# Patent

## Title
System and method for generating a cyclic redundancy check

## Abstract

A cyclic redundancy check generator includes a plurality of shift registers, each shift register corresponding to a coefficient of a general polynomial key word. A plurality of programmable registers are programmed based on a specific polynomial key word. The specific key word programmed to the plurality of programmable registers is compared to the general polynomial key word to determine which shift registers corresponding to coefficients of the general polynomial key word are to take a predetermined value in order to convert the general polynomial key word into the specific polynomial key word.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. patent application Ser. No. 11/385,962, filed Mar. 21, 2006 (now U.S. Pat. No. 7,418,648), which is a continuation of U.S. patent application Ser. No. 10/039,585, filed on Jan. 4, 2002 (now U.S. Pat. No. 7,216,285), which claims the priority benefit of U.S. Provisional Patent Application Ser. No. 60/338,137, filed Nov. 9, 2001. All of these applications are hereby incorporated by reference in their entirety.


FIELD OF THE INVENTION
The invention generally relates to electronic systems. The invention relates more specifically to systems and methods for generating cyclic redundancy check.
BACKGROUND OF THE INVENTION
A popular method for error detection for digital signals is the Cyclic Redundancy Check (CRC). CRC works by treating the message string that is sent between a transmitter and a receiver as a single binary word. The single binary word is divided by a key word that is agreed upon by both the transmitter and the receiver ahead of time. The remainder that is left after dividing the single binary word by the key word is known as a check word. The transmitter sends both the message string and the check word to the receiver. The receiver then verifies the data by dividing the data by the key word. If the remainder, obtained by dividing the data by the key word, matches the check word, then the receiver can be sure that the data is indeed the correct message string from the transmitter.
In the context of CRC, key words are usually numbers and are presented in the form of polynomials whose coefficients are in the form of the binary bits of the key word. A popular key word is X16+X12+X5+1 known as the X25 standard. Key words will herein be referred to as polynomial key words.
CRC is often implemented in hardware that is specific to a given polynomial key word. A CRC that is implemented in hardware is herein referred to as a CRC generator. Thus, a system that has to verify data using various different polynomial key words will need a separate CRC generator that is dedicated to each distinct polynomial key word. For example, FIG. 1 is a block diagram that illustrates a CRC generator that employs a 3rd order polynomial key word, X3+X2+1.
In FIG. 1, exclusive-OR gates (XOR gates) 110, 112, and 116 are communicatively coupled to each other and to corresponding shift registers 102, 104 and 106. Input 101 is initially received at XOR gate 110. The output of the CRC generator in FIG. 1 is 118.
FIG. 2 is block diagram that illustrates a CRC generator that employs a 1st order polynomial key word, X1+1. In FIG. 2, XOR gates 210, and 212 are communicatively coupled to each other and to corresponding shift registers 202, and 204. Input 220 is initially received at XOR gate 210. The output of the CRC generator in FIG. 2 is 222. A system with multiple CRC generators can be unwieldy and inefficient.
SUMMARY OF THE INVENTION
A Cyclic Redundancy Check (CRC) system comprises N+1 shift registers. N+1 logic gates having first inputs communicate with outputs of corresponding ones of said N+1 shift registers. N+1 programmable registers store a corresponding CRC coefficient of a 3rd to Nth order CRC polynomial key word, wherein N is an integer greater than two. N+1 multiplexers communicate with outputs of corresponding ones of said N+1 logic gates. At least N of said N+1 multiplexers communicate with corresponding ones of at least N of said N+1 programmable registers.
Further areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.



