RFC-139: Faster Erasure Coding (#139)

[Rendered](https://github.com/ordian/RFCs/blob/main/text/0139-faster-erasure-coding.md)
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+# RFC-0139: Faster Erasure Coding
+
+|                 |                                                                                             |
+| --------------- | ------------------------------------------------------------------------------------------- |
+| **Start Date**  | 7 March 2025                                                                    |
+| **Description** | Faster algorithm for Data Availability Layer                                                                    |
+| **Authors**     | ordian                                                                                            |
+
+## Summary
+
+This RFC proposes changes to the erasure coding algorithm and the method for computing the erasure root on Polkadot to improve performance of both processes.
+
+## Motivation
+
+The Data Availability (DA) Layer in Polkadot provides a foundation for
+shared security, enabling Approval Checkers and Collators to download
+Proofs-of-Validity (PoV) for security and liveness purposes respectively.
+As the number of parachains and PoV sizes increase, optimizing the performance
+of the DA layer becomes increasingly critical.
+
+[RFC-47](https://github.com/polkadot-fellows/RFCs/blob/main/text/0047-assignment-of-availability-chunks.md)
+proposed enabling systematic chunk recovery for Polkadot's DA to improve
+efficiency and reduce CPU overhead. However, while it helps under the assumption of
+good network connectivity to a specific one-third of validators (modulo some
+backup tolerance on backers), it still requires re-encoding. Therefore,
+we need to ensure the system can handle load in the worst-case scenario.
+The proposed change is orthogonal to RFC-47 and can be used in conjunction with it.
+
+Since RFC-47 already requires a breaking protocol change (including changes to
+collator nodes), we propose bundling another performance-enhancing breaking
+change that addresses the CPU bottleneck in the erasure coding process, but using
+a separate node feature (`NodeFeatures` part of `HostConfiguration`) for its activation.
+
+## Stakeholders
+
+- Infrastructure providers (operators of validator/collator nodes)
+  will need to upgrade their client version in a timely manner
+
+## Explanation
+
+We propose two specific changes:
+
+1. Switch to the erasure coding algorithm described in the Graypaper,
+Appendix H. SIMD implementations of this algorithm are available in:
+
+   - [Rust](https://github.com/AndersTrier/reed-solomon-simd)
+   - [C++](https://github.com/catid/leopard)
+   - [Go](https://github.com/celestiaorg/go-leopard)
+
+2. Replace the Merkle Patricia Trie with a Binary Merkle Tree for computing the erasure root.
+
+The reference root merklization implementation can be found [here](https://github.com/paritytech/erasure-coding/blob/512e77472beb877fe0881a857623d54d97b82bc4/src/merklize.rs#L9-L197).
+
+### Upgrade path
+
+We propose adding support for the new erasure coding scheme on both validator and collator sides without activating it until:
+1. All validators have upgraded
+2. Most collators have upgraded
+
+Block-authoring collators that remain on the old version will be unable to produce valid candidates until they upgrade. Parachain full nodes will continue to function normally without changes.
+
+An alternative approach would be to allow collators to opt-in to the new erasure
+coding scheme using a reserved field in the candidate receipt. This would allow
+faster deployment for most parachains but would add complexity.
+
+Given there isn't urgent demand for supporting larger PoVs currently, we recommend prioritizing simplicity with a way to implement future-proofing changes.
+
+In short, the following steps are proposed:
+1. Implement the changes a and wait for most collators to upgrade.
+2. Activate RFC-47 via `Configuration::set_node_feature` runtime change.
+3. Activate the new erasure coding scheme using another `Configuration::set_node_feature` runtime change.
+
+## Drawbacks
+
+Bundling this breaking change with RFC-47 might reset progress in updating collators. However, the omni node initiative should help mitigate this issue.
+
+## Testing, Security, and Privacy
+
+Testing is needed to ensure binary compatibility across implementations in multiple languages.
+
+## Performance and Compatibility
+
+### Performance
+
+According to [benchmarks](https://gist.github.com/ordian/0af2822e20bf905d53410a48dc122fd0):
+- A proper SIMD implementation of Reed-Solomon is 3-4× faster for encoding and up to 9× faster for full decoding
+- Binary Merkle Trees produce proofs that are 4× smaller and slightly faster to generate and verify
+
+### Compatibility
+
+This requires a breaking change that can be coordinated following the same approach as in RFC-47.
+
+## Prior Art and References
+
+JAM already utilizes the same optimizations described in the Graypaper.
+
+## Unresolved Questions
+
+None.
+
+## Future Directions and Related Material
+
+Future improvements could include:
+- Using ZK proofs to eliminate the need for re-encoding data to verify correct encoding
+- Removing the requirement for collators to compute the erasure root for the collator protocol