LDPC-CC Parity Check Coding for Variable-Length Error Correction
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Solution Overview
Problem
Current LDPC-CC technologies are limited in their time-varying periods, particularly for coding rates beyond 2, 3, and multiples of 3, which restricts their error correction capabilities and adaptability in variable-length communication systems.
Innovation Solution
The development of a method for LDPC-CC encoding and decoding using parity check polynomials with a coding rate of (n−1)/n, where n is an integer greater than or equal to 2, and the time-varying period q is a prime number greater than 3, allowing for encoding and decoding of information sequences of arbitrary lengths using specific parity check polynomial equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LDPC-CC with time-varying periods of 2, 3, or multiples of 3 is used, then the error correction capability is improved for those specific periods, but the adaptability to other time-varying periods and coding rates deteriorates
Solution Approach 1:
The patent develops a universal LDPC-CC encoding and decoding method that can handle any time-varying period q (prime number greater than 3) and any coding rate (n-1)/n where n≥2. The parity check polynomial structure with parameters a#g,k,r and b#g,r allows the system to adapt to different time-varying periods and coding rates without requiring separate specialized codes for each case, thus achieving multi-functionality and universality.
Solution Approach 2:
The patent employs parameter changes by defining the parity check polynomial with variable parameters a#g,k,r and b#g,r that can be adjusted based on the time index g and the specific application requirements. This allows the LDPC-CC to adapt its structure dynamically to match different time-varying periods and coding rates, resolving the contradiction between optimized performance for specific periods and general adaptability.
2Device complexity
If fixed-length LDPC code blocks are used, then the encoding and decoding structure is simplified, but the ability to handle variable-length communication frames deteriorates
Solution Approach 1:
The patent applies dynamics by using a convolutional code structure instead of a fixed block code. The LDPC-CC encoder processes information sequences of arbitrary length through shift registers and mod 2 adders, allowing the code length to vary dynamically based on the input data while maintaining a regular and systematic encoding/decoding structure. This resolves the contradiction between structural simplicity and variable-length adaptability.
3Ease of operation
If padding or puncturing processing is applied to adjust sequence length, then the fixed-length LDPC code block can be matched to variable-length frames, but the coding rate changes or redundant sequences are transmitted
Solution Approach 1:
The patent extracts the necessary code length flexibility directly from the convolutional LDPC-CC structure itself, rather than adding padding or puncturing operations. By using shift registers and a systematic parity check polynomial approach, the encoder naturally produces codewords of the required length without needing to extract or add redundant elements, thus eliminating the need for padding or puncturing processing.
Data Source
AI summary
An encoding method and encoder of a time-varying LDPC-CC with high error correction performance are provided. In an encoding method of performing low density parity check convolutional coding (LDPC-CC) of a time varying period of q using a parity check polynomial of a coding rate of (n−1)/n (where n is an integer equal to or greater than 2), the time varying period of q is a prime number greater than 3, the method receiving an information sequence as input and encoding the information sequence using Equation 1 as a g-th (g=0, 1, . . . , q−1) parity check polynomial to satisfy 0.