LDPC Check Node Update Using Exponential Approximation
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Solution Overview
Problem
The existing check node update rule in LDPC decoders is complex due to hyperbolic tangent functions and many multiplication operations, making it difficult to implement efficiently, especially when compared to the variable node update rule which only involves summing operations.
Innovation Solution
A method for approximating the check node update rule using a sum of exponential functions, specifically g′(x) = e^(-x) - e^(-2x) + 2 - α, which simplifies the update operation and reduces the number of required operations, allowing for performance comparable to the belief propagation algorithm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the check node update rule uses the BP algorithm with hyperbolic tangent functions and multiplication operations, then decoding accuracy is improved, but computational complexity increases significantly
Solution Approach 1:
The patent transforms the check node update rule by changing the functional form from hyperbolic tangent with multiplication to exponential functions. Specifically, it uses the approximation tanh(x) ≈ 1 - 2e^(-2x) to convert the complex update rule into a form that requires only addition and exponentiation operations, thereby reducing computational complexity while maintaining decoding accuracy
Solution Approach 2:
The patent replaces the traditional Sum-Product algorithm mechanics with a simplified exponential-based update mechanism. By substituting the hyperbolic tangent function and multiplication operations with exponential functions and addition operations, it creates a new computational mechanism that is easier to implement in hardware while preserving the belief propagation decoding accuracy
2Ease of manufacture
If the check node update rule is simplified using only summing operations like variable node update, then ease of implementation is improved, but decoding performance deteriorates
Solution Approach 1:
The patent introduces exponential functions into the check node update rule, changing it from simple summing operations to a form that includes exponentiation. This modification maintains ease of implementation by avoiding complex hyperbolic tangent calculations while improving decoding performance through the exponential approximation of the tanh function, which better captures the non-linear relationships in the belief propagation algorithm
Data Source
AI summary
A method is provided for updating a check node in a low density parity check (LDPC) decoder, including: transmitting log-likelihood ratio (LLR) messages from variable nodes to a plurality of check nodes; decomposing the LLR messages in a plurality of node messages for each check node; and updating each check node using a modified function g(x), which is a function g′(x) comprising a sum operation of exponential functions based on the node messages.