LDPC Convolutional Rate Matching for Erasure Correction Circuits
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Solution Overview
Problem
Current erasure correction codes face challenges in efficiently changing coding rates in response to varying communication quality, leading to increased circuit scales for encoders and decoders, which hinders transmission efficiency and erasure correction capability.
Innovation Solution
The development of a low-density parity check convolutional code (LDPC-CC) with a coding rate of 1/3 and a time-varying period of 3, defined by specific parity check polynomials, allows for the insertion of known information to adjust the coding rate, reducing the circuit scales of encoders and decoders.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the block length of Reed-Solomon code is increased to improve correction capability, then the erasure correction capability is improved, but the amount of computation and circuit scale increase
Solution Approach 1:
The patent changes the fundamental parameter of the error correction code from Reed-Solomon to LDPC code, which has a different mathematical structure based on sparse parity-check matrices. This parameter change allows achieving the same or better correction capability with reduced computational complexity and smaller circuit scale, as LDPC codes can be decoded using iterative belief propagation algorithms that are more efficient for large block lengths
Solution Approach 2:
The patent substitutes the algebraic structure of Reed-Solomon codes with the graph-theoretic structure of LDPC codes represented by Tanner graphs and sparse parity-check matrices. This structural substitution enables the use of message-passing algorithms instead of traditional algebraic decoding, reducing the computational burden and circuit complexity while maintaining or improving correction capability
2Reliability
If the block length of Reed-Solomon code is increased to improve correction capability, then the erasure correction capability is improved, but the amount of computation increases
Solution Approach 1:
The patent changes the code type from Reed-Solomon to LDPC, which fundamentally alters the decoding complexity characteristics. LDPC codes with sparse parity-check matrices enable iterative decoding that converges quickly with fewer computational operations compared to Reed-Solomon decoding, especially for long block lengths, thereby reducing the amount of computation and energy consumption
Solution Approach 2:
The patent introduces dynamic iterative decoding for LDPC codes where the decoding process adapts through multiple passes of belief propagation. The number of iterations can be adjusted dynamically based on channel conditions and error patterns, allowing the system to achieve the required correction capability with minimal computation rather than always performing maximum-length decoding
3Device complexity
If Reed-Solomon code is used with fixed block length, then the coding structure is simple, but the adaptability to varying communication quality is reduced
Solution Approach 1:
The patent implements dynamic adaptability by allowing the LDPC code's coding rate and block length to be adjusted based on communication channel conditions. The sparse parity-check matrix structure of LDPC codes enables flexible configuration of code parameters without fundamentally changing the decoding architecture, allowing the system to adapt to varying quality requirements while maintaining structural simplicity
Solution Approach 2:
The patent creates a universal LDPC decoding framework that can handle multiple coding rates and block lengths through the same belief propagation algorithm. The sparse parity-check matrix can be configured for different coding scenarios, making the system multi-functional and adaptable to various communication quality conditions without requiring separate dedicated decoders for each code configuration
Data Source
AI summary
An encoding method changes an encoding rate of an erasure correcting code. One cycle is defined as 12k bits (wherein k represents a natural number) which is an encoding output using LDPC-CC with an encoding rate of 1/2, and includes information and parity. From the one cycle, only the information is arranged in the output order of the encoding output to obtain 6k bit information X6i, X6i+1, X6i+2, X6i+3, X6i+4, X6i+5, . . . , X6(i+k−1) X6(i+k−1)+1, X6(i+k−1)+2, X6(i+k−1)+3, X6(i+k−1)+4, and X6(i+k−1)+5. Known information is inserted in 3k pieces of information (Xj) among the 6k bit information, so that when 3k pieces of mutually different j is divided by 3, there is a remainder of 0 regarding k pieces, there is a remainder of 1 regarding k pieces, and there is a remainder of 2 regarding k pieces, to thereby obtain the parity from the information containing the known information.