LDPC Erasure Decoding Using Dual GF(2) Test Codewords
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Solution Overview
Problem
Current methods for data transmission over Binary Erasure Channels (BEC) using Low Density Parity Check (LDPC) codes lack an effective erasure decoding algorithm, resulting in a heavy workload and limited error correcting capability for receivers.
Innovation Solution
A method and system for LDPC code erasure decoding that generates two code words using values and inverses in the Galois field GF(2) at erasure locations, followed by hard decoding operations using Majority Logic Decoding (MLD) to determine a successful erasure decoding result, thereby increasing error correcting capacity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If hard decoding algorithm (Bit Flip) is used for LDPC code decoding in BEC, then decoding operation can be performed, but the workload for operation is heavy and error correcting capability is limited
Solution Approach 1:
The patent segments the decoding problem by dividing erasure locations into different groups and processing them through multiple decoding rounds. In each round, only specific erasure locations are filled with test values and decoded, rather than processing all erasure locations simultaneously. This segmentation reduces the computational workload per operation while maintaining error correcting capability through iterative processing.
Solution Approach 2:
The patent applies preliminary action by pre-filling erasure locations with test values (0 or 1) before decoding operations. By preparing test code words with assumed values at erasure positions beforehand, the system can efficiently perform hard decoding operations without complex soft decoding calculations, thus reducing operational workload while achieving error correction.
2Reliability
If soft decoding algorithm (SPA) is used, then error correcting capability is improved, but it cannot be used for hard decoding in BEC where only hard values are available
Solution Approach 1:
The patent inverts the conventional approach by adapting hard decoding algorithms to work effectively for BEC erasure channels. Instead of trying to apply soft decoding (SPA) to hard values, the invention modifies hard decoding by systematically filling erasure locations with test values and using parity check equations to determine correct values, thereby making hard decoding adaptable to erasure channel characteristics.
Solution Approach 2:
The patent changes the parameter representation by working with hard values (0 and 1) in GF(2) field instead of soft probability values. The method transforms the decoding problem into finding consistent hard values that satisfy parity check equations, changing the mathematical domain from soft probability space to discrete binary space while maintaining error correcting capability.
3Ease of operation
If conventional hard decoding is used for erasure channels, then decoding can be performed with available hard values, but the capability of error correcting is limited
Solution Approach 1:
The patent implements feedback mechanisms through iterative decoding rounds. After each decoding round, the results are checked against parity check equations, and incorrect assumptions about erasure location values are corrected in subsequent rounds. This feedback loop continuously improves error correcting capability while maintaining ease of operation through systematic re-evaluation of erasure positions.
Solution Approach 2:
The patent replaces complex soft decoding mechanics with simpler hard decoding operations enhanced by systematic test value assignment. Instead of using probability calculations and message passing algorithms, the method substitutes mechanical parity check equation solving with binary value assignments and verification, achieving improved error correction with simpler operations.
Data Source
AI summary
The present invention discloses a method for LDPC code erasure decoding, including: generating a first code word through setting a value as a value in Galois field having two elements GF(2) at each of erasure locations in a code word; generating a second code word through setting the value as an inverse value of the value in GF(2) at each of the erasure locations in the code word; conducting a MLD error correcting operation for the first code word and the second code word to get a first result of hard decoding and a second result of hard decoding respectively; determining a result of erasure decoding according to the first result of hard decoding and the second result of hard decoding. Thus the present invention allows LDPC code erasure decoding aimed at the BEC, and increases the error correcting capability for BED signal transmitted data.