Abstract:
A method for generating at least one error checking code includes creating a modified input data word, including (k+m) bits, by combining an input data word, having n-bits, with at least a previously calculated at least one error checking code, including in-bits, where n≦k, and calculating a first m-bit error checking code from at least a first selected portion of the modified input data word.

Description:
FIELD OF THE INVENTION 
     The present invention relates to a data processing system and method and, more particularly, to a system and method for performing error-checking. 
     BACKGROUND TO THE INVENTION 
     Cyclic Redundancy Check (CRC) is a term used to describe a family or range of error-checking codes that are used in data communication systems. CRC is based on finite field polynomial arithmetic. Some common Cyclic Redundancy Check standards are CRC-8, CRC-12, CRC-16, CRC-32, and CRC-CCIT. 
     CRC can be performed in serial or parallel modes. In parallel mode, the width of input data to a parallel CRC module is determined by a width, k, of the data bus. A generator polynomial function is used to compute the CRC output from two inputs. Typically, these two inputs are an input data word, data-in, and an initial value, init. The choice of generator polynomial can be varied according to desired performance and environment. It is known in the art that certain polynomials are more effective than others. At the start of the entire CRC process, the initial value is given as start value, but in subsequent CRC calculations it assumes a value derived from a previous CRC calculation. 
     There are at least two possible general CRC procedures that might be applied when preparing to transmit data. The first possible procedure passes all original data to be transmitted through the CRC module to generate a final output CRC value of data width m. The output CRC value is appended to the end of the original input data and the entire contents, that is, original data and output CRC value, are transmitted to a receiver. The receiver splits the received data into received input data words and received output CRC value. The receiver has a CRC module that performs the same CRC calculations on the received input data. If the received input data has been transmitted without any errors, then the CRC value, of data width m, calculated by the receiving CRC module will match the CRC value that was appended to the end of the original data. The absence of such a match provides a basis for performing error detection and correction. 
     A second possible CRC procedure appends a number, m, of zero bits to the end of the original data to be transmitted to produce extended data. The number, m, is governed by the number of bits of the CRC output value. This extended data is passed through the CRC module to produce an m bit CRC output value. The CRC output value replaces the appended m zero bits at the end of the data which produces revised extended data. The revised extended data is transmitted to a receiver. The entire length of the received data is fed into the CRC module of the receiver. The receiver CRC module performs the same CRC calculations using all of the received data. The receiving CRC module will give an output CRC value of zero if the transmission has been error free. 
       FIG. 1  shows schematically a CRC device or method  100  comprising a basic parallel CRC module  105 , having an m-bit wide CRC initialisation value input  110 , a k-bit wide data input  115 , and an m-bit wide CRC output  120 . An overall CRC calculation, for a data stream comprising more than k bits, is produced by dividing the data stream into a number of k-bit wide input data words and calculating a partial CRC result for a given input data word presented at the k-bit wide data input  115  and passing the partial CRC back to be used as the initial CRC value for the next partial CRC calculation using the next k-bit wide input word of the data stream. For example, the CRC module might use a 32-bit initial value and 128 bits of input data (k bits of data) to produce a 32-bit CRC output value  120 . The transmitted packet would comprise a number of data bits followed by a number of CRC bits in the form of a Frame Check Sequence, FCS. 
     It can be appreciated that if the data stream does not contain an integer multiple of k-bit words, the final few bits of that data stream will not represent a complete data word suitable for processing by the parallel CRC module. 
     The accurate calculation of the final partial CRC on this final data word is required to support error free transmission of data. A problem can thus occur when the last data word is incomplete, that is, the number of valid data bits, n, of the data stream is less than the k bits of the data word used by the CRC module. 
     There are two general methods in the prior art for using parallel CRC&#39;s to accommodate such a final word having less than an anticipated number of bits. These two methods will be explained below with reference to  FIGS. 2 and 3  respectively. Both are given as specific examples using k=128 bit data words and m=32 bit CRC modules to produce 32-bit CRC outputs. Both methods are given with an assumption that the data is transmitted most significant bit, msb, first. Thus, the data [127:120] is the first byte of data of a 128-bit data word or data stream. The last word of data in each solution is accompanied by a mod  230  signal which signifies how many of the data bits in the last data word are valid. 
