DA Sampling Calculator

Interactive calculator for the Logos Blockchain data availability sampling protocol. Models sampling as a binary hypothesis test and allows interactive exploration of how protocol parameters affect Type I error, Type II error, grey zone width, wasted slots, and blockchain security horizon.

Background

Logos Blockchain DA uses column sampling to verify data availability without downloading the entire dataset. A node draws S columns uniformly at random and applies a threshold decision rule: declare the blob available if at least τ out of S samples succeed.

This produces two error types that cannot be minimised independently:

Type I error α(τ) — data is unrecoverable but sampling concludes it is recoverable. Threatens chain safety.
Type II error β(τ, Δ) — data is recoverable but sampling concludes it is unrecoverable. Wastes slots, threatens liveness.

The calculator computes exact hypergeometric expressions for both errors and derives all downstream quantities from them.

Parameters

Parameter	Description	Default
N	Total columns = total subnetworks (N = r·K)	2048
r	RS expansion factor	2
K	Reconstruction threshold = N/r	1024
S	Sample size (columns drawn per round)	20
τ	Acceptance threshold (declare available if ≥ τ successes)	20
Δ	Grey zone width (derived from ε target)	500
ε	Error bound target	10⁻⁴
N_B	Blobs per block	1024
n	Number of validator nodes	50
f	Slot fill rate	1/30
T	Slots per epoch	388800

Tabs

Detection Probability

Shows P(data detected as recoverable) as a function of N_A/N (fraction of available columns). Illustrates the grey zone between unrecoverable (N_A ≤ K) and certified recoverable (N_A ≥ K+Δ) regions.

α & β Curves

Plots α(τ) and β(τ, Δ) on a log₁₀ scale as functions of the threshold τ. The intersection of the two curves shows the jointly optimal τ* that minimises max{α, β}.

Multi-Δ Overlay

Compares α and β curves for multiple Δ values simultaneously, showing how the grey zone width affects the tradeoff.

τ* vs ε Sweep

Plots the jointly optimal τ*(ε) and Δ*(ε) as functions of the error bound ε for multiple sample sizes S. Shows how tightening ε requires increasing Δ.

Network Bounds

Shows the network-level error bounds as a function of validator count n:

Left panel: P(majority accepts unrecoverable block) = 2ⁿ · ε^{N_B·⌈n/2⌉}
Right panel: P(majority rejects recoverable block) = 2ⁿ · [1−(1−ε)^{N_B}]^{⌈n/2⌉}

Chernoff Bound

Plots the Chernoff-based bounds for the grey zone regime.

Block Builder

Shows the q-quantile of the hitting time τ_{N_B,q} — the number of blobs a block builder must consider to fill a block with N_B valid blobs, as a function of ε and N_B.

Wasted Slots

Shows the average number of wasted slots per epoch as a function of validator count n, across three regimes (Code 2 basic upper bound, Code 3 tight Chernoff upper bound, Code 4 lower bound).

Blockchain

Shows the median time T₁/₂ to the first invalid block accepted by a majority of validators, as a function of validator count n and error bound ε.

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