LDPC Convolutional Coding with Flexible Rates and Tail-Biting
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Solution Overview
Problem
Current methods lack a systematic approach for generating Low-Density Parity Check Convolutional Codes (LDPC-CCs) with coding rates no smaller than 1/2 and not satisfying (n−1)/n, and do not utilize improved tail-biting schemes effectively for LDPC block codes based on parity check polynomials.
Innovation Solution
The development of an encoding and decoding method for LDPC-CCs using predetermined parity check matrices with specific mathematical expressions for parity check polynomials, allowing for row and column permutations to achieve coding rates of (n−1)/n, and incorporating improved tail-biting schemes to enhance error correction capabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If LDPC-CC encoding is performed with coding rates not satisfying (n-1)/n, then coding flexibility is improved, but systematic generation methods are lacking
Solution Approach 1:
The patent applies parameter changes by modifying the parity check matrix structure and applying row/column permutations to generate LDPC-CC codes with arbitrary coding rates. By changing the parameters of the parity check polynomial and the permutation operations, the system can systematically generate codes for any coding rate, not just (n-1)/n rates, thereby achieving both coding flexibility and systematic generation.
2Reliability
If improved tail-biting schemes are incorporated, then error correction capability is improved, but implementation complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-defining the tail-biting constraints and parity check relationships before the actual encoding process. The improved tail-biting scheme is incorporated into the parity check matrix structure in advance, allowing the encoder to systematically handle the tail-biting conditions without requiring complex real-time calculations, thus reducing implementation complexity while maintaining high error correction capability.
3Adaptability or versatility
If row and column permutations are applied to parity check matrices, then coding rates of (n-1)/n are achieved, but matrix transformation complexity increases
Solution Approach 1:
The patent applies parameter changes by using systematic row and column permutation patterns that transform the base parity check matrix into forms suitable for (n-1)/n coding rates. The permutation operations follow defined mathematical relationships that maintain the low-density structure while achieving the desired coding rates, thereby balancing adaptability with manageable transformation complexity.
Data Source
AI summary
An encoding method of generating an encoded sequence by performing encoding of a given encoding rate based on a predetermined parity check matrix. The predetermined matrix is either a first parity check matrix or a second parity check matrix. The first parity check matrix corresponds to a low density parity check (LDPC) convolutional code that uses a plurality of parity check polynomials, and the second parity check matrix is generated by performing at least one of row permutation and column permutation on the first parity check matrix. A parity check polynomial satisfying zero of the LDPC convolutional code is expressible by using a specific mathematical expression.