BRIEF DESCRIPTION OF THE DRAWINGS
The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which:
FIG. 1 is a block diagram that illustrates a prior art CRC generator that employs a 3rd order polynomial key word;
FIG. 2 is block diagram that illustrates a prior art CRC generator that employs a 1st order polynomial key word;
FIG. 3A is block diagram that illustrates an exemplary N-bit capable CRC generator;
FIG. 3B is a block diagram that illustrates the most significant bit (MSB) to the least significant bit (LSB) in relation to programmable registers;
FIG. 4 is a block diagram that illustrates the position of the MSB that is associated with a qth order polynomial key word;
FIG. 5 is a block diagram that illustrates a 3-bit capable CRC generator;
FIG. 6 is a block diagram that illustrates the position of the MSB that is associated with a X3+X2+1 key word;
FIG. 7 is a block diagram that illustrates the position of the MSB that is associated with a X1+X0 key word;



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
A system and method for generating a cyclic redundancy check is described. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention. Embodiments are described herein according to the following outline:
1.0 OPERATIONAL CONTEXT AND FUNCTIONAL OVERVIEW
2.0 N-BIT CAPABLE CRC GENERATOR
3.0 ILLUSTRATIVE EXAMPLE OF THE FLEXIBILITY OF AN N-BIT CAPABLE CRC GENERATOR
5.0 EXTENSIONS AND ALTERNATIVES
1.0 Operational Context and Functional Overview
In certain embodiments of the present invention, a universal CRC generator is used in a system that receives digital signals. The universal CRC generator can be programmed to be a specific polynomial key word CRC generator. Thus, one set of hardware can be adapted for any given polynomial key word. For example, for purposes of explanation, assume that a transmitter of a bitstream and a receiver of the same bitstream agree upon a key word that can be represented by the polynomial, X16+X12+X5+1. The universal CRC can be programmed to be an X16+X12+X5+1 polynomial key word CRC generator. Generally, an Nth polynomial key word CRC generator is also referred to as an N-bit CRC generator. Each time that the key word is changed, the universal CRCgenerator can be re-programmed to correspond to the new key word. It is to be noted that an Nth order polynomial key word has (N+1) bits.
Thus, in certain embodiments of the present invention, the universal CRC generator is a CRC generator that is capable of being a N-bit CRC generator, where N is a positive integer that is selected corresponding to the highest order polynomial key word that the universal CRC generator is expected to use. A universal generator that is capable of being an N-bit CRC generator is herein referred to as an “N-bit capable” CRC generator.
According to certain embodiments of the present invention, the universal CRC generator can be re-programmed to correspond to a new polynomial key word by programming the values of certain programmable registers that are part of the universal CRC generator and by programming certain selection inputs for multiplexers that are also part of the universal CRC generator. The programming of the registers and selection inputs for the multiplexers are explained in greater detail herein.
2.0 N-Bit Capable CRC Generator
According to certain embodiments of invention, FIG. 3A is block diagram that illustrates an N-bit capable CRC generator. An N-bit capable CRC generator is a universal CRC generator for which the highest order polynomial key word is N. Thus, an N-bit capable CRC generator can be used for polynomial key words of orders ranging from 1 to N. The N-bit CRC generator of FIG. 3A comprises the following as indicated in List A.
List A:
1) N+1 number of shift registers, namely, Xn 310, X(n-1) 312, . . . , X0 314;
2) N+1 number of exclusive-OR gates, namely, XORn 316, XOR(n-1) 318, . . . , XOR0 320;
3) 3N+1 number of multiplexers, namely, Man 322, Ma(n-1) 324, Mb(n-1) 326, Mc(n-1) 328, . . . , Ma0 330, Mb0 332, Mb0 334; and
4) N+1 programmable registers, namely, Yn 336, Y(n-1) 338, . . . , Y0 340.
The broken line 302 in FIG. 3A indicates that the following components as indicated in List B are not shown on FIG. 3A for want of space.
List B:
1) shift registers X(n-2), X(n-3), up to X1;
2) exclusive-OR gates XOR(n-2), XOR(n-31), . . . , up to XOR1;
3) multiplexes Ma(n-2), Mb(n-2), Mc(n-2), . . . , up to Ma1, Mb1, Mc1,
4) programmable registers Y(n-2), Y(n-3), . . . , up to Y1;
Each of the shift registers X is communicatively coupled to a corresponding exclusive-OR gate (XOR gate) and to adjacent multiplexers M. For example, in FIG. 3A, shift register Xn 310 is communicatively coupled to a corresponding XOR gate, XORn 316. Specifically, line 368 is shown as the output from Xn 310. Line 368 is also the input to XOR gate, XORn 316. Similarly, shift register Xn-1 312 is communicatively coupled to a corresponding XOR gate, XORn-1 318, etc. Line 378 is shown as the output from Xn-1 312. Line 378 is also the input to XOR gate, XORn-1 318. However, shift register X0 314 is communicatively coupled to only one XOR gate, viz., XOR0 320. Line 390 is shown as the output from X0 314. Line 390 is also the input to XOR gate, XOR0 320.