       FIG. 2  shows a first parallel CRC system  200 . It uses a number of CRC modules  205 ,  210 ,  215 ,  220  of different, incrementing, data widths to calculate the possible CRC results for a given data word. The results are fed into a multiplexer  225  along with a mod signal  230  that provides information on the number of valid data bits in the final word. The mod signal  230  allows the multiplexer  225  to select the appropriate output of the CRCs  205  to  220 . As mentioned above, the mod signal  230  provides and indication of the number of valid data bits in a current word for which a CRC value is being calculated. For example, processing a data stream of 136 bits would use the 128-bit CRC module  220  to produce a first or partial CRC output and the 8-bit CRC module to produce a second CRC output. The first and second partial results are used to calculate the overall CRC output  235  for the 136-bit data stream. This approach is a fast method of accommodating variable length data streams. However, the design is large and, hence, area and power inefficient when implemented in silicon, that is, in hardware. 
       FIG. 3  shows a second parallel CRC system  300 . It is based on an incremental process. A number, m, of 8-bit CRC modules  305 ,  310 ,  315 ,  320  are arranged in series such that each CRC passes a partial CRC result  325   a ,  325   b ,  325   c  to the next CRC in the sequence until the final, or maximum, CRC result  330  is calculated. Assuming that a 128-bit data word is to be processed, the first CRC module  305  takes the first 8 bits  335  of the data word, performs the CRC calculation, then feeds the partial CRC result  325   a  obtained to the next CRC module  310 . The next CRC module  310  uses the partial CRC result  325   a  together with the next 8 bits  340  of the 128-bit data stream to produce a second partial CRC result  325   b  and so on until the final 8 bits  350  of the data stream are processed by the final CRC module  320  to produce a final or overall CRC result  330 . The partial CRC results  325   a ,  325   b ,  325   c  and final CRC result  330  are fed into, or selected by, a multiplexer  225  that uses a mod signal  230  to select the correct CRC partial or final result to produce an appropriate CRC output  235  according to the length of the input data word being processed. It will be appreciated that variable length data can be accommodated using this design, providing the data length is an integer multiple of the number of bits processed by CRCs  305  to  320 . This approach uses less area than the first but is slower because of the serial nature by which the CRC partial results are passed along the chain of CRC modules. Also, a further disadvantage is that the data width of each cascaded CRC module has to be chosen so as to anticipate or accommodate the number of valid data bits, n. 
     Prior art CRC calculations have been performed using either or a combination of the above two solutions. They use CRC calculations over a range of data widths and have a multiplexer with a mod signal to determine which CRC result is the correct one for the number of valid data bits within a given word. Multiple calculations are required and many CRC modules are required, along with a multiplexer, for performing and selecting the appropriate CRC result. It is apparent from the foregoing that the determination of the CRC output for variable length data or the last data word of a data stream is inefficient in terms of both area, time and power consumption and the number of valid bits in the last word has to be designed into the circuit and is generally inflexible. 
     It is an object of embodiments of the present invention, at least, to mitigate some of the problems of the prior art. 
     SUMMARY OF INVENTION 
     Accordingly, a first aspect of embodiments of the present invention provides a data processing method for generating at least one error checking code; the method comprising the steps of creating a modified input data word, comprising (k+m) bits, using an input data word, having n-bits, and at least a previously calculated at least one error checking code, comprising m-bits; calculating an intermediate m-bit error checking code using a first selected portion (k msbits of (k+m)-bit word) of the modified input data word and calculating the at least one error checking code by combining the intermediate m-bit error checking code and a second selected portion (m lsbits of (k+m)-bit word) of the modified input data word to produce the at least one error checking code. 
     Embodiments of the present invention can be applied to any existing method by which CRC calculations are performed to accommodate a variable number of data bits, especially if the number of data bits is not an integer multiple of the number of data bits of an available CRC module. 
     It will be appreciated that within the context of the embodiments of the present invention, the phrase “error-checking” comprises at least one of error detection and error correction and, preferably, both error detection and error correction. Similarly, error-checking codes are used to give effect to at least one of error detection and error correction and, preferably, both. 
     Preferred embodiments provide a method in which the step of creating comprises the step of deriving the (m+n−1)th to the mth bits of the modified input data word from at least one of the input data word and at least part of the previously calculated at least one error checking code. 
