Reed-Solomon Proximity Gaps - Interactive Visualization

0.500

Code Rate ($\rho = k/n$)

0.530

$H_q(\delta)$ Entropy

0.470

List-Decode Capacity

0.465

Random Words Bound

0.030

Entropy Gap

0.005

Capacity Gap

Regime Indicator

Unique Decoding: $\delta \leq (1-\rho)/2$

Johnson: $\delta \leq 1-{\rho}^{1/2}$

Random Words (DG25)

Capacity: $\delta \leq 1-\rho$

Attack Zone: $\delta > 1-\rho$

UDR: $(1-\rho)/2$

LDR: $1-{\rho}^{1/2}$

Random Words

Violation Zone

Green (UDR): Guaranteed unique decoding. Blue (LDR): Johnson bound regime. Purple: Random words bound. Red: Beyond all bounds.

Capacity $(1-\rho)$

List-Decode $(1-H_q(\delta))$

Compares the original capacity conjecture $(1-\rho)$ with the actual list-decoding capacity bound using q-ary entropy.

$H_q(x)$ Entropy

Identity $(x)$

The gap $H_q(x) - x \leq 1/\log_2(q)$ characterizes the difference between capacity conjectures.