Systematic Code Decoding with Lower-Dimensional Erasure Recovery
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current systematic code decoding methods for erasure channels are inefficient due to high-dimensional equations, requiring excessive computational time, especially when dealing with large quantities of original packets, as seen in the Raptor code decoding process where decoding 10,000 times can take approximately three and a half days on a common personal computer.
Innovation Solution
A decoding apparatus and method that extracts non-erased original packets from encoded packets, uses these to parse for erased packets through lower-dimensional equations with fewer unknown variables, significantly reducing the computational load by combining non-erased and erased packets to obtain complete original packets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional systematic code decoding methods are used for erasure channels, then complete original packets can be recovered, but decoding time becomes excessively long due to high-dimensional equations
Solution Approach 1:
The patent segments the decoding process into two distinct phases: first extracting non-erased original packets directly from encoded packets, then separately parsing for erased packets using lower-dimensional equations. This segmentation reduces the overall computational complexity and decoding time while maintaining complete packet recovery.
Solution Approach 2:
The patent extracts non-erased original packets from the encoded packet set before performing the main decoding operation. By taking out these easily recoverable packets first, the remaining decoding problem involves fewer unknown variables, reducing the equation dimension from K variables to F variables where F < K, thus significantly reducing computational time.
2Reliability
If high-dimensional equations are used to decode all original packets, then complete original packet sets are obtained, but operation amount becomes excessively large
Solution Approach 1:
The patent performs partial decoding by first extracting only the non-erased packets that can be directly obtained, then performs decoding only for the erased packets using a reduced system of equations. This partial action approach avoids the unnecessary computational burden of solving the full high-dimensional system for all packets when some are already known.
Solution Approach 2:
By extracting and setting aside the non-erased original packets before the main decoding process, the patent reduces the number of unknown variables in the equation system from K to F, where F is the number of erased packets. This extraction step significantly reduces computational complexity while preserving decoding accuracy.
3Reliability
If matrix multiplication operations are performed on high-dimensional intermediate packets, then original packets are recovered, but decoding efficiency becomes unacceptably low
Solution Approach 1:
The patent segments the packet recovery process into two stages: direct extraction of non-erased packets without matrix operations, and subsequent recovery of erased packets using reduced-dimensional equations. This segmentation eliminates unnecessary matrix multiplication operations on high-dimensional data, improving decoding efficiency while maintaining complete recovery.
Solution Approach 2:
The patent extracts and processes non-erased packets separately from erased packets. By taking out the non-erased packets that require no complex operations, the remaining matrix multiplication operations are performed on lower-dimensional data structures, significantly improving computational efficiency and productivity.
Data Source
AI summary
Embodiments of the present invention disclose a systematic code decoding method and an apparatus. The method includes: extracting a non-erased original packet from an acquired encoded packet that has passed through an erasure channel; and then by using the erased original packet as an unknown variable, obtaining an erased original packet by parsing according to a first equation. Because a quantity F of erased original packets is far less than a total quantity K of original packets, a dimension of the first equation that includes F unknown variables is far lower than a dimension of an equation indicating a correspondence between an encoded packet and an intermediate packet. An operation amount required for parsing the relatively low-dimensional first equation is far smaller, thereby greatly reducing an operation amount required for decoding.