The polynomial is also able to detect burst-errors up to 15 bit. However, this is only true for a fixed data length. However, the number of transmitted bits in the CAN frames varies depending on the automatically introduced stuff-bits. This leads to a cut of the Hamming distance to two for some dedicated bit patterns. Still, any single bit-error is detected, and the probability of undetected multiple bit-errors is very low.
In the Classical CAN message there are not such fixed stuff-bits. The bit CRC is specified for data frames with a length of larger than 16 byte. It is often used in Bluetooth and other wireless communication protocols. The name sounds rather complex and intimidating. However, after reading this article you should have a good understanding of what a CRC is and how it works. CRC is an error detection code used for verifying the integrity of data.
It works just like a checksum and is appended to the end of the payload data and transmitted or stored along with that data. This data is only appended for the sake of error detection and data integrity. CRCs are specifically designed to detect common data communication errors. It can also detect when the order of the bits or bytes changes.
CRCs can easily be implemented in hardware — another reason for their widespread use. Before we take a deep dive into how a CRC works, there is one important concept that we need to understand first: The endianness.
The endianness is the order of bytes with which data words are stored. We distinguish the following to types:. However, in many cases, we use CRCs that consist of mulitple bytes. So the question arises which endianness to use for CRC? Mathematically spoken, a CRC is the remainder of a modulo-2 polynomial division of the data.
So, the CRC can be written as. The polynomial can be any mathematical polynomial without any coefficients up to the order of the CRC bit size.
So if we want a CRC with 8 bits, the highest exponent of the polynomial must be 8 as well. As you can imagine from the simple equation above, choosing a different polynomial will result in a different CRC for the same data. So sender and receiver need to agree on a common polynomial, or else they will always end up with a different CRC and assume that the data got corrupted on the way.
Depending on the use case, some polynomials are better suited than others. Picking the right one is a topic on its own and beyond the scope of this article.
Any such polynomial can be represented in binary form by going through the exponents from highest to lowest and writing a 1 for each exponent that is present 8, 2, 1 and 0 in our example and a 0 for each absent exponent 7, 6, 5, 4, 3 in this case :. The above is the big-endian representation of the polynomial.
For its little-endian representation, simply reverse the order of bits:. Modulo-2 arithmetic is performed digit by digit bit by bit on binary numbers. There is no carry or borrowing in this arithmetic. Each digit is considered independent from its neighbours. The curious thing about modulo-2 arithmetic is that both addition and subtraction yield the same result.
The sum or the difference of two bits can be computed with an XOR operation: The result is 1 if exactly one of the two bits is 1, otherwise the result is 0. As there is no carry or borrowing, the same applies not only for individual bits, but for binary numbers of any length, for example:. We get this result by applying the XOR operator on each pair of bits individually:.
The only difference is that we use modulo-2 subtraction XOR instead of arithmetic subtraction for calculating the remainders in each step. The result of the division quotient is written on top of the calculation, the remainder at the bottom. There are different types of CRCs. They are categorized by the degree of the polynomial they use. As the first exponent of a polynomial of degree n is always present by definition otherwise it would have a lower degree , its binary representation always begins with a 1.
For that reason, the first bit of a binary polynomial representation is always dropped when computing a CRC in software. So the bit size of the resulting binary representation is always n for a polynomial of degree n.
Since the this error can be imperceptible, evidence of this error exists when the user notices information packets being dropped, the meter not showing up online or information is stale and not updating. Setra Systems, Inc. All Rights Reserved.
Signs of CRC Error Since the this error can be imperceptible, evidence of this error exists when the user notices information packets being dropped, the meter not showing up online or information is stale and not updating. Recent Posts. Download the PDF now.
0コメント