Further, each of the shift registers X in FIG. 3A is communicatively coupled to corresponding adjacent multiplexers M. For example, shift register Xn 310 is communicatively coupled to adjacent multiplexers Man 322 and Ma(n-1) 324. Specifically, line 366 is shown as an output from shift register Xn 310. Line 366 is also the input to multiplexer Man 322. Line 372 is shown as an output from multiplexer Man-1 324. Line 372 is also an input to shift register Xn 310.
Similarly, shift register Xn-1 312 is communicatively coupled to adjacent multiplexers Man-1 324, etc. Specifically, line 376 is shown as an output from shift register Xn-1 312. Line 376 is also the input to multiplexer Man-1 324. Line 382 is shown as an output from multiplexer Man-2 (note that Man-2 is not shown in FIG. 3A). Line 382 is also an input to shift register Xn-1 312.
Shift register X0 314 is communicatively coupled to adjacent multiplexer Ma0 330. Specifically, line 391 is shown as an output line from shift register X0 314. Line 391 is also an input line to multiplexer Ma0 330. Line 393 is shown as an output line from multiplexer Mb0 332. Line 393 is also an input line to shift register X0 314
Further, all shift registers Xn 310, X(n-1) 312, . . . , X0 314 in FIG. 3A are communicatively coupled to multiplexer Mout 342 via lines An 344, An-1 346, . . . , up to A0 348. For example, shift register Xn 310 is connected to Mout 342 via line An 344. Shift register Xn-1 312 is connected to Mout 342 via line An-1 346, etc. Further, CRC output 350 is the output of the N-bit capable CRC generator.
Each XOR gate is additionally communicatively coupled to corresponding adjacent multiplexers. For example, in FIG. 3A, XOR gate XOR(n-1) 318 is communicatively coupled to adjacent corresponding multiplexers Ma(n-1) and Mc(n-1) 328. Specifically, line 380 is shown as an input line from multiplexer Mc(n1-1) 328 to XOR gate XOR(n-1) 318. Line 374 is an output line from XOR gate XOR(n-1) 318 to multiplexer Ma(n-1) 324.
Similarly, XOR gate XOR0 320, is communicatively coupled to adjacent corresponding multiplexers Ma0 330 and M Mc0 334, etc. Specifically, line 396 is shown as an input line from multiplexer M Mc0 334 to XOR gate XOR0 320. Line 388 is an output line from XOR gate XOR0 320 to multiplexer Ma0 330. However, XOR gate XORn 316 is communicatively coupled to only one adjacent corresponding multiplexer Man 322. Line 364 is shown as an output line from XORn 316 to multiplexer Man 322.
Programmable registers Yn 336, Y(n-1) 338, . . . , Y0 340 are each communicatively coupled to a corresponding multiplexer. For example, programmable register Yn 336 is communicatively coupled to multiplexer Man 322, programmable register Y(n-1) 338 is coupled to multiplexer Ma(n-1) 324, etc.
For simplicity, programmable registers Yn 336, Y(n-1), . . . , Y0 340 are collectively referred to herein as Y registers.
The Y registers are programmed based on the given polynomial key word. To explain, each Y register in the N-bit capable CRC generator is associated with one term in the general Nth-order polynomial, CnXn+Cn-1Xn-1Cn-2Xn-2+ . . . +C2X2+C1X1+C0X0, where Cn, Cn-1, Cn-2, . . . , C2, C1, and C0 are the coefficients of the general Nth-order polynomial and are constants.
Each Y register corresponds to one coefficient of the general Nth-order polynomial. Specifically, programmable register Yn 336 in FIG. 3A corresponds to coefficient Cn, programmable register Yn-1 338 corresponds to coefficient Cn-1 and so on. The given polynomial key word is compared to the general Nth order polynomial to determine which of the coefficients of the general Nth-order polynomial are to take the value of zero in order to convert the Nth-order general polynomial into the given polynomial key word.
