Modified Column Codewords for Double-Covered Error Correction
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Solution Overview
Problem
Existing error correction systems in data communications face challenges such as wasted parity space, reduced error correction performance due to single-covered parity bits, and increased implementation complexity from using multiple types of codewords and extra parity-on-parity bits.
Innovation Solution
The system generates modified column codewords by multiplying initial parity by a generator matrix, ensuring all data and parity bits are double-covered in two types of codewords without extra parity-on-parity bits, reducing implementation complexity and enhancing error correction capabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If parity-on-parity (POP) values are added to double-cover column parity, then error detection capability is improved, but code rate decreases due to wasted parity space
Solution Approach 1:
The patent merges the functions of column parity and POP values by integrating them into a unified column codeword structure. Instead of treating POP as separate additional parity bits, the invention combines column parity generation with the double-covering requirement, eliminating redundant parity space while maintaining error detection capability.
Solution Approach 2:
The column parity bits are designed to serve multiple functions simultaneously: they provide error detection for column errors and are themselves double-covered through the row codeword structure. This multi-functionality eliminates the need for separate POP values, preserving code rate while maintaining reliability.
2Reliability
If parity-on-parity (POP) values are computed and transmitted, then column parity double-coverage is achieved, but implementation complexity increases due to multiple codeword types
Solution Approach 1:
The patent combines column parity and POP functionality into a single column codeword type. By merging these distinct codeword types into one unified structure, the system achieves column parity double-coverage without requiring separate POP computation and transmission, thereby reducing implementation complexity.
Solution Approach 2:
Instead of adding POP values to column parity as traditionally done, the invention inverts the approach by making column parity itself double-covered through the row codeword structure. This reversal eliminates the need for separate POP handling and simplifies the overall system architecture.
3Reliability
If three types of codewords (row, column, POP) are used to ensure double-coverage, then error correction performance is improved, but encoder/decoder complexity increases
Solution Approach 1:
The patent merges the three distinct codeword types into two unified types: row codewords and column codewords. By combining POP functionality into the column codeword structure, the system maintains error correction performance while reducing encoder/decoder complexity through fewer distinct codeword handling routines.
Solution Approach 2:
The column codeword is designed to fulfill multiple roles simultaneously: it provides column error correction, ensures double-coverage of parity bits, and eliminates the need for separate POP processing. This multi-functionality reduces operational complexity while maintaining robust error correction capabilities.
Data Source
AI summary
A method and system are provided for error correction. After row encoding and column encoding, additional codeword data (ACD) and modified parity (P′) may be concurrently created, for each of a plurality of modified column codewords (CCW′), by multiplying initial calculated parity P by a generator matrix G. Each CCW′ may include an ACD portion and a P′ portion such that each bit in the P′ portion of a selected CCW′ is present in the ACD portion for one of the other CCW′. In contrast to known approaches, the method and system may provide modified column codewords such that all data and parity bits are present in two codewords while using only two types of codewords, and without using extra parity-on-parity bits. In a set of modified column codewords, each bit in the modified parity in one modified codeword is present in another codeword.