General CRC Syndrome Detector

Detect errors in input data frames according to generator polynomial

Library

CRC sublibrary of Error Correction and Detection

Description

The General CRC Syndrome Detector block computes checksums for its entire input frame. This block accepts a binary column vector input signal.

The block's second output is a vector whose size is the number of checksums, and whose entries are 0 if the checksum computation yields a zero value, and 1 otherwise. The block's first output is the set of message words with the checksums removed.

The first output is the data frame with the CRC bits removed and the second output indicates if an error was detected in the data frame.

The block's parameter settings should agree with those in the General CRC Generator block.

You specify the number of checksums the block calculates for each frame by the Checksums per frame parameter. If the Checksums per frame value is k, the size of the input frame is n, and the degree of the generator polynomial is r, then k must divide n - k*r, which is the size of the message word.

This block supports double and boolean data types. The block inherits the output data type from the input signal.

Example

Suppose the received codeword has size 16, the generator polynomial has degree 3, Initial states is [0], and Checksums per frame is 2. The block computes the two checksums of size 3, one from the first half of the received codeword, and the other from the second half of the received codeword, as shown in the following figure. The initial states are not shown in this example, because an initial state of [0] does not affect the output of the CRC algorithm. The block concatenates the two halves of the message word as a single vector of size 10 and outputs this vector through the first output port. The block outputs a 2-by-1 binary frame vector whose entries depend on whether the computed checksums are zero. The following figure shows an example in which the first checksum is nonzero and the second checksum is zero. This indicates that an error occurred in transmitting the first half of the codeword.

Signal Attributes

The General CRC Syndrome Detector block has one input port and two output ports. These ports accept binary column vector signals.

Dialog Box

Generator polynomial

A binary or integer row vector specifying the generator polynomial, in descending order of powers.

Initial conditions

A binary scalar or a binary row vector of length equal to the degree of the generator polynomial, specifying the initial state of the internal shift register.

Direct method

When you select this check box, the object uses the direct algorithm for CRC checksum calculations. When you clear this check box, the object uses the non-direct algorithm for CRC checksum calculations.

Reflect input bytes

When you select this check box, the block flips the input data on a bytewise basis prior to entering the data into the shift register. For this application, the input frame length (and any current input frame length for variable-size signals) divided by the value for the Checksums per frame parameter minus the degree of the generator polynomial, which you specify in the Generator polynomial parameter, must be a multiple of eight. When you clear this check box, the block does not flip the input data.

Reflect checksums before final XOR

When you select this check box, the block flips the CRC checksums around their centers after the input data are completely through the shift register. When you clear this check box, the block does not flip the CRC checksums.

Final XOR

Specify the value with which the CRC checksum is to be XORed as a binary scalar or vector. The block applies the XOR operation just prior to appending the input data. The vector length is the degree of the generator polynomial that you specify in the Generator polynomial parameter. When you specify the final XOR value as a scalar, the block expands the value to a row vector with a length equal to the degree of the generator polynomial. The default value of this parameter is 0, which is equivalent to no XOR operation.

Checksums per frame

Specify the number of checksums the block calculates for each input frame. This value must be a positive integer. The input frame length (and any current input frame length for variable-size signals) must be a multiple of this parameter value.

Algorithm

For a description of the CRC algorithm as implemented by this block, see Cyclic Redundancy Check Codes in Communications System Toolbox™ User's Guide.

References

[1] Sklar, Bernard. Digital Communications: Fundamentals and Applications. Englewood Cliffs, N.J., Prentice-Hall, 1988.

[2] Wicker, Stephen B., Error Control Systems for Digital Communication and Storage, Upper Saddle River, N.J., Prentice Hall, 1995.

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