The Y registers that correspond to coefficients that have a value of zero are programmed to have a bit value of zero. The Y registers that correspond to coefficients that have a value of 1 are programmed to have a bit value of 1.
The value of each bit in the Y register determines which input is selected at the corresponding multiplexer to be an output. For example, if programmable register Yn 336 is programmed to have a bit value of 1, multiplexer Man 322 will receive the value 1 as an input from programmable register Yn 336. In FIG. 3A, it can be seen that multiplexer Man 322 has 2 input lines, labeled “1” and “0” respectively. Since the value 1 is received from programmable register Yn 336 multiplexer Man 322 will select the input line labeled “1” to be the output of Man 322 for a particular cycle.
FIG. 3B is a block diagram that illustrates the most significant bit (MSB) to the least significant bit (LSB) in relation to the programmable registers Y 370. Bit Bn corresponds to the value in register Yn 336, and is the MSB if the value of Yn 336 is the first occurring “1” bit. Similarly, bit Bn-1 corresponds to the value in register Yn-1 338, etc. Bit Bo corresponds to the value in register Y0 340, and is the LSB.
For ease of explanation, multiplexers with the same superscript as illustrated in FIG. 3A are said to belong to the same family. As can be seen in FIG. 3A, multiplexers that belong to the same family are communicatively coupled to form part of a feedback loop. For example, multiplexer Ma(n-1) 324 is communicatively coupled to multiplexer Mb(n-1) 326 that is in turn communicatively coupled to multiplexer Mc(n-1) 328. Multiplexer Ma0 330 is communicatively coupled to multiplexer Mb0 332 that is in turn communicatively coupled to multiplexer Mc0 334. However, multiplexer Man 322, being the sole member in its family is communicatively coupled only to one multiplexer that belongs to another family, viz., multiplexer Mb(n-1) 326.
Selection inputs such as, Last-X(n-1) 352, Last-X(n-2) (not shown in FIG. 3A), . . . , Last-X0 354, are received as inputs into corresponding multiplexers with subscripts “b” and “c” and that belong to the same family. For example, Last-X(n-1) 352 is a selection input into multiplexers Mb(n-1) 326 and Mcn-1) 328, and Last-X0 354 is a selection input into multiplexers Mb0 332 and Mc0 334, etc.
Further, all selection inputs, namely, Last-X(n-1) 352, Last-X(n-2) (not shown in FIG. 3A), . . . , Last-X0 354 are input into multiplexer Mout 342. It is to be noted that, in certain embodiments, there is no Last-Xn selection input.
For simplicity in explaining the function of the components in FIG. 3A, selection inputs such as Last-X(n-1) 352, Last-X(n-2) (not shown in FIG. 3A), . . . , Last-X0 354 are collectively referred to herein as Last-X selection inputs.
Generally, selection inputs such as, Last-X(n-1) 352, Last-X X(n-2) (not shown in FIG. 3A), . . . , Last-X0 354, are programmed to be a specific value based on the most significant bit (MSB) of the Y registers. For purposes of illustration, assume that the given polynomial key word is a qth order polynomial, where q is a positive integer that is less than N. FIG. 4 is a block diagram that illustrates the position of the MSB that is associated with a qth order polynomial key word
In FIG. 4, bit Bn has the value of the Yn register that is programmed as described herein. Bit Bn-1 has the value of the Yn-1 register, bit Bn-2 has the value of the Yn-2 register, . . . , bit Bq has the value of the Yq register, bit Bq-1 has the value of the Yq-1 register, bit Bq-2 has the value of the Yq-2 register, . . . , bit B2 has the value of the Y2 register, bit B1 has the value of the Y1 register, and bit B0 has the value of the Y0 register.
