Distributed Reed-Solomon Coding for Low-Complexity Network Decoding
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Solution Overview
Problem
Purely random code constructions for distributed error correction codes achieve maximum communication throughput but result in exponentially high decoding complexity at the receiver, making them impractical for deployment.
Innovation Solution
An efficient linear distributed error correction code construction using a single-source Reed-Solomon decoding algorithm, where each relay node encodes and decodes source files using a Vandermonde parity check matrix and generator matrix, reducing decoding complexity and enabling practical implementation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If purely random code construction is used for distributed error correction codes, then maximum communication throughput is achieved, but decoding complexity becomes exponentially high
Solution Approach 1:
The patent transforms the decoding problem by changing the algebraic structure parameters - using polynomial representations and finite field arithmetic instead of general linear algebra operations. This parameter transformation reduces the decoding complexity from exponential to polynomial time while maintaining the maximum throughput capability through careful selection of code construction parameters.
Solution Approach 2:
The patent replaces the generic mechanical decoding process with a specialized algebraic system based on Reed-Solomon code structures. By substituting the general-purpose decoding mechanism with this tailored algebraic approach, the system achieves both maximum throughput and reduced complexity through structured mathematical operations.
2Reliability
If high error correction capacity is achieved through random code construction, then reliability is improved, but practical implementation becomes infeasible due to complexity
Solution Approach 1:
The patent maintains high error correction capacity by preserving the fundamental parameters of random code construction (code rate, block length) while changing the operational parameters of the decoding algorithm. This allows the system to achieve both high reliability and implementation feasibility through separate optimization of code parameters and algorithmic complexity.
Solution Approach 2:
The patent extracts the essential error correction functionality from the complex random code framework and implements it through a simplified Reed-Solomon based algorithm. By taking out only the necessary error correction operations and implementing them through efficient algebraic methods, the system achieves practical feasibility while maintaining high reliability.
3Device complexity
If standard Reed-Solomon decoding algorithm is used, then decoding complexity is reduced, but direct application to distributed error correction requires adaptation
Solution Approach 1:
The patent segments the distributed error correction problem into multiple independent Reed-Solomon decoding instances. Each relay node's transmitted data is processed through adapted Reed-Solomon decoding, with the overall system achieving distributed error correction by combining results from multiple segmented decoding operations. This segmentation enables the use of standard algorithms while maintaining distributed system functionality.
Solution Approach 2:
The patent creates a universal decoding framework that adapts the Reed-Solomon algorithm to serve multiple functions in distributed error correction. The same core decoding algorithm handles both traditional error correction and the distributed scenario where multiple relays transmit encoded data, achieving versatility through parameter adaptation rather than requiring separate specialized algorithms.
Data Source
AI summary
A computer-based distributed error correction scheme with an efficient decoding algorithm is disclosed. The efficiency of the corresponding decoding algorithm, based on standard single source Reed-Solomon error correcting codes, makes the practical employment of the DECC feasible. Various implementation examples are also provided.