     Preferably, the step of creating comprises the step of deriving the (m+n−1)th to the mth bits of the modified input data word from at least one of the input data word and the whole of the previously calculated at least one error checking code. 
     Embodiments provide a method in which the step of creating comprises the step of deriving the m least significant bits of the modified input data word from at least one of m bits having a predetermined value and the previously calculated at least one error checking code. 
     Preferred embodiments are provided in which the step of deriving comprises the step of setting at least the n least significant bits of the modified data word to the predetermined value. 
     Preferably, embodiments provide a method in which the step of deriving comprises the step of deriving the (m−n) most significant bits of the m least significant bits of the modified input data word from the previously calculated at least one error checking code. 
     Preferred embodiments provide a method in which the step of deriving comprises the step of setting all of the m least significant bits of the modified input data word to the predetermined value. 
     Preferably, embodiments provide a method in which the step of calculating the at least one error checking code by combining the intermediate m-bit error checking code and a second selected portion (m lsbits of (k+m)-bit word) of the modified input data word to produce the at least one error checking code comprises the step of performing a finite field arithmetic operation using the intermediate m-bit error checking code and the second selected portion (m lsbits of (k+m)-bit word) of the modified input data word to produce the at least one error checking code. 
     Preferably, the finite field arithmetic operation comprises at least one of GF(p) addition or multiplication. Preferably, the GF(p) addition or multiplication is performed over a GF(2) field. 
     A second aspect of embodiments of the present invention provides a data processing system for generating at least one error checking code; the system comprising means to create a modified input data word, comprising (k+m) bits, using an input data word, having n-bits, and at least a previously calculated at least one error checking code, comprising m-bits; means to calculate an intermediate m-bit error checking code using a first selected portion (k msbits of (k+m)-bit word) of the modified input data word and means to calculate the at least one error checking code by combining the intermediate m-bit error checking code and a second selected portion (m lsbits of (k+m)-bit word) of the modified input data word to produce the at least one error checking code. 
     Preferably, there is provided a system in which the means to create comprises means to derive the (m+n−1)th to the mth bits of the modified input data word from at least one of the input data word and at least part of the previously calculated at least one error checking code. 
     Preferred embodiments provide a system in which the means to create comprises means to derive the (m+n−1)th to the mth bits of the modified input data word from at least one of the input data word and the whole of the previously calculated at least one error checking code. 
     Embodiments provide a system in which the means to create comprises means to derive the m least significant bits of the modified input data word from at least one of m bits, having a predetermined value, and the previously calculated at least one error checking code. 
     Preferably, there is provided a system in which the means to derive comprises means to set at least the n least significant bits of the modified data word to the predetermined value. 
     Preferred embodiments provide a system in which the means to derive comprises means to derive the (m−n) most significant bits of the m least significant bits of the modified input data word from the previously calculated at least one error checking code. 
     Embodiments preferably provide a system in which the means to derive comprises means to set all of the m least significant bits of the modified input data word to the predetermined value. 
     Preferred embodiments provide a system in which the means to calculate the at least one error checking code by combining the intermediate m-bit error checking code and a second selected portion (m lsbits of (k+m)-bit word) of the modified input data word to produce the at least one error checking code comprises means to perform a finite field arithmetic operation using the intermediate m-bit error checking code and the second selected portion (m lsbits of (k+m)-bit word) of the modified input data word to produce the at least one error checking code. 
     Preferably, embodiments provide a system in which the finite field arithmetic operation comprises at least one of GF addition or multiplication. 
     It will be appreciated that embodiments of the present invention can be realised using software designed to run on a processor such as, for example, a DSP. Suitably, a third aspect of embodiments of the present invention provides a computer program for generating at least one error checking code; the computer program comprising executable code to create a modified input data word, comprising (k+m) bits, using an input data word, having n-bits, and at least a previously calculated at least one error checking code, comprising m-bits; executable code to calculate an intermediate m-bit error checking code using a first selected portion (k msbits of (k+m)-bit word) of the modified input data word and executable code to calculate the at least one error checking code by combining the intermediate m-bit error checking code and a second selected portion (m lsbits of (k+m)-bit word) of the modified input data word to produce the at least one error checking code. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings in which: 
         FIG. 1  shows a basic parallel CRC module; 
         FIG. 2  shows a prior art system for performing CRC calculations; 
         FIG. 3  shows a second prior art system for performing CRC calculations; 
         FIG. 4  shows a block diagram of the variable data width parallel CRC according to a first embodiment; 
         FIG. 5  shows a first process for modification of an input data word; 
         FIG. 6  shows a second process for modification of an input data word; 
         FIG. 7  shows a third process for modification of an input data word; and 
         FIG. 8  shows a specific embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit the invention to the particular forms disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the claims. Like numbers refer to like elements throughout the description of the figures. 
