Burst Error Correction in Cyclic Codes Using OQDD Check Matrices
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Solution Overview
Problem
Current burst correction methods for cyclic codes, such as Deterministic Burst Correction (DBC) and Probabilistic Burst Correction (PBC), are inadequate for effectively correcting burst errors in cyclic codes and Low Density Parity Check (LDPC) codes, as they lack specific implementation methods and detailed decoding processes.
Innovation Solution
A probabilistic burst correction method using an Overlapped Quasi Dual Diagonal Matrix check matrix is introduced, which calculates a correction vector, determines the burst length and position, and generates an error mode polynomial to correct the received codeword, specifically applicable to cyclic codes like Reed Solomon and Bose Chaudhuri Hocquenghem codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Deterministic Burst Correction (DBC) is used with correction capability l, then bursts of length l or shorter can be corrected, but bursts of length l+1 cannot be corrected
Solution Approach 1:
The patent transforms the rigid deterministic correction capability into a flexible probabilistic correction capability by changing the decoding parameter from fixed threshold to probabilistic confidence level. The syndrome magnitude is compared against a dynamically determined threshold based on desired correction probability, allowing the system to adaptively correct bursts of varying lengths beyond the fixed Reiger bound limitation.
2Reliability
If Probabilistic Burst Correction (PBC) is used, then longer bursts can be corrected at high probability, but specific implementation methods for cyclic codes are not provided
Solution Approach 1:
The patent segments the PBC implementation into distinct functional modules: syndrome calculation unit, magnitude comparison unit, threshold determination unit, and correction application unit. This modular segmentation provides a concrete implementation framework for cyclic codes while maintaining the probabilistic correction capability, reducing implementation complexity through structured organization.
Solution Approach 2:
The patent introduces an intermediary threshold value that mediates between the syndrome magnitude and the correction decision. This threshold acts as a bridge that translates the probabilistic requirement into a deterministic comparison operation, providing a practical implementation method for PBC in cyclic codes without requiring complex probabilistic computations.
3Productivity
If conventional cyclic code decoding is used, then decoding can be performed efficiently, but burst error correction capability is limited by the Reiger bound
Solution Approach 1:
The patent applies partial correction by focusing only on the most significant syndrome components for comparison against the threshold. Rather than processing all syndrome bits equally, it selectively uses the magnitude information to make correction decisions, achieving improved burst correction capability while maintaining decoding efficiency through selective processing of critical parameters.
Data Source
AI summary
A method, a device, and an apparatus for correcting bursts are disclosed. The method includes: calculating a correction vector according to a received codeword and a check matrix, wherein the check matrix is an Overlapped Quasi Dual Diagonal Matrix; determining a length and position of a burst according to a longest zero element vector between two nonzero elements in the correction vector when the correction vector is nonzero; and calculating out an error mode according to the correction vector and the length of the burst, obtaining an error mode polynomial according to the error mode, correcting the received codeword according to the error mode polynomial, and obtaining a corrected codeword polynomial. The PBC-based implementation method for cyclic codes herein can correct more burst errors than the conventional cyclic code decoding method.