Turbo Encoding with Bijective Symbol Mapping for Higher Code Distance
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Solution Overview
Problem
Existing binary turbo codes in digital communications have limitations in error correction performance due to their reliance on binary symbols, which restricts the minimum cumulative Euclidean distance between codewords, impacting the correction power, especially in non-binary turbo codes used in wireless and wired communications.
Innovation Solution
A bijective transformation of information symbols before or after interleaving in the turbo-coding process, modifying both the order and value of symbols, is introduced to increase the minimum cumulative Euclidean distance between codewords, enhancing the correction power of non-binary turbo codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If binary turbo codes are used in digital communications, then the system complexity is low and implementation is simple, but the error correction performance is limited due to restricted minimum cumulative Euclidean distance between codewords
Solution Approach 1:
The patent applies parameter changes by transitioning from binary symbols (GF(2)) to non-binary symbols (GF(q) where q>2). This fundamental parameter change in the symbol domain enables increased minimum cumulative Euclidean distance between codewords, directly improving error correction performance while maintaining turbo code structure
Solution Approach 2:
The patent introduces a transformation dimension by applying bijective transformations to information symbols before encoding. This additional transformation layer modifies the symbol values to maximize dispersion, creating a new dimension of optimization beyond traditional binary encoding
2Reliability
If non-binary turbo codes are used to improve correction power, then the minimum cumulative Euclidean distance between codewords increases, but the complexity of the encoding and decoding processes increases
Solution Approach 1:
The patent applies preliminary action by performing bijective transformation on information symbols before they enter the turbo encoding process. This pre-transformation optimizes the symbol distribution to maximize cumulative Euclidean distance, enabling the system to achieve better correction power while managing complexity through structured preprocessing
Solution Approach 2:
The patent changes the parameter domain from binary to non-binary (GF(q)) and introduces transformation functions that modify symbol values. These parameter changes enable increased correction power through enhanced symbol dispersion while maintaining a systematic approach to encoding
3Reliability
If information symbols are transformed before interleaving, then the dispersion between symbols is maximized and correction performance improves, but the processing complexity increases
Solution Approach 1:
The patent performs the bijective transformation of information symbols as a preliminary action before interleaving and encoding. This preprocessing step maximizes symbol dispersion and sets optimal conditions for subsequent encoding operations, improving correction performance while organizing complexity into manageable sequential stages
Data Source
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AI summary
The invention relates to a method for generating a signal, comprising a step of turbo-coding a set of information symbols supplying, on the one hand, the information symbols and, on the other hand, redundancy symbols, comprising following the steps, to obtain the redundancy symbols, of: - a coding (21A) of the set of information symbols by a first coder, - an interleaving (23A) of the set of information symbols, - a coding (22A) of the set of information symbols interleaved by a second coder. According to the invention, the step of turbo-coding also includes a bijective transformation (24A) of the information symbols, which is performed before and/or after the step of interleaving, the transformation modifying the value of at least two of the information symbols prior to the coding of the information symbols by the first and/or the second coder.