     The present invention may be embodied as systems, methods, and/or computer program products. Accordingly, the present invention may be embodied in hardware and/or in software (including firmware, resident software, micro-code, etc.). Furthermore, the present invention may take the form of a computer program product on a computer-usable or computer-readable storage medium having computer-usable or computer-readable program code embodied in the medium for use by or in connection with an instruction execution system. In the context of this document, a computer-usable or computer-readable medium may be any medium that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. 
     The computer-usable or computer-readable medium may be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. More specific examples (a nonexhaustive list) of the computer-readable medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable compact disc read-only memory (CD-ROM). Note that the computer-usable or computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory. 
       FIG. 4  shows a variable data length CRC module  400  comprising a modification module  405 , a parallel CRC module  105 , for producing an m-bit wide CRC output, and a finite field arithmetic element for performing Galois Field arithmetic, GF(p), preferably in the form of an exor gate. The CRC module might be used to calculate error-checking codes for messages for exchange between transmission and reception portions of a communication system. The modification module comprises three inputs; namely, a modification signal input  410 ′ for receiving a modification signal  410 , a k-bit data word input  415 ′ for receiving an input data word  415 , having n valid data bits, and an initialisation value input  420 ′ for receiving an initialisation value  420 , having m bits. The modification module  405  is arranged to perform pre-processing of the input data words  415 , presented at the data word input  415 ′, for which respective CRC values are required. The modification signal input  410 ′ receives the modification signal  410 , which provides an indication of how many bits of the input data word  415  are valid. The input data word  415  might be one data word of a number of data words  415   a  to  415   d  forming part of a data stream  415 ″ for which an overall CRC value is required. 
     The modification signal  410  can take values in the range of zero to k inclusive, where k corresponds to the width of the input data word  410 , or, more accurately, the width of the data word input  415 ′. The initialisation value input  420 ′ is used to receive an initialisation value  420  for the CRC. For example, if the CRC-32 standard is to be complied with, the initialisation value might be 0xFFFFFFFF. Once the CRC process is running, subsequent initialisation values are derived from the CRC value  440  produced at the output  440 ′ of the CRC module  400  for each input data word. 
     The modification module  405  comprises two outputs; namely, a modified data word  720 , carried by a corresponding modified data word output bus  720 ′, and modification data  725 , carried by a corresponding modification data bus  725 ′. The modified data word output  720 ′ forwards the k-bit modified input data word  720  for processing by the parallel CRC module  105 . 
     The modification data output  725 ′ carries the modification data  725  to the exor gate  435 , where it is combined by the output  430  of the parallel CRC module  105 . The output  430  of the parallel CRC module  105  is carried by a corresponding CRC output bus  430 ′. The combination of the modification data  725  and the CRC output  430  of the parallel CRC module  105  is used to produce the overall CRC output  440  via a corresponding bus  440 ′. The parallel CRC module  105  also comprises an initialisation input  425 ′, which is always initialised to zero  425 . 
     The operation of the CRC module  400  will now be described. 
     If an input data word  415  contains only valid data bits, that is, n=k, then the modification signal  410  remains at k or zero. In preferred embodiments, the modification signal, in such circumstances, remains at zero. The modification module  405  is arranged to produce a (k+m)-bit word. In general, the most significant k bits of the (k+m)-bit word are derived from the input data word with an appropriate number of leading zero bits to form a k-bit word. It will be appreciated that in the case where n=k, no such leading zero bits will be prefixed to the input data word  415 . To the end of the most significant k bits is appended m zero bits to form the least significant m bits of the (k+m)-bit word. The m bit initialisation value  420  is combined with the (k+m)-bit word using a finite field arithmetic operation. In preferred embodiments, the finite field operation is GF(2) addition or multiplication, which is preferably implemented using an XOR gate. In preferred embodiments, the combination is performed by aligning the msb bit of the initialisation value  420  with the msb of the input data word  415  and performing an exclusive-or operation between the initialisation value  420  and the (k+m)-bit word using that alignment. It will be appreciated that in the case where n=k, the msb of the k or n-bit input data word  415  will be in the msb position of the (k+m)-bit word. The first k bits of the (k+m)-bit word, that is, the modified input data word  720 , are forwarded from the modification module  405  to the parallel CRC module  105  via the bus  720 ′, where they are subjected to a CRC process in the usual manner to produce an m-bit output  430  via the parallel CRC bus  430 ′. The m least significant bits of the (k+m)-bit word form the modification data  725  and are output via the modification data bus  725 ′ to the arithmetic element  435 , where the modification data  725  is combined with the output  430  of the parallel CRC module  105  to produce an overall CRC value for n or k-bit input data word  415 . This process is repeated for each input data word for which n=k. 