Since the given polynomial key word is a qth order polynomial, the first occurring “1” bit corresponds to the value of the Yq register. In FIG. 4, the first occurring “1” bit is in Yq register and so Yq is the MSB. Since the first “1” bit corresponds to the value of the Yq register, the i) selection input Last-Xq (not shown in FIG. 3A) is programmed to be equal to 1. All other selection inputs such as, Last-Xn-1 352, Last-Xn-2 (not shown in FIG. 3A), . . . , Last-X0 354, are programmed to have a value of zero.
The value of each selection input, such as Last-Xn-1 352, Last-Xn-2 (not shown in FIG. 3A), . . . , Last-X0 354 determines which input lines 362, 370, 394, 358, 392, . . . , 387, 386, 395, 358, is selected at the corresponding multiplexers, Mbn-1 Mcn-1, . . . , Mb0, Mc0 to be output from the multiplexers Mbn-1 Mcn-1, . . . , Mb0, Mc0.
For example, if selection input Last-Xn-1 352 is programmed to have the value of 1, multiplexer Mbn-1 326 and multiplexer Mcn-1 328 will each receive the value 1 as an input. In FIG. 3A, it can be seen that multiplexer Mbn-1 326 and multiplexer Mcn-1 328 each has 2 input lines, labeled “1” and “0”. Since the value 1 is received as the selection input by multiplexer Mbn-1 and multiplexer Mcn-1, multiplexer Mbn-1 and multiplexer Mcn-1 will each select the input line labeled “1” to be their output for a particular cycle.
As explained herein, there is no Last-Xn selection input because there are no multiplexers that control the primary input into the XOR gate, XORn 316. XORn 316, being the first XOR gate in an N-bit capable CRC generator will always receive the primary input.
In FIG. 3A, multiplexer Mout 342 has N+1 input lines, namely, An 344, An-1 346, . . . , up to A0 348. If selection input Last-Xn-1 352 has a value of 1, then multiplexer Mout 342 will select An-1 346 to be CRC output 350. Similarly, if Last-Xn-2 (not shown in FIG. 3A) has a value of 1, then multiplexer Mout 342 will select An-2 (not shown in FIG. 3A) to be CRC output 350, and so on.
Even though there is no Last-Xn selection input, the effect of a selection input Last-Xn can be obtained by making the selection of An 344 as the default selection when all the selection inputs, namely, Last-X(n-1) 352, Last-X(n-2) (not shown in FIG. 3A), Last-X0 354 have a value of zero.
Additionally, multiplexers with the subscript “b”, such as Mb(n-1) 326, Mb(n-2) (not shown in FIG. 3A), Mb(n-3) (not shown in FIG. 3A), . . . , Mb0 332 are communicatively coupled to each other. Specifically, line 392 is an output line from Mb(n-1) 326. Line 392 is also an input line to Mb(n-2) (not shown in FIG. 3A). As previously explained herein, line 393 is shown as an output line from multiplexer Mb0 332. Line 393 is also an input line to shift register X0 314.
Multiplexers with the subscript “c” each receive a primary input, P 356. For example, multiplexers Mc(n-1) 328, Mc(n-2) (not shown in FIG. 3A), Mc(n-3) (not shown in FIG. 3A), . . . , Mc0 334 each receive a primary input, P 356. XOR gate XORn 316 also receives primary input, P 356. Typically, primary input P 356 is a bitstream that is input into the XOR gates at the rate of one bit per cycle.
All multiplexers in the N-bit capable CRC generator have 2 input lines. One input line is labeled “1” and the other input line is labeled “0” as indicated in FIG. 3A.
The arrangement of the components in List B, i.e. the components that not shown in FIG. 3A, are the same as the arrangement of the components Y(n-1) 338, XOR(n-1) 318, Ma(n-1) 324, Mbn-1 326, and Mc(n-1) 328 relative to each other.
3.0 Illustrative Example of the Flexibility of an N-Bit Capable CRC Generator
Typically, N is equal to 64 or larger for the universal CRC generator. However, for simplicity of explanation, assume that that N=3 for the N-bit capable CRC generator. FIG. 5 is a block diagram that illustrates a 3-bit capable CRC generator 500. A 3-bit capable CRC generator can be used for polynomial key words of orders ranging from 1 to 3.
