Near-MDS Linear Network Code for Wireless Packet Reliability
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Solution Overview
Problem
Wireless networks face challenges in maintaining high reliability due to packet loss and retransmission requirements, especially in critical systems where low packet loss and retransmission rates are essential, and existing network coding techniques restrict the number of encoded packets that can be transmitted beyond K+1, limiting reliability and increasing retransmission rates.
Innovation Solution
The method involves generating a near-maximum distance separable linear network code by creating a message matrix and a network code matrix that maps K message packets to N encoded packets, ensuring any combination of K+1 columns is linearly independent, allowing for increased reliability by transmitting more encoded packets than necessary, which can be decoded even if some packets are lost during transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional network coding transmits only K+1 encoded packets, then decoding is possible with minimum transmissions, but reliability is limited and retransmission rates increase
Solution Approach 1:
The patent pre-generates more than K+1 encoded packets (N encoded packets where N > K+1) before transmission. This preliminary action ensures that even if some packets are lost during transmission, the recipient will still receive at least K+1 packets needed for decoding, thereby improving reliability without requiring retransmissions
Solution Approach 2:
The patent changes the parameter of encoded packet quantity from the traditional minimum of K+1 to a larger number N. This parameter change increases the probability that the recipient receives sufficient packets for successful decoding, thus improving reliability while maintaining transmission efficiency through single-shot encoding
2Reliability
If more encoded packets are transmitted beyond K+1, then reliability improves, but computational complexity increases
Solution Approach 1:
The patent segments the encoding process into two phases: (1) pre-generation of N encoded packets using systematic network coding where the first K packets are original data and the remaining N-K packets are encoded combinations, and (2) selection of K+1 packets for transmission. This segmentation allows efficient generation of multiple encoded packets without proportionally increasing computational complexity
Solution Approach 2:
The patent uses systematic network coding where the first K encoded packets are identical copies of the original K message packets. This copying approach simplifies the encoding process as no complex computation is needed for these packets, reducing overall computational complexity while still providing the benefit of having N > K+1 packets available
3Reliability
If network coding is applied to increase encoded packets, then packet error rates reduce, but the number of bits transmitted increases
Solution Approach 1:
The patent applies partial network coding by generating N encoded packets where only N-K packets are actual encoded combinations, while the first K packets are original message packets transmitted in plain form. This partial application of network coding provides redundancy to reduce packet error rates without the overhead of fully encoding all packets, thus limiting the increase in total bits transmitted
Data Source
AI summary
A method for network coding using a near-maximum distance separable linear network code includes generating a message matrix where each column of the message matrix corresponds to one of K message packets and each element in a column of the message matrix corresponds to one of the symbols of the corresponding message packet. The method also includes generating a network code matrix to map the K message packets to N encoded packets, where any combination of K+1 columns of the network code contains at least K columns that are linearly independent. Further, the method includes multiplying the message matrix by the network code matrix to generate a transmission matrix, where each column of the transmission matrix corresponds to an encoded packet for wireless transmission.