CRC Generator Polynomial Selection for Random and Burst Error Detection
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Solution Overview
Problem
Existing CRC systems face difficulties in detecting random and burst errors in binary information transmission due to unreliable transmission circuitry, making it challenging to find an effective generator polynomial for generating redundancy.
Innovation Solution
A method that involves choosing a generator polynomial for Euclidean division, where the polynomial satisfies conditions such as high Hamming weight or the ability to detect a specific number of consecutive erroneous bits, optimizing redundancy for error detection in binary information transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a conventional generator polynomial is used for CRC redundancy generation, then the system can detect some errors, but it fails to systematically detect both random errors and burst errors effectively
Solution Approach 1:
The patent changes the parameters of the generator polynomial by imposing specific constraints: the polynomial must have a degree less than the redundancy length, and its coefficients must follow a particular pattern (with the highest and lowest degree coefficients being 1, and intermediate coefficients being 0 or 1). These parameter changes enable systematic detection of both random and burst errors while maintaining polynomial simplicity.
Solution Approach 2:
The patent segments the error detection capability into two distinct parts: one for detecting random errors and another for detecting burst errors. By designing the generator polynomial to satisfy specific mathematical conditions, the system can independently target each error type, making the overall detection mechanism more systematic and reliable.
2Reliability
If the redundancy length is increased to detect more errors, then the detection capability improves, but the transmission overhead increases
Solution Approach 1:
The patent optimizes the relationship between redundancy length and generator polynomial degree by constraining the polynomial degree to be less than the redundancy length. This parameter optimization allows the system to achieve maximum error detection capability with minimal redundancy bits, preventing unnecessary transmission overhead while maintaining strong detection performance.
3Reliability
If a complex generator polynomial is used to detect burst errors, then the detection of consecutive erroneous bits improves, but the computational complexity increases
Solution Approach 1:
The patent changes the structural parameters of the generator polynomial by enforcing a specific coefficient pattern where the highest and lowest degree coefficients are 1, and intermediate coefficients are restricted to 0 or 1. This parameter constraint simplifies the polynomial computation while maintaining the ability to detect burst errors of length up to the redundancy length.
Solution Approach 2:
The patent applies partial action by not requiring the generator polynomial to detect all possible error patterns, but rather focusing on detecting burst errors up to a specific length (equal to the redundancy length). This selective approach reduces computational complexity while providing sufficient protection against the most common error types.
Data Source
AI summary
A method is for transmitting a binary information word (MI) coded on r bits to which is attached a redundancy (CRC) coded on s bits, s and r being integers. The redundancy (CRC) signals the appearance of erroneous bits after the transmission, and is obtained by carrying out a Euclidian division of the information word (MI) to be transmitted by a generator polynomial coded on at most s bits. The generator polynomial is chosen so that it satisfies at least one of the following conditions, namely that the Hamming weight of the multiples of the generator polynomial is greater than or equal to a chosen threshold, or the generator polynomial allows the detection of at least 2s-1-3 consecutive erroneous bits.