     However, if the input data word  415  contains n&lt;k valid data bits, then the modification signal  410  has a non-zero value which defines the number, n, of valid data bits within the input data word  415 . It will be appreciated that such an input data word might occur if the data stream  415 ″ to be transmitted comprises a number of bits that is not an integer multiple of k. In such circumstances, the modification signal might take values in the range of 1 to (k−1) inclusive. Again, the (k+m)-bit word is formed such that the n bits of the input data form for the least significant bits of a k-bit word, with the remaining, leading, (k−n) bits being set to zero, and m zeros are appended to such a k-bit word to form the (k+m)-bit word. Having formed the (k+m)-bit word comprising (k−n) zeros, followed by the n-bit input data word and the m appended zeros, the initialisation value  420  is ex-or&#39;ed with the (k+m)-bit word such that the msb of the initialisation value is aligned with the msb bit of the n-bit input data word. Therefore, if n≧m, the m bits of the initialisation value  420  will be combined with the m most significant bits of the input data word  415 . However, if n&lt;m, it will be appreciated that the first n bits of the initialisation value  420  will be combined with the n bits of the input data word  415  and the remaining (m−n) bits of the initialisation value are combined with the first (m−n) bits of the m appended zeros. The first k-bits of the (k+m)-bit word, representing the modified input data word  720 , are forwarded, via the bus  720 ′, to the parallel CRC module  105  for use in producing the parallel CRC output  430  via the corresponding bus  430 ′. The modification data  726 , which may comprise data derived from a portion of the initialisation value  420 , according to whether or not n≧m or n&lt;m, is forwarded to the exor gate  435  where it is combined with the output  430  of the parallel CRC module  105 . 
       FIG. 5  illustrates the above processing for the case where n=k, that is, the number of valid data bits  610  of an input data word equals the width of the input data word bus  415 ′ of the CRC module  400 . It can be seen that the (k+m)-bit word  500  comprises k or n bits  502  derived from the data input word  415  in the k most significant bit positions and also has m zeros  504  appended. The initialisation value  420  is combined with the (k+m)-bit word using an exclusive-or operation such that there is bit alignment between the most significant bits of the n-bit input data word  415  and the initialisation value  420  to produce a modified (k+m)-bit word  506 . The (k+m)-bit word  506  comprises the modified input data word  720  and the m zeros; the latter forming the modification data  725 . 
       FIG. 6  shows the processing  600  undertaken by the modification module  405  when the number  610  of bits, n, of an input data word is less thank but n≧m. It can be seen that the (k+m)-bit word  500  comprises n bits  502 , derived from the data input word  415 , in the n least significant bit positions of the first or most significant bit positions of the (k+m)-bit word. The leading (k−n) bit positions are padded with zeros  602 . The (k+m)-bit word also comprises m appended zeros  504 . The initialisation value  420  is combined with the (k+m)-bit word using an exclusive-or operation such that there is bit alignment between the most significant bits of the n-bit input data word  415  and the initialisation value  420  to produce a modified (k+m)-bit word  506 . The (k+m)-bit word  506  comprises the modified input data word  720  and the m zeros; the latter forming the modification data  725 . 
