Repeat Zigzag-Hadamard Codes for Low-SNR Low-Rate Decoding
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Solution Overview
Problem
Existing low-rate channel coding schemes, such as Hadamard codes and super-orthogonal convolutional codes, suffer from low coding gain and high complexity, especially in the low signal-to-noise ratio (SNR) regime, and iterative decoding methods like repeat-accumulate and low-density parity-check codes experience performance loss and slow convergence.
Innovation Solution
The introduction of repeat-zigzag-Hadamard (RZH) codes, which are serially concatenated turbo-like codes with an outer repetition code and an inner punctured zigzag-Hadamard code, offering a simpler encoder and decoder structure and flexible coding rates, along with efficient decoding algorithms like APP Hadamard decoding and belief propagation schemes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Hadamard codes and super-orthogonal convolutional codes are used for low-rate channel coding, then the coding scheme is simple to implement, but the coding gain is low and performance is far from the Shannon limit
Solution Approach 1:
The code is segmented into an outer repetition code and an inner zigzag-Hadamard code, creating a serially concatenated structure that combines the simplicity of repetition codes with the performance benefits of Hadamard codes, achieving both ease of implementation and high coding gain
Solution Approach 2:
The patent creates a composite coding scheme by combining two different code types (repetition code and zigzag-Hadamard code) into a single structured system, where the outer code provides redundancy and the inner code provides coding gain, resulting in a code that achieves performance close to the Shannon limit while maintaining implementation simplicity
2Reliability
If repeat-accumulate codes or low-density parity-check codes are used to approach Shannon capacity, then the code rate can be optimized, but iterative decoding suffers from performance loss and extremely slow convergence speed in the low-rate region
Solution Approach 1:
The patent extracts the iterative decoding complexity from the system by using a non-iterative maximum likelihood decoding approach for the zigzag-Hadamard code, removing the performance loss and slow convergence issues associated with iterative decoding while maintaining capacity-approaching performance
Solution Approach 2:
The patent uses repetition coding to create multiple copies of information bits, which can be decoded using simple majority voting or maximum likelihood decoding without iteration, achieving both capacity-approaching performance and fast decoding convergence
3Productivity
If turbo-Hadamard codes are used to achieve good performance with faster convergence, then the decoding speed improves, but a relatively large Hadamard order is required which increases the decoder complexity
Solution Approach 1:
The patent applies local quality by using a zigzag pattern in the Hadamard code construction that concentrates the coding gain in specific positions, allowing the use of smaller Hadamard orders while maintaining performance, thus reducing decoder complexity without sacrificing convergence speed
Solution Approach 2:
The patent changes the structure parameter of the Hadamard code by introducing the zigzag pattern, which transforms the traditional Hadamard code into a zigzag-Hadamard code with improved performance characteristics, enabling faster convergence with lower complexity decoders
Data Source
AI summary
An encoder includes an outer repetition encoder, an interleaver for permuting encoding from said outer repetition encoder; and an inner encoder for encoding information from the interleaver to provide a repeat zigzag-Hadamard code. In an exemplary embodiment, a common bit of a zigzag-Hadamard segment of encoding from said inner encoder is a repetition of a last parity bit of a previous zigzag-Hadamard segment of encoding from said inner encoder and said common bit is punctured.