In FIG. 5, shift register X3 506 is communicatively coupled to corresponding XOR gate, XOR3 504. Specifically, line 550 is an output line from shift register X3 506. Line 550 is also an input line to XOR gate, XOR3 504.
Further, shift register X3 506 is communicatively coupled to adjacent multiplexers Ma3 502 and Ma2 508. Specifically, line 548 is an output line from shift register X3 506. Line 548 is also an input line into Ma3 502. Line 554 is output line from Ma2 508. Line 554 is also an input line into shift register X3 506.
Similarly, shift register X2 516 is communicatively coupled to corresponding XOR gate, XOR2 514, and to adjacent multiplexers Ma2 508 and Ma1 518. Specifically, line 566 is an output line from shift register X2 516. Line 566 is also an input line to XOR gate, XOR2 514. Line 568 is an output line from shift register X2 516. Line 568 is also an input line into multiplexer Ma2 508. Line 572 is output line from multiplexer Ma1 518. Line 572 is also an input line into shift register X2 516.
Shift register X1 526 is communicatively coupled to corresponding XOR gate, XOR1 524, and to adjacent multiplexers Ma1 518 and Ma3 528. Specifically, line 584 is an output line from shift register X1 526. Line 584 is also an input line to XOR gate, XOR1 524. Line 586 is an output line from shift register X1 526. Line 586 is also an input line into multiplexer Ma1 518. Line 590 is output line from multiplexer Ma0 528. Line 590 is also an input line into shift register X1 526.
Shift register X0 536 is communicatively coupled to XOR gate, XOR0 534. In addition, shift register X0 536 is communicatively coupled to adjacent multiplexer Ma0 528. Specifically, line 595 is an output line from shift register X0 536. Line 595 is also an input line to XOR gate, XOR0 534. Line 593 is an output line from shift register X0 536. Line 593 is also an input line into multiplexer Ma0 528. Line 590 is output line from multiplexer Ma0 528.
Further, all shift registers X3 506, X2 516, X1 526, X0 536 are communicatively coupled to multiplexer Mout 589 via output lines A3 546, A2 570, A1 588, and A0 591, respectively. CRC Output 534 is the output of the 3-bit capable CRC generator 500.
Each XOR gate is additionally communicatively coupled to either one or two corresponding adjacent multiplexers. In FIG. 5, XOR gate, XOR3 504 is communicatively coupled to one adjacent corresponding multiplexer Ma3 502. Line 552 is an output line from XOR gate, XOR3 504. Line 552 is also an input line to multiplexer Ma3 502.
Similarly, XOR gate, XOR2 514, is communicatively coupled to adjacent corresponding multiplexers Ma2 508 and Mc2 512. Line 564 is an output line from XOR gate, XOR2 514. Line 564 is also an input line to multiplexer Ma2 508. Line 562 is an output line from multiplexer Mc2 512. Line 562 is also an input line to XOR gate, XOR2 514.
XOR gate, XOR1 524, is communicatively coupled to adjacent corresponding multiplexers Ma1 518 and Mc1 522. Line 582 is an output line from XOR gate, XOR1 524. Line 582 is also an input line to multiplexer Ma1 518. Line 580 is an output line from multiplexer Mc1 522. Line 580 is also an input line to XOR gate, XOR1 524.
XOR gate, XOR0 534, is communicatively coupled to adjacent corresponding multiplexers Ma0 528 and Mc1 532. Line 597 is an output line from XOR gate, XOR0 534. Line 597 is also an input line to multiplexer Ma0 528. Line 598 is an output line from multiplexer Mc0 532. Line 598 is also an input line to XOR gate, XOR0 534.
Programmable registers Y3 538, Y2 540, Y1 542, and Y0 544 are each communicatively coupled to corresponding multiplexers Ma3 502, Ma2 508, Ma1 518, Ma0 528 respectively.
For example, programmable register Y3 502 is communicatively coupled to Ma3 502. Similarly, programmable register Y2 540 is coupled to Ma2 508. Programmable register Y1 532 is coupled to Ma1 518. Programmable register Y0 544 is coupled to Ma0 528.