     Referring to  FIG. 7  there is shown the processing  700  undertaken by the modification module  405  when the number  610  of bits, n, of an input data word is less than k and n&lt;m. It can be seen that the (k+m)-bit word  500  comprises n bits  502  derived from the data input word  415  in the n least significant bit positions of the k most significant bit positions of the (k+m)-bit word. The leading (k−n) bit positions are padded with zeros  602 . The initialisation value  420  is combined with the (k+m)-bit word using an exclusive-or operation such that there is bit alignment between the most significant bits of the n-bit input data word  415  and the initialisation value  420  to produce a modified (k+m)-bit word  506 . It will be appreciated that since n&lt;m the combination of the (k+m)-bit word and the initialisation value  420  also modifies the first (m−n) most significant bits  702  of the m least significant bits of the (k+m)-bit word. The remaining n bits of the m least significant bits of the (k+m)-bit word are padded with zeros  504 . Therefore, the (k+m)-bit word  506  comprises the modified input data word  720  and m-bit modification data  725  having some data derived from the initialisation value and n appended zeros. 
     The parallel CRC module  105  can be implemented in a number of ways. For example, the parallel CRC module might be initialised to zero and all of the (k+m) bits might be processed by the CRC module  105  as usual. Alternatively, the parallel CRC module  105  might be initialised using zeros and k-bits of the (k+m)-bit word might be processed by the CRC module  105  as usual with the CRC result being combined, preferably using an xor operation, with the remaining m bits of the (k+m)-bit word. 
     In other embodiments, the initialisation value used for the parallel CRC module  105  might be derived from the modified input data word itself. For example, the first m bits of the k-bit or (k+m) bit modified input data word might be used to initialise the parallel CRC module  105 , with the remaining k bits being processed as usual. 
     Although the above embodiments have been described with reference to a CRC generator, it will be appreciated that the present invention is equally applicable to a CRC checker. 
     It will be appreciated that in cases where the parallel CRC module  105  is always initialised to zero, the initialisation in  425 ′ will not be needed, that is, in the actual implementation, the initialisation input  425  is optional according to the actual realisation of embodiments of the present invention. Furthermore, it has been found that embodiments of the present invention are particularly suitable for hardware implementation. 
     The above embodiments have been described with reference to the modification signal providing an indication of the number of valid data bits being presented or to be processed. However, embodiments can equally well be realised in which the modification signal is used to derive or calculate the amount of valid data being presented or to be processed. For example, a value of the modification signal of “4” might represent “4” valid data bits in one embodiment or “4” valid data bytes in another embodiment. Therefore, in such embodiments, the modification signal might provide an indication of the number of valid data bits or bytes being presented for processing. 
     Furthermore, the above embodiments have been described with reference to combining the output of the parallel CRC module  105  with the modification data. The combination uses an exor gate. However, embodiments are not limited to such an arrangement. Embodiments can be realised in which the whole (k+m)-bit word of modified input data is fed into the parallel CRC module and processed to produce a respective output. In such an embodiment, the modification data would be processed by the parallel CRC module  105  itself rather than being added to the parallel CRC module result using the exor gate. Therefore, such an embodiment would use neither the exor date  435  nor the modification data bus  725 ′. 
     Although the above embodiment has been described with reference to processing and positioning data with reference to most significant bits and least significant bits for a given operation, embodiments can equally well be realised in which the processing and positioning of data is done with reference to least significant bits and most significant bits if the given operation/s is/are reversed. For example,  FIG. 5  illustrates the most significant bit as being on the LHS of the diagram and the least significant bits as being towards the RHS of the diagram. However, this can be reversed. Such a reversal would also entail reversal of the initialisation value, that is, the msb&#39;s of the initialisation value would appear on the RHS and the lsb&#39;s of the initialisation value would appear on the LHS of the drawing. 
       FIG. 8  illustrates a further embodiment  800  of the present invention. As compared to the embodiment  400  shown in  FIG. 4 , the modification data  720  is not forwarded to an xor gate. The modification data  720  is instead forwarded to the parallel CRC modules as a (k+m)-bit word  802  via a (k+m)-bit wide bus  802 ′. Alternatively, the parallel CRC module  105  might be initialised using the first m bits of the (k+m)-bit word, with the remaining k-bits being processed as usual. 
     The parallel CRC module  105  might be implemented by combining the output of the parallel CRC with the modified data word using an exor gate and feeding the result back into the parallel CRC. Alternatively, the parallel CRC register might be loaded with the modified input data word or at least a portion thereof. 
     The reader&#39;s attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference. 
     All of the features disclosed in this specification (including any accompanying claims, abstract and drawings) and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. 
     Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. 
     The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.