LDPC Shortening Patterns for Variable Codeword Lengths
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Solution Overview
Problem
Current LDPC codes used in communication systems, such as DVB-S2, are limited to only two codeword lengths, which restricts their extendibility and flexibility, especially in high-order modulation schemes like 16-QAM, 64-QAM, and 256-QAM, where bit reliabilities differ, necessitating a method to generate LDPC codewords with various lengths without requiring new parity-check matrices.
Innovation Solution
The method involves using shortening and puncturing techniques optimized for specific modulation schemes, where the LDPC encoder generates LDPC codewords with varying lengths by modifying the parity-check matrix, considering the structural features of the DVB-S2 LDPC code, and applying shortening patterns that maintain optimal degree distribution and cycle characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If LDPC codes are designed with fixed codeword lengths (e.g., DVB-S2 standard with 16200 and 64800), then the code structure and parity-check matrix are simplified and optimized, but the system loses flexibility and extendibility to support various codeword lengths required by different modulation schemes
Solution Approach 1:
The parity-check matrix is divided into multiple sub-matrices or blocks, allowing selective combination to form different codeword lengths. The code is segmented into base blocks that can be repeated or truncated to achieve various lengths without redesigning the entire parity-check matrix.
Solution Approach 2:
A single base parity-check matrix design serves multiple functions by supporting various codeword lengths through parameter adjustment. The same fundamental code structure is made universal to work with different modulation schemes (QPSK, 16-QAM, 64-QAM, 256-QAM) by changing only the length parameters, not the core matrix structure.
2Reliability
If new parity-check matrices are designed for each codeword length to optimize performance, then the communication reliability improves, but the memory storage requirement and system complexity increase significantly
Solution Approach 1:
Instead of storing multiple unique parity-check matrices, the system stores a single base matrix that is copied or replicated to generate the required parity-check matrices for different codeword lengths. This copying approach maintains optimal performance while dramatically reducing memory requirements.
Solution Approach 2:
The system achieves different codeword lengths by changing parameters (such as repetition count, truncation position, or puncturing pattern) of a single base parity-check matrix rather than changing the matrix structure itself. This parameter-based adaptation maintains reliability while minimizing storage needs.
3Reliability
If LDPC codes are optimized for specific modulation schemes, then the performance in that scheme improves, but the code cannot be efficiently adapted to other modulation schemes with different bit reliability characteristics
Solution Approach 1:
The LDPC code structure incorporates dynamic elements that allow adaptation to different modulation schemes. The code can dynamically adjust its effective structure through selective puncturing, shortening, or repetition patterns based on the specific modulation scheme being used, maintaining optimal performance across QPSK, 16-QAM, 64-QAM, and 256-QAM.
Data Source
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AI summary
A method and apparatus for encoding and decoding a channel in a communication system using a Low-Density Parity-Check (LDPC) code. The encoding method includes determining a modulation scheme for transmitting a symbol; determining a shortening pattern in consideration of the determined modulation scheme; grouping columns corresponding to an information word in a parity-check matrix of the LDPC code into a plurality of column groups; ordering the column groups; determining a range of a resulting information word desired to be obtained by shortening the information word; based on the range of the resulting information word, performing column group-by-column group shortening on the ordered column groups of the information word, according to the determined shortening pattern; and LDPC-encoding the shortened information word.