Channel Code Construction for Decoder Reuse Across Code Lengths
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional code modification schemes fail to efficiently reuse decoders for new code lengths and dimensions, leading to increased complexity and error rates, especially when modifying existing {N, K} codes to {N′, K′} codes, as new decoding algorithms are required, which can be less efficient.
Innovation Solution
A method to modify the original code by a combined shortening and extending operation, creating a new {N′, K′} code that can be efficiently decoded using the existing decoder for the original {N, K} code, by modifying the check matrix to include zero columns and additional rows, allowing the decoder to reuse the new code with reduced computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional code modification schemes are used to change code length and dimension, then new {N′, K′} codes can be generated, but decoder reuse becomes inefficient and complexity increases
Solution Approach 1:
The check matrix H′ is segmented into distinct blocks: an identity matrix block I_{p+q} and a submatrix block containing the original check matrix H. This segmentation allows the decoder to process different parts of the code separately, maintaining efficiency while accommodating new code dimensions. The segmented structure enables selective application of decoding operations to relevant subsets of the code.
Solution Approach 2:
The patent introduces an intermediate check matrix structure that acts as a bridge between the original code and the modified code. This intermediate structure, with its specific block form containing zero blocks and identity matrices, allows the original decoder to operate on a subset of equations while the remaining equations are handled through the structured modifications, thus enabling decoder reuse with minimal additional complexity.
2Reliability
If new decoding algorithms are developed for modified codes, then correct decoding is achieved, but computational complexity and error rates increase
Solution Approach 1:
The modified check matrix structure is designed to be universal, allowing the same decoder architecture to handle both original and modified codes. By embedding the original check matrix H within a larger structured matrix H′ that includes identity blocks and zero blocks, the decoder can universally process both code types using the same algorithm, maintaining reliability without requiring separate decoding paths.
Solution Approach 2:
The check matrix is pre-structured with identity matrices and zero blocks in specific positions before decoding occurs. This preliminary structuring of H′ ensures that during decoding, certain equations are already in a favorable form that reduces computational burden. The pre-computed structure enables the decoder to skip certain complex calculations that would otherwise be necessary.
3Adaptability or versatility
If check matrix is modified by adding rows and columns, then new code dimensions are achieved, but minimum distance properties may deteriorate
Solution Approach 1:
The modifications to the check matrix are applied locally rather than uniformly across the entire matrix. Specifically, identity matrices and zero blocks are placed in specific local regions of H′, while the core submatrix retains the original structure and properties of H. This localized modification approach preserves the minimum distance properties of the original code in the critical regions while allowing dimensionality changes in less critical areas.
Data Source
AI summary
The present disclosure provides a code generator for generating an {N′, K′} code for encoding and/or decoding data transmitted in a communication channel from an {N, K} code, wherein N and N′ are code lengths, K and K′ are code dimensions. The code generator is configured to shorten the {N, K} code to obtain an intermediate code, and to extend the intermediate code to obtain the {N′, K′} code. The present disclosure also provides a corresponding code construction method. Further, the present disclosure provides a device for encoding and/or decoding data transmitted in a communication channel, the device being configured to encode and/or decode the data based on an {N′, K′} code generated from the {N, K} code.