Product Code Decoding with Extended Parity Check Re-Decoding
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Solution Overview
Problem
Current decoding methods for product codes in radio communication and storage devices without feedback channels face challenges in achieving very low bit error rates due to the complexity of maximum likelihood decoding and the need for two independent decoders when horizontal and vertical codes differ.
Innovation Solution
A method and device for decoding a product code using soft decision information, which involves generating extended parity check matrices and combining independent soft decision information for decoding failed horizontal codewords, reducing decoding complexity and hardware requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If maximum likelihood decoding scheme using soft decision information is used for product code, then decoding performance is improved, but decoding complexity and device complexity increase
Solution Approach 1:
The patent segments the decoding process into two distinct phases: a first decoding process using the original extended parity check matrix, and a second decoding process using a modified extended parity check matrix. This segmentation allows the system to achieve improved decoding performance through the second process while keeping the overall complexity manageable by structuring the operations in discrete, organized steps rather than a monolithic complex process.
Solution Approach 2:
The patent performs preliminary action by first attempting to decode horizontal codewords using the original extended parity check matrix in the first decoding process. This preliminary decoding attempt identifies which codewords have been successfully decoded and which have failed, allowing the system to then focus computational resources only on the failed codewords in the second decoding process, thereby reducing overall complexity while maintaining performance.
2Reliability
If two independent decoders are implemented for horizontal and vertical codes, then decoding performance is improved, but device complexity and hardware requirements increase
Solution Approach 1:
The patent implements a universal decoder that performs multiple functions: it decodes both horizontal and vertical codewords, and it operates in two different decoding modes using two different extended parity check matrices. This single multi-functional decoder replaces what would traditionally require two separate independent decoders, thereby reducing hardware requirements and device complexity while maintaining the decoding performance benefits of processing both horizontal and vertical codes.
Solution Approach 2:
The patent merges the functionality of separate horizontal and vertical decoders into a single integrated decoding device. By combining these functions and implementing them within one decoder structure that can switch between different parity check matrices, the system achieves the performance of multiple independent decoders while reducing the actual hardware complexity and resource requirements.
3Reliability
If extended parity check matrix is used for re-decoding failed horizontal codewords, then error correction capability is improved, but decoding complexity increases
Solution Approach 1:
The system performs preliminary identification of failed horizontal codewords through the first decoding process before applying the more complex second decoding process with the modified extended parity check matrix. This preliminary action filters the set of codewords that need intensive processing, so the increased complexity of using the modified matrix is applied only where necessary, not to all codewords uniformly.
Solution Approach 2:
The patent applies partial action by using the modified extended parity check matrix only for the subset of horizontal codewords that failed the first decoding process, rather than applying it to all codewords. This selective application provides enhanced error correction capability exactly where needed (for failed codewords) while avoiding the unnecessary complexity overhead for successfully decoded codewords.
Data Source
AI summary
A method for a decoding device to decode a codeword matrix of a product code includes: generating a first extended parity check matrix for a vertical code; decoding a horizontal codeword of a plurality of rows in the codeword matrix to thus perform a first decoding process; generating a second extended parity check matrix by removing a column corresponding to a row of the first decoding-succeeded horizontal codeword from the first extended parity check matrix; and decoding the first decoding-failed horizontal codeword by using the second extended parity check matrix to thus perform a second decoding process. Therefore, the simple and reliable product code decoding method is provided.