Generator Matrix Selection for Short-Block Linear Error Codes
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Solution Overview
Problem
Existing error correction codes in digital communication systems are inadequate for constructing binary error correction codes under channel uncertainty, which is essential for reliable and efficient data transmission in modern communication systems.
Innovation Solution
A coded modulation device and method that determines candidate generator matrices to construct linear error correcting codes, optimizing for non-coherent metrics and providing performance approaching orthogonal codes, while using fewer signaling dimensions, and is adapted for efficient short block-length codes suitable for 3GPP resource grids in LTE/NR transmission systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing error correction codes are used in digital communication systems, then data transmission can be performed, but the system performance is inadequate under channel uncertainty and cannot achieve reliable transmission with optimal efficiency
Solution Approach 1:
The patent changes the fundamental parameters of error correction codes by transitioning from traditional binary codes to non-binary codes over finite fields GF(q) where q > 2. This parameter change enables the system to achieve better performance under channel uncertainty while maintaining manageable complexity through algebraic structure exploitation.
Solution Approach 2:
The patent combines multiple mathematical structures (finite fields, generator matrices, signal constellations) to create composite coding schemes that integrate error correction capabilities with modulation techniques, achieving superior reliability under uncertainty by merging algebraic code theory with signal processing principles.
2Device complexity
If traditional linear error correction codes are used, then implementation complexity is reduced, but performance under channel uncertainty is inadequate
Solution Approach 1:
The patent extends traditional binary error correction codes into higher-dimensional non-binary spaces by utilizing finite fields GF(q) with q > 2. This dimensional extension allows the codes to capture more information per symbol while maintaining linear code structure, achieving better uncertainty performance without proportionally increasing implementation complexity.
Solution Approach 2:
The patent designs generator matrices that serve multiple functions simultaneously: they define the linear code structure for efficient encoding, determine the signal constellation mapping for modulation, and provide the algebraic framework for decoding. This multi-functionality reduces overall system complexity while improving performance.
3Reliability
If non-binary linear codes over GF(q) with q > 2 are used, then performance under channel uncertainty is improved, but the complexity of code construction and implementation increases
Solution Approach 1:
The patent segments the code construction process into systematic steps: defining finite field arithmetic operations, constructing generator matrices with specific algebraic properties, mapping to signal constellations, and establishing decoding procedures. This segmentation makes the complex construction process more manageable and implementable.
Solution Approach 2:
The patent performs preliminary actions by pre-defining the algebraic structure of finite fields GF(q), pre-constraining generator matrix forms to satisfy specific properties, and pre-establishing mapping rules between code symbols and signal constellation points. These preliminary actions simplify the actual encoding and decoding operations during transmission.
4Productivity
If shorter block lengths are used for error correction codes, then transmission efficiency is improved, but error correction capability is reduced
Solution Approach 1:
The patent changes the code rate parameters by using non-binary alphabets GF(q) where each symbol carries log2(q) bits of information. This parameter change allows shorter block lengths to achieve the same transmission efficiency as longer binary codes, while the algebraic structure of non-binary codes provides enhanced error correction capability despite the reduced block length.
Data Source
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AI summary
A coded modulation device (20) for determining one or more linear error correcting codes, wherein the coded modulation device comprises: - a calculation unit (201) configured to determine two or more candidate generator matrices, each candidate generator matrix defining a linear error correcting code and comprising values selected from a predefined set of values, each candidate generator matrix providing a set of codeword vectors from input vectors, said input vectors comprising values selected from said predefined set of values; - A metric determination unit (202) configured to associate a vector metric to each pair of codeword vectors provided by each candidate generator matrix for a predefined modulation scheme and to associate a matrix metric to each candidate generator matrix, a matrix metric associated with a candidate generator matrix being the minimum value among the vector metrics associated with the pairs of codeword vectors provided by said candidate generator matrix; - a selection unit (203) configured to select the one or more candidate generator matrices that are associated with the highest matrix metric among said two or more candidate generator matrices, wherein the one or more linear error correcting codes are represented by said selected one or more candidate generator matrices.