LDPC Parity Check Matrix with Puncturing for Variable Code Rates
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Solution Overview
Problem
Block Low Density Parity Check (LDPC) codes in future-generation communication systems are limited by their fixed code rate, making them unsuitable for high-speed data transmission, as they are not free to support various code rates ranging from low to high.
Innovation Solution
The solution involves generating a parity check matrix for LDPC codes that can support multiple code rates by adding columns of degrees 1 and 2 to the existing matrix, allowing for puncturing of bits during decoding to adjust the code rate, thereby enabling flexible code rate support using a single Coder-Decoder (CODEC).
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If block LDPC codes with fixed code rates (1/2 or 1/3) are used, then excellent performance gain during high-speed data transmission is achieved, but the code rate flexibility is limited making them unsuitable for various code rate requirements
Solution Approach 1:
The patent applies universality by designing a single base parity check matrix that can serve multiple code rates (1/2, 1/3, 2/5, etc.) through selective column puncturing. The base matrix contains all necessary columns that can be systematically removed based on the desired code rate, making one matrix structure universal for multiple coding scenarios.
Solution Approach 2:
The patent changes the parameter of code rate by controlling which columns are punctured from the base parity check matrix. By varying the puncturing pattern and density, different effective code rates are achieved from the same base matrix, allowing continuous adaptation to different transmission requirements.
2Reliability
If multiple separate parity check matrices are designed for different code rates, then each code rate can be optimized independently, but the device complexity and hardware requirements increase
Solution Approach 1:
Instead of designing separate parity check matrices for different code rates, the patent creates one universal base matrix that can generate multiple code rates through puncturing. This reduces hardware complexity by eliminating the need for multiple matrix storage and processing units.
Solution Approach 2:
The patent merges multiple code rate requirements into a single base parity check matrix structure. All code rate-specific columns are incorporated into the base matrix, and the desired code rate is achieved by selecting and puncturing appropriate columns, thereby combining multiple functions into one structure.
3Adaptability or versatility
If code rate flexibility is increased by using multiple parity check matrices, then various code rates can be supported, but the coding and decoding complexity increases
Solution Approach 1:
The patent segments the base parity check matrix into information columns and parity columns, and further segments parity columns into puncturable and non-puncturable subsets. This segmentation allows systematic control over which columns to remove for different code rates, simplifying the encoding and decoding processes compared to handling completely separate matrices.
Solution Approach 2:
The patent performs preliminary action by pre-designing the base parity check matrix with all necessary columns for multiple code rates already in place. The matrix is prepared in advance with columns arranged and labeled for easy identification and selective puncturing, eliminating the need for complex real-time matrix selection during encoding/decoding operations.
Data Source
AI summary
An apparatus and method for transmitting and receiving a signal in a communication system are provided. The signal transmission apparatus generates a parity check matrix for an LDPC code in accordance with a code rate to be used and generates a codeword vector by encoding an information vector using the parity check matrix. When the code rate is a first code rate, the signal transmission apparatus generates a first parity check matrix as the parity check matrix for the LDPC code. When the code rate is the second code rate, the signal transmission apparatus generates a second parity check matrix supporting a second code rate lower than the first code rate by adding columns of a degree of 1 and columns of a degree of 2 to the first parity check matrix and generates the second parity check matrix as the parity check matrix for the LDPC code.