Coding Modulation Matrix Layout to Reduce Short Cycles
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Solution Overview
Problem
Existing channel coding and modulation methods, such as analog fountain codes, suffer from non-optimized short cycles and non-uniform weight allocation, leading to inefficiencies in coding and decoding performance.
Innovation Solution
Implement binary phase shift keying (BPSK) mapping and coding modulation using a generator matrix optimized through a progressive edge-growth algorithm to allocate non-zero elements with varying weights, reducing short cycles and improving weight distribution for enhanced decoding performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a maximum minimum variable node degree (max-min) matrix is used, then the minimum variable node degree is maximized, but short cycles cannot be avoided or reduced
Solution Approach 1:
The patent changes the construction parameters of the generator matrix by introducing a progressive edge-growth algorithm that dynamically adjusts the selection criteria for variable nodes. Instead of simply maximizing minimum degree, the algorithm considers the growth of cycles and the distribution of degrees progressively, thereby reducing short cycles while maintaining high minimum degree.
Solution Approach 2:
The progressive edge-growth algorithm incorporates feedback mechanisms where each step of matrix construction uses information from previous steps. The algorithm tracks the current state of the matrix, evaluates potential short cycle formations, and adjusts subsequent node selections accordingly, creating a feedback loop that prevents short cycle formation while maintaining degree constraints.
2Reliability
If a short analog fountain code (short analog fountain code, SAFC) matrix is used, then variable nodes with minimum reliability are selected, but a variable node with a small connection weight is repeatedly selected, and a short cycle is easily formed
Solution Approach 1:
The patent modifies the selection parameters by introducing a progressive evaluation metric that combines reliability assessment with cycle detection. The algorithm dynamically adjusts selection criteria based on the current matrix state, preventing repeated selection of nodes with small connection weights that would form short cycles, while still prioritizing nodes with minimum reliability.
Solution Approach 2:
The algorithm performs preliminary evaluation of potential node selections before actually adding them to the matrix. It predicts whether selecting a node with minimum reliability would create short cycles, and if so, it adjusts the selection beforehand to avoid the harmful effect, thereby preventing short cycle formation proactively.
3Ease of operation
If a weight coefficient-progressive edge-growth (weight coefficient-progressive edge-growth, WC-PEG) matrix is used, then distribution of connection edges is determined based on a PEG algorithm, but weight distribution uniformity of the WC-PEG matrix is poor
Solution Approach 1:
The patent introduces a weight balancing parameter in the progressive edge-growth algorithm that monitors and adjusts the distribution of connection weights. The algorithm dynamically modifies weight assignments during matrix construction to maintain uniformity, preventing concentration of weights in specific regions while preserving the structural benefits of the PEG algorithm.
Solution Approach 2:
The algorithm incorporates feedback mechanisms that continuously evaluate weight distribution uniformity during matrix construction. When imbalance is detected, the algorithm adjusts subsequent weight assignments to correct the imbalance, creating a feedback loop that maintains uniform weight distribution throughout the matrix generation process.
Data Source
AI summary
A data transmission method and a related apparatus. A sending device performs binary phase shift keying BPSK mapping on a to-be-transmitted bit sequence to obtain a first sequence. The sending device performs coding modulation on the first sequence based on a generator matrix or a first sub-matrix including some rows of the generator matrix, to obtain a symbol sequence. The sending device sends the symbol sequence to a receiving device through a channel.