Concatenated Code Decoding by Ordered Noise Guessing
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Solution Overview
Problem
Existing channel coding systems face inefficiencies in decoding speed and accuracy, particularly with convolutional codes, which require complex probabilistic models and algorithms, while block codes struggle to approach channel capacity due to large block sizes and computational impracticality.
Innovation Solution
A method that decodes block codes by guessing noise sequences instead of codewords, allowing for deterministic decoding with bounded complexity and separating noise inversion from codeword validation, enabling faster decoding speeds and approaching channel capacity without requiring syndrome computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If convolutional codes are used to approach channel capacity, then error correction performance is improved, but decoding complexity and processing time increase due to probabilistic models and Viterbi algorithm
Solution Approach 1:
The patent inverts the traditional decoding approach by guessing the noise sequence instead of guessing the codeword directly. This inversion transforms the complex probabilistic search into a deterministic process with bounded complexity, achieving capacity-approaching performance without the computational burden of Viterbi algorithms
Solution Approach 2:
The patent changes the fundamental parameter being guessed from codeword to noise sequence. By ordering and guessing noise sequences instead of codewords, the system achieves both fast decoding speeds and capacity-approaching error correction performance, resolving the contradiction between reliability and complexity
2Reliability
If block codes use large block sizes to approach channel capacity, then error correction performance is improved, but computational impracticality increases
Solution Approach 1:
The patent inverts the decoding paradigm by guessing noise sequences rather than codewords. This inversion allows block codes to achieve capacity-approaching performance with practical block sizes and bounded computational complexity, eliminating the need for arbitrarily large blocks
Solution Approach 2:
The patent performs preliminary ordering of noise sequences before the actual decoding process. This preliminary action enables the decoder to systematically explore noise possibilities in order of likelihood, achieving both high reliability and computational efficiency with practical block sizes
3Productivity
If block codes use small block sizes for fast decoding, then decoding speed is improved, but channel capacity approachability deteriorates
Solution Approach 1:
The patent inverts the traditional approach by guessing noise sequences instead of codewords. This inversion enables fast deterministic decoding while simultaneously achieving capacity-approaching error correction performance, resolving the contradiction between speed and reliability
Data Source
AI summary
Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. This process is deterministic, has bounded complexity, asymptotically achieves channel capacity as in convolutional codes, but has the decoding speed of a block code. In some embodiments, the decoder tests a bounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted. Abandonment decoding nevertheless approximates maximum likelihood decoding within a tolerable bound and achieves channel capacity when the abandonment threshold is chosen appropriately.