Double-Extended Hamming Code Matrix for Lower-Decoding Complexity
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Solution Overview
Problem
Existing Hamming codes, including single-extended and double-extended versions, suffer from high encoding and decoding complexity, and their performance is not optimal, especially for specific code lengths, limiting their effectiveness in communication systems.
Innovation Solution
A double-extended Hamming code is developed with a target parity-check matrix determined by a function from a predetermined set, reducing operation quantity and complexity, thereby improving encoding and decoding efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If double-extended Hamming code is used to improve error correction performance, then reliability is improved, but device complexity increases
Solution Approach 1:
The parity-check matrix is segmented into multiple blocks, each block corresponding to a specific function from a predetermined function set. This segmentation allows the decoding process to be divided into manageable steps, reducing overall complexity while maintaining the error correction capabilities of the double-extended Hamming code.
Solution Approach 2:
The patent changes the parameters of the parity-check matrix by selecting specific functions from a predetermined function set to define the matrix structure. This parameter optimization reduces the operation quantity required for decoding while preserving the reliability benefits of the double-extended Hamming code.
2Reliability
If conventional Hamming code extension methods are used to improve detection and error correction capabilities, then reliability is improved, but device complexity increases
Solution Approach 1:
Instead of using conventional extension methods that simply add parity bits or rows, this patent changes the structural parameters of the parity-check matrix by incorporating specific functions from a predetermined function set. This approach achieves enhanced detection and error correction capabilities while controlling complexity through optimized matrix construction.
Solution Approach 2:
The patent uses a systematic approach where the parity-check matrix is constructed by copying and combining standardized function blocks from a predetermined function set. This modular copying method simplifies the design process and reduces implementation complexity compared to custom extensions.
Data Source
AI summary
An encoding method includes: obtaining a generator matrix for encoding, where the generator matrix is determined based on a target parity-check matrix of a Hamming code for encoding, the target parity-check matrix is based on a target function for decoding, the target function is used to determine a not-all-zero row vector extended based on the target parity-check matrix, and the target function is one of a predetermined function set; encoding information bits using the generator matrix to obtain an encoded data stream; and sending the encoded data stream.