Pivot Position Sequencing in Linear Network Coding for Easier Decoding
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Solution Overview
Problem
Current sparse Random Linear Network Coding (RLNC) solutions face inefficiencies in decoding complexity and coding overhead, especially with large blocks of data, due to low ratios of directly insertable coded packets and poor performance under bursty packet losses.
Innovation Solution
A method for encoding data that randomizes the selection of pivot candidate positions for encoding vectors across rounds, ensuring no repetition and using a permutation based on finite field properties to minimize overlaps and enhance stability under bursty losses, without requiring feedback from the decoder.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If sparse code is used with large block size, then decoding complexity is reduced and system design is simplified, but the ratio of directly insertable coded packets becomes low under bursty packet losses
Solution Approach 1:
The patent applies dynamics by making the pivot candidate position selection adaptive rather than static. The encoder dynamically adjusts pivot candidate positions based on feedback from the decoder about which positions have already been filled, ensuring that each transmission round targets unfilled positions. This dynamic adaptation maintains high ratios of directly insertable packets even under bursty loss conditions while preserving the low decoding complexity of sparse codes.
Solution Approach 2:
The patent implements feedback mechanisms where the decoder informs the encoder about which pivot positions have been successfully filled. This feedback enables the encoder to select pivot candidate positions that are more likely to be directly insertable in subsequent rounds, improving the ratio of useful packets received under bursty loss conditions without increasing decoding complexity.
2Adaptability or versatility
If random pivot candidate positions are selected for each round, then performance independence from channel conditions is achieved, but the ratio of directly insertable coded packets remains low
Solution Approach 1:
The system transitions from static random selection to dynamic adaptive selection. While maintaining the ability to operate independently of channel conditions, the encoder now dynamically adjusts pivot candidate positions based on decoder feedback about filled positions. This ensures that random selection targets unfilled positions, maximizing the ratio of directly insertable packets while preserving adaptability to various channel conditions.
Solution Approach 2:
The patent applies preliminary action by having the encoder pre-select pivot candidate positions from unfilled positions before each transmission round, based on feedback about which positions are already filled. This preliminary selection ensures that transmitted packets have a higher probability of being directly insertable, improving productivity while maintaining the adaptability benefits of random selection.
3Ease of manufacture
If linear sequence of pivot candidate positions is used, then implementation simplicity is maintained, but performance deteriorates under bursty packet losses due to high overlap probability
Solution Approach 1:
The system evolves from a static linear sequence to a dynamic selection process. Instead of following a fixed linear sequence, the encoder dynamically selects pivot candidate positions from the set of unfilled positions based on decoder feedback. This maintains implementation simplicity while dramatically improving performance under bursty losses by avoiding the high overlap probability inherent in linear sequences.
Solution Approach 2:
The patent changes the parameter of pivot position selection from a fixed linear sequence to a dynamic set-based selection. By maintaining the selection from unfilled positions and using feedback to update the set of available positions, the system achieves better performance under bursty losses while keeping the implementation relatively simple through set management rather than complex algorithms.
Data Source
AI summary
A method for encoding data comprises choosing a sequence of pivot candidate positions for a sequence of g encoding vectors to encode a block of g data symbols in a round of coded packets by: providing a set of g pivot candidate positions; choosing a pivot candidate position for the sequence from the set of pivot candidate positions; removing the chosen pivot candidate position from the set of pivot candidate positions; and repeating until the set of pivot candidate positions is empty and the sequence of chosen pivot candidate positions for the round is non-linear. A set of encoding vectors is generated based on the chosen sequence of pivot candidate positions, each encoding vector comprising zero valued coefficients for positions within the encoding vector before the pivot candidate position for the encoding vector and a non-zero valued coefficient for at least the pivot candidate position.