Storage Sector Recovery Using Matrix-Decoded Redundancy Codes
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Solution Overview
Problem
Current digital data storage systems lack efficient methods for recovering from sector errors within a single media, particularly in large-scale storage systems, due to limitations in redundancy schemes and unpredictable latency or capacity issues, especially in write-once-read-many (WORM) storage systems like quartz glass.
Innovation Solution
A computer-implemented method for reading from a storage medium that uses redundancy data with separate redundancy codes, where each code is a linear sum of information payloads from different sectors weighted by coefficients, allowing for decoding and recovery of missing information sectors by computing the inverse matrix of the coefficients matrix.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional redundancy schemes (spare sectors, read-after-write) are used for sector error recovery, then data reliability is improved, but storage overhead increases or capacity becomes unpredictable
Solution Approach 1:
The patent segments the storage medium into information sectors and redundancy sectors, where each redundancy sector stores a linear combination of information sectors. This segmentation allows for efficient error recovery by using specific redundancy sectors only when needed, rather than reserving large fixed spare areas throughout the media.
Solution Approach 2:
The patent changes the parameter of redundancy representation from fixed spare copies to dynamic linear combinations. By storing data as linear combinations with coefficients, the system can recover any lost sector as long as enough redundancy sectors are intact, optimizing the balance between reliability and storage overhead.
2Reliability
If complex media-wide redundancy systems are used, then sector error recovery capability is improved, but device complexity increases
Solution Approach 1:
The patent replaces complex mechanical redundancy systems (physical spare sectors, read-after-write verification) with a mathematical approach using linear algebra. The decoding process uses matrix operations to recover lost data, substituting mechanical complexity with computational simplicity.
Solution Approach 2:
The redundancy sectors serve multiple functions: they can recover any single lost sector in the group, work across different storage media types, and provide systematic error correction. This universal approach simplifies the overall system design compared to media-specific redundancy schemes.
3Ease of operation
If fixed-rate data supply is required for optical media playback, then device simplicity is maintained, but flexibility in redundancy schemes is reduced
Solution Approach 1:
The patent performs preliminary encoding of redundancy sectors during the write operation, calculating linear combinations of information sectors before playback. This preliminary action allows the playback device to simply read at fixed rates without complex real-time decoding, maintaining ease of operation while enabling flexible redundancy schemes.
Data Source
AI summary
A method of reading from a storage medium to recover a group of information sectors, each comprising a respective information payload. The medium stores redundancy data comprising a plurality of separate redundancy codes for the group, each code being a linear sum of terms, each term in the sum being the information payload from a different respective one of the information sectors in the group weighted by a respective coefficient of a set of coefficients for the redundancy code. The method comprises, after the redundancy data has already been stored on the medium: identifying a set of k′ information sectors to be recovered; selecting k′ of the redundancy codes; determining a square matrix E of the k′ information sectors by the k′ sets of coefficients of the selected codes; determining a matrix D being a matrix inverse of E; and recovering the k′ information payloads from the inverse matrix D.