Subsymbol Erasure Coding for Lower-Complexity Data Recovery
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Solution Overview
Problem
Existing coding systems, such as Reed-Solomon codes, face inefficiencies in computational effort and overhead due to their optimality conditions, which limit their ability to handle varying error rates and block lengths, especially in applications with unknown or variable transmission conditions.
Innovation Solution
The implementation of subsymbol based coding, which generates output symbols from input symbols using functions like XOR operations and transforms generator or parity-check matrices into binary matrices, allowing for a trade-off between computational effort and overhead efficiency, enabling reduced computational effort with minimal additional overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Reed-Solomon codes are used to ensure optimal error protection, then data reliability is improved, but computational effort and overhead increase
Solution Approach 1:
The patent segments symbols into multiple subsymbols (e.g., 4 subsymbols per symbol). This segmentation allows the decoder to process only the necessary subsymbols for data recovery rather than processing entire symbols, reducing computational effort while maintaining reliability through selective subsymbol processing
Solution Approach 2:
The patent introduces a new dimension of granularity by operating at the subsymbol level rather than the symbol level. This dimensional change enables fine-grained processing where only affected subsymbols need to be decoded and processed, significantly reducing computational complexity while preserving data recovery capability
2Adaptability or versatility
If Reed-Solomon codes are used to handle varying error rates, then adaptability is improved, but overhead efficiency deteriorates
Solution Approach 1:
By segmenting symbols into subsymbols, the system can adapt to varying error rates by processing only the minimum necessary subsymbols for recovery. This reduces overhead because transmitted data contains only the essential subsymbol information needed for different error scenarios, rather than fixed overhead for worst-case conditions
Solution Approach 2:
The patent enables dynamic adaptation to error rates by allowing the decoder to adjust its processing based on the actual number and position of erased subsymbols. This dynamic approach optimizes overhead efficiency by transmitting only the necessary subsymbol data rather than fixed overhead amounts
3Ease of operation
If fixed block length codes are used to simplify encoding, then ease of operation is improved, but adaptability to variable transmission conditions deteriorates
Solution Approach 1:
The patent maintains encoding simplicity by using fixed block lengths at the subsymbol level while achieving adaptability through selective processing. The encoder operates on fixed-size subsymbol blocks, but the decoder can handle variable error rates by processing only the necessary subsymbols, combining simplicity with flexibility
Data Source
AI summary
An encoder uses output symbol subsymbols to effect or control a tradeoff of computational effort and overhead efficiency to, for example, greatly reduce computational effort for the cost of a small amount of overhead efficiency. An encoder reads an ordered plurality of input symbols, comprising an input file or input stream, and produces output subsymbol. The ordered plurality of input symbols are each selected from an input alphabet, and the generated output subsymbols comprise selections among an output subsymbol alphabet. An output subsymbol is generated using a function evaluator applied to subsymbols of the input symbols. The encoder may be called one or more times, each time producing an output subsymbol. Output subsymbols can then be assembled into output symbols and transmitted to their destination. The functions used to generate the output subsymbols from the input subsymbols can be XOR's of some of the input subsymbols and these functions are obtained from a linear code defined over an extension field of GF(2) by transforming each entry in a generator or parity-check matrix of this code into an appropriate binary matrix using a regular representation of the extension field over GF(2). In a decoder, output subsymbols received by the recipient are obtained from output symbols transmitted from one sender that generated those output symbols based on an encoding of an input sequence (file, stream, etc.).