Binary Erasure Channel Input Form
Performance Visualization
The chart compares channel capacity, code rate, unerased bits, and erased bits for the submitted values.
Example Data Table
| Scenario | Erasure Probability | Block Length | Information Bits | Capacity | Code Rate | Expected Erased Bits |
|---|---|---|---|---|---|---|
| Low Erasure Link | 0.05 | 512 | 420 | 0.95 | 0.820313 | 25.6 |
| Moderate Erasure Link | 0.20 | 1024 | 700 | 0.80 | 0.683594 | 204.8 |
| Stress Condition | 0.40 | 2048 | 950 | 0.60 | 0.463867 | 819.2 |
Formula Used
1) Channel capacity: C = 1 - ε
For a binary erasure channel, the theoretical maximum reliable information rate equals one minus the erasure probability.
2) Code rate: R = k / n
This measures how many useful information bits are placed in each coded block.
3) Expected erased bits: E[X] = nε
This estimates the average number of erased symbols in a block of length n.
4) Variance of erased bits: Var(X) = nε(1 - ε)
This uses the binomial model because each bit is either erased or preserved.
5) Reliability condition: R ≤ C
Reliable transmission requires the code rate to remain below or equal to channel capacity in theory.
How to Use This Calculator
- Enter the erasure probability as a decimal between 0 and 1.
- Provide the full block length for the coded transmission.
- Enter the information bits contained in that block.
- Set the trial count and confidence level for reporting context.
- Choose a decoder threshold for practical margin comparison.
- Click Calculate Channel Metrics to generate results.
- Review the summary cards, full metrics table, and plotly chart.
- Export the results using the CSV or PDF buttons.
Frequently Asked Questions
1) What is a binary erasure channel?
A binary erasure channel is a communication model where each transmitted bit is either received correctly or replaced by an erasure symbol. The receiver knows which positions were lost, which makes it different from a bit-flip channel.
2) Why is the capacity equal to 1 minus ε?
Each bit survives with probability 1 minus ε. Since the receiver knows erased positions, the average usable information per channel use is exactly the non-erased fraction.
3) What does code rate mean here?
Code rate is the ratio of information bits to total transmitted bits. A lower rate adds more redundancy, which generally improves recovery from erasures.
4) What happens when rate exceeds capacity?
When code rate is above channel capacity, dependable recovery becomes theoretically impossible for large blocks. The system lacks enough redundancy to compensate for the average erasure level.
5) Why does the calculator show expected erased bits?
Expected erased bits provide a direct estimate of how many positions may be lost in each block. This helps size redundancy, compare coding strategies, and judge decoder difficulty.
6) What is the recoverability index?
The recoverability index compares capacity to code rate. Values above one indicate the design sits under the theoretical limit, while values below one suggest the design is too aggressive.
7) Is the decoder threshold an exact limit?
No. It is a practical reference value entered by the user. Real thresholds depend on the chosen coding family, decoder algorithm, finite block length, and implementation details.
8) Can I use this calculator for LDPC or fountain codes?
Yes, as a planning tool. It gives useful baseline channel and redundancy metrics, but exact performance still depends on the selected code structure and decoder behavior.