Non-Binary LDPC Encoder Parity Matrix for Parallel Low-Complexity Coding
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Solution Overview
Problem
Existing non-binary quasi-cyclic LDPC encoders face challenges in achieving low complexity operations while maintaining parallel processing performance and improved error correction capabilities.
Innovation Solution
The proposed LDPC encoder employs a parity check matrix with specific sub-matrix arrangements and scaling elements, allowing for reduced complexity in inverse matrix multiplication through structured calculations, thereby enhancing error correction performance and parallel processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a parity check matrix with specific sub-matrix arrangements and scaling elements is used, then error correction performance is improved and calculation complexity is reduced, but device complexity increases due to structured matrix design requirements
Solution Approach 1:
The parity check matrix is segmented into multiple sub-matrices (information part matrix and parity part matrix) with specific structures. Each sub-matrix has defined properties (e.g., identity matrices, zero matrices, scaled cyclic matrices) that enable independent processing and reduce overall calculation complexity while maintaining error correction capabilities.
Solution Approach 2:
Different regions of the parity check matrix are assigned different local qualities or structures. The information part matrix and parity part matrix have distinct sub-matrix arrangements, and specific positions contain identity matrices, zero matrices, or scaled cyclic matrices based on their functional requirements, optimizing both error correction and computational efficiency.
2Productivity
If inverse matrix multiplication complexity is reduced through structured calculations, then encoding speed increases, but manufacturing precision requirements increase for implementing the structured matrix operations
Solution Approach 1:
The parity check matrix uses specific parameter choices for sub-matrices (identity matrices, zero matrices, scaled cyclic matrices with scaling elements from Galois fields) that transform the inverse matrix multiplication into simpler structured operations. This parameterization enables faster computation while the structured nature provides inherent precision through deterministic calculation patterns.
3Productivity
If parallel processing performance is maintained in non-binary quasi-cyclic LDPC encoding, then processing throughput increases, but calculation complexity increases due to non-binary operations
Solution Approach 1:
The encoding process is segmented into parallelizable operations based on the block-diagonal structure of the parity check matrix. The information part matrix and parity part matrix can be processed independently or in parallel stages, enabling throughput optimization while the structured sub-matrices reduce individual operation complexity.
Solution Approach 2:
Complex non-binary arithmetic operations are replaced with simpler structured matrix operations (multiplication by scaling elements, cyclic shifts, additions) that are easier to implement in parallel hardware. The structured parity check matrix transforms complex field arithmetic into more manageable operations suitable for parallel processing.
Data Source
AI summary
An LDPC encoder is described with memory for storing a parity check matrix and a calculation unit to encode information bits into a codeword with reference to the parity check matrix. The parity check matrix includes an information part matrix and a parity part matrix. In the parity part matrix, Z*Z sub-matrices are sub-matrices, other than a zero matrix, and are arranged in each of the m rows and m columns. A sub-matrix is a scaled cyclic matrix obtained by shifting elements of an identity matrix by one to the left and multiplying the shifted elements by a scaling element. Except for the scaled cyclic matrix, the remaining sub-matrices are a zero matrix or an identity matrix, and the scaling element is an element allowing the parity part matrix to satisfy a full rank condition on a Galois field.