Seeded Error-Correcting Codes for Stateless Noisy Channels
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Solution Overview
Problem
Existing error correcting codes for computationally bounded channels require a trusted setup and are often stateful, making them unsuitable for transparent and concurrent transmission, and lack efficient solutions for uniquely decodable codes with high pseudodistance.
Innovation Solution
The development of seeded error correcting codes with a public-coin setup and stateless encoding, utilizing cryptographic hash functions and permutation functions with k-wise delta-dependence, enables efficient pseudounique decoding and list-decodability against a large fraction of errors, ensuring robustness against noise in computationally bounded channels.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If known solutions for computationally bounded channels are used, then better rates are achieved, but a trusted setup with secret keys is required
Solution Approach 1:
The patent replaces expensive, hard-to-instantiate secret randomness with cheap, easily generated public randomness. The construction uses public-coin samplability where the encoder and decoder can be efficiently sampled using only public randomness, eliminating the need for difficult-to-instantiate secret keys while maintaining security against computationally bounded adversaries.
Solution Approach 2:
The patent substitutes the cryptographic primitive requirement from secret-key-based encryption to public-coin samplability. Instead of relying on secret randomness that is difficult to instantiate, the system uses public randomness that can be efficiently generated and shared, replacing a complex cryptographic mechanism with a simpler, more practical approach.
2Reliability
If known solutions are used, then error correction capability is improved, but stateful encoding is required
Solution Approach 1:
The patent extracts and removes the stateful component from the encoding process. By designing a stateless encoder, the system eliminates the need for maintaining encoder state across multiple encoding operations, thereby avoiding the security vulnerabilities and synchronization issues that arise from stateful operation while preserving error correction capabilities.
Solution Approach 2:
Instead of requiring the encoder to maintain state (traditional approach), the patent inverts the approach by designing a stateless encoder that achieves the same error correction goals. This inversion allows concurrent transmission and data storage applications without requiring synchronization or state management, while still providing robust error correction against computationally bounded adversaries.
3Productivity
If list decoding relaxation is applied, then better rates are achieved, but unique decodability is lost
Solution Approach 1:
The patent changes the parameter of error tolerance from the traditional unique decoding radius to a larger effective radius achievable through list decoding, while maintaining unique decodability through pseudodistance. By constructing codes with high pseudodistance against computationally bounded adversaries, the system achieves unique decodability at error rates that would traditionally require list decoding, effectively changing the operational parameters of the code.
Data Source
AI summary
The invention relates to systems, methods, network devices, and machine-readable media for encoding an input message with robustness against noise by executing a compressing hash function on the input message, encoding an output of the hash function and the input message to generate a single combined message, executing a permutation function on the combined message, and encoding the result of the permutation function with a list-decodable code.