Stochastic GF(q) LDPC Decoding with Parity Check Factor Graphs
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Solution Overview
Problem
Current decoding methods for non-binary Low Density Parity Check (LDPC) codes are complex and lack efficient stochastic decoding solutions, which are essential for error correction in data communication systems.
Innovation Solution
A stochastic decoding method and system that processes encoded symbols using a parity check matrix with elements of a Galois field, employing logic circuitry with variable nodes, permutation nodes, and parity check nodes to perform Galois field operations, determining probability messages and output symbols until a stopping criterion is satisfied.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-binary LDPC codes are used to improve error correcting capability, then error correction performance is improved, but decoding complexity increases
Solution Approach 1:
The patent replaces traditional deterministic decoding algorithms (belief propagation, minimum sum algorithm) with a stochastic decoding approach using random walkers on the factor graph. This substitution transforms the complex algebraic operations into simpler random walks, reducing decoding complexity while maintaining error correction performance for non-binary LDPC codes over GF(q)
2Measurement precision
If traditional deterministic decoding algorithms are used, then decoding accuracy is maintained, but computational complexity increases
Solution Approach 1:
The patent substitutes complex deterministic computations with stochastic random walks. The random walkers traverse the factor graph and collect syndrome information, replacing the need for complex belief propagation calculations. This achieves comparable decoding accuracy with reduced computational power requirements
Solution Approach 2:
The patent introduces random walkers as intermediary agents that traverse the factor graph and collect syndrome information. These walkers serve as mediators between the received codeword and the decoding decision, simplifying the computational process by using random sampling instead of deterministic algorithms
Data Source
AI summary
A decoding method and system for stochastic decoding of linear codes with the parity check matrix comprising elements of a Galois field is provided. Each encoded sample of a set of encoded samples is first scaled by a scaling factor proportional to a noise level of the set of encoded samples. Each of the scaled encoded samples is then converted into a corresponding probability. For each probability a corresponding probability message is the generated by encoding each probability as a sequence of symbols or bits. Each probability message is then provided to a respective variable node of a logic circuitry for stochastic decoding. The logic circuitry represents a factor graph of the parity check matrix of the linear code. Using the logic circuitry each probability message is passed through the factor graph by performing for each received symbol at the variable nodes the equality function, at the permutation nodes one of multiplication and division, and at the parity check nodes the parity check function, wherein each of the variable nodes provides an output symbol in dependence upon each received symbol.