log₂M / E[τ] against Pe
How long does it take to approach capacity?
Compare stop feedback with fixed-length coding at the same target error rate.
Comparing required lengths…
Why does stop feedback help?
The theory behind the experiments.
Wait for evidence, then send one stop signal
The decoder can finish early when the evidence is clear and wait for more symbols when it is ambiguous.