For ease of explanation, multiplexers with the same superscript as illustrated in FIG. 5 are said to belong to the same family. As can be seen in FIG. 5, multiplexers that belong to the same family are communicatively coupled to form part of a feedback loop. For example, multiplexer Ma2 508 is communicatively coupled to multiplexer Mb2 510 that is in turn communicatively coupled to multiplexer Mc2 512. Specifically, line 556 is an output line from multiplexer Ma2 508. Line 556 is also an input line to multiplexer Mb2 510. Line 560 is an input line from multiplexer Mb2 510 to multiplexer Mc2 512.
Similarly, Ma1 518 is communicatively coupled to Mb1 520 that is in turn communicatively coupled to Mc1 522. Specifically, line 574 is an output line from multiplexer Ma1 518. Line 574 is also an input line to multiplexer Mb1 520. Line 578 is an input line from multiplexer Mb1 520 to multiplexer Mc1 522.
Ma0 528 is communicatively coupled to Mb0 530 that is in turn communicatively coupled to Mc0 532. Specifically, line 592 is an output line from multiplexer Ma0 528. Line 592 is also an input line to multiplexer Mb0 530. Line 596 is an input line from multiplexer Mb0 530 to multiplexer Mc0 532.
However, Ma3 502, being the sole member in its family is communicatively coupled to multiplexer Mb2 510. Line 547 is an output line from multiplexer Ma3 502 to multiplexer Mb2 510.
Inputs Last-X2 583, Last-X1 587, and Last-X0 585 are selection inputs into corresponding multiplexers with subscripts “b” and “c” and which belong to the same family. For example, Last-X2 583 is a selection input into multiplexers Mb2 510 and Mc2 512. Last-X1 587 is a selection input into multiplexers Mb1 520 and Mc1 522. Last-X0 585 is a selection input into multiplexers Mb0 530 and Mc0 532. Further, all selection inputs Last-X2 583, Last-X1 587, and Last-X0 585 are input into multiplexer Mout 589.
Additionally, multiplexers with the subscript “b”, such as Mb2 510, Mb1 520. Mb0 530 are communicatively coupled to each other. Multiplexers with the subscript “c” each receive a primary input, P 501 through line 503. For example, multiplexers Mc2 512, Mc1 522 and, Mc0 532 each receive a primary input, P 501. XOR gate XOR3 504 also receives primary input, P 501 through line 503. Typically, primary input P 501 is a bitstream that is to be checked for error by the CRC generator 500. Primary input P 501 is input into the XOR gates at the rate of one bit per cycle.
As a first illustration, assume that a CRC generator is needed to implement a given 320 polynomial key word of order 3. Further assume that the given polynomial is as follows:

X3+X2+1

The 3-bit capable CRC described with reference to FIG. 5 can be converted to specifically implement the polynomial key word, X3+X2+1. In other words, by programming the values of the Y registers and the Last-X selection inputs, the 3-bit capable CRC generator becomes a X3+X2+1 key word CRC generator. For purposes of explanation, the given polynomial key word is re-written to explicitly show coefficients and missing terms. Thus, the given polynomial key word, X3+X2+1, can be re-written as: (1)X3+(1)X2+(0)X1+(1)X0 
Referring to FIG. 5, programmable register Y3 538 corresponds to coefficient of X3 of the given key word polynomial. Thus, programmable register Y3 538 is programmed to have the value of 1. In response to receiving the value of 1 from programmable register Y3 538, multiplexer Ma3 502, will select input line labeled “1”.
Similarly, programmable register Y2 540 corresponds to coefficient X2 of the given key word polynomial. Thus, programmable register Y2 540 is programmed to have the value of 1. In response to receiving the value of 1 from programmable register Y2 540, multiplexer Ma2 508, will select input line labeled “1”.
Programmable register Y1 542 corresponds to coefficient X1 of the given key word polynomial. Thus, programmable register Y1 542 is programmed to have the value of 0. In response to receiving the value of 0 from programmable register Y1 542, multiplexer Ma1 518, will select input line labeled
Programmable register Y0 544 corresponds to coefficient X0 of the given key word polynomial. Thus, programmable register Y0 544 is programmed to have the value of 1. In response to receiving the value of 1 from programmable register Y0 544, multiplexer Ma0 528, will select input line labeled “1”.
