Message Residue Folding for Faster CRC Computation
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Solution Overview
Problem
Computing message residues, such as CRC, imposes significant computational overhead, which can be burdensome for data integrity protection in various protocols.
Innovation Solution
The technique involves repeatedly folding a message into a smaller set of equivalent data segments using inexpensive operations, allowing for the postponement of exact residue computation until the message is reduced, utilizing pre-computed constants and Galois-field multiplication to speed up the process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional CRC computation is performed on the entire message, then data integrity protection is achieved, but computational overhead and processing time increase significantly
Solution Approach 1:
The message is divided into multiple segments, and the folding operation processes these segments in a hierarchical manner. The most significant segment is folded into the least significant segments, reducing the overall message size progressively. This segmentation allows the computationally intensive residue computation to be performed on a smaller reduced message rather than the entire original message.
Solution Approach 2:
The folding operation is performed as a preliminary step before the final residue computation. By pre-reducing the message size through folding operations that preserve the mathematical characteristics needed for CRC, the subsequent residue computation becomes much faster while still maintaining data integrity protection.
2Reliability
If message residue computation is performed frequently for data integrity checks, then corruption detection capability is maintained, but computational resources and die impact increase
Solution Approach 1:
The folding operation segments the message processing into hierarchical stages, reducing the computational workload for each residue computation. This allows frequent integrity checks to be performed with reduced resource consumption at each check point.
Solution Approach 2:
The patent changes the parameter of message size by reducing it through folding operations before residue computation. This parameter transformation maintains the mathematical properties needed for corruption detection while significantly reducing the computational resources required for each integrity check.
3Productivity
If the message is reduced to smaller segments, then processing speed increases, but the mathematical characteristics needed for accurate residue determination may be lost
Solution Approach 1:
The folding operation is specifically designed as a preliminary reduction step that preserves the mathematical characteristics required for accurate CRC computation. By performing this reduction beforehand, the patent achieves both faster processing and maintained accuracy in the subsequent residue computation.
Solution Approach 2:
The folding operation acts as an intermediary transformation that bridges the original message and the final residue computation. This intermediate step reduces message size while maintaining the mathematical properties needed for accurate CRC, effectively mediating between the need for speed and the need for accuracy.
Data Source
AI summary
A description of techniques of determining a modular remainder with respect to a polynomial of a message comprised of a series of segments. An implementation can include repeatedly accessing a strict subset of the segments and transforming the strict subset of segments to into a smaller set of segments that are equivalent to the strict subset of the segments with respect to the modular remainder. The implementation can also include determining the modular remainder based on a set of segments output by the repeatedly accessing and transforming and storing the determined modular remainder.