The Last-X selection inputs are programmed to be a specific value based on the most significant bit (MSB). FIG. 6 is a block diagram that illustrates the position of the MSB that is associated with the polynomial key word, X3+X2+1. In FIG. 6, bit 610 has the value of the Y3 register that is programmed to have a value of 1 described above. Since the first occurring “1” bit corresponds to the value of the Y3 register, bit 610 represents the MSB.
Similarly, bit 612 has the value of the Y2 register that is programmed to have a value of 1. Bit 614 has the value of the Y1 register that is programmed to have a value of 0. Bit 616 has the value of the Y0 register that is programmed to have a value of 1. Bit 616 is the LSB.
Since the first occurring “1” bit corresponds to the value of the Y3 register, all Last-X selection inputs, namely, Last-X2 583, Last-X1 587, and Last-X1 585 in FIG. 5 are programmed to have a value of zero.
The value of each Last-X selection input determines which input is selected at the corresponding multiplexers to be output from said multiplexers. For example, since selection input Last-X2 583 is programmed to have the value of 0, multiplexer Mb2 510 and multiplexer Mc2 512 will each receive the value 0 as an input. In FIG. 5, it can be seen that multiplexer Mb2 510 and multiplexer Mc2 512 each has 2 input lines, labeled “1” and “0”. Since the value 0 is received as the selection input, multiplexer Mb2 510 and multiplexer Mc2 512 will each select the input line labeled “0” to be their output for a particular cycle.
In FIG. 5, multiplexer Mout 589 has 4 input lines, namely, A3 546, A2 570, A1 588, A0 591. Since all the selection inputs, namely, Last-X2 583, Last-X1 587, Last-X0 585, have the value of 0, multiplexer Mout 589 will select A3 546 to be CRC output 534.
Thus, by programming the Y registers and the Last-X selection inputs as described above, the 3-bit capable CRC generator is equivalent to the CRC generator as described in FIG. 1 herein.
Further, the same 3-bit capable CRC generator can be programmed to implement a given polynomial key word that is of an order that is lower than 3. Assume that the given polynomial is as follows:

X1+1

For purposes of explanation, the given polynomial key word, X1+1, is re-written to explicitly show coefficients and missing terms. Thus, the given polynomial key word, X1+1, can be re-written as:

(0)X3+(0)X1+(1)X1+(1)X0 

In FIG. 5 programmable register Y3 538 corresponds to coefficient of X3 of the given key word polynomial. Thus, programmable register Y3 538 is programmed to have the value of 0. In response to receiving the value of 0 from programmable register Y3 538, multiplexer Ma3 502, will select input line labeled “0”.
Similarly, programmable register Y2 540 corresponds to coefficient X2 of the given key word polynomial. Thus, programmable register Y2 540 is programmed to have the value of 0. In response to receiving the value of 0 from programmable register Y2 540, multiplexer Ma2 508, will select input line labeled “0”.
Programmable register Y1 542 corresponds to coefficient X1 of the given key word polynomial. Thus, programmable register Y1 542 is programmed to have the value of 1. In response to receiving the value of 1 from programmable register Y1 542, multiplexer Ma1 518, will select input line labeled “1”.
Programmable register Y0 544 corresponds to coefficient X0 of the given key word polynomial. Thus, programmable register Y0 544 is programmed to have the value of 1. In response to receiving the value of 1 from programmable register Y0 544, multiplexer Ma0 528, will select input line labeled “1”.
The Last-X selection inputs are programmed to be a specific value based on the most significant bit (MSB) of the Y registers. FIG. 7 is a block diagram that illustrates the position of the MSB that is associated with a X1+X0 key word. In FIG. 7, bit 710 has the value of the register Y3 that is programmed to have a value of 0 described above. Similarly, bit 712 has the value of the Y2 register that is programmed to have a value of 0.
Bit 714 has the value of the Y1 register that is programmed to have a value of 1. Since the first occurring “1” bit corresponds to the value of the Y1 register, bit 714 represents the MSB. Bit 716 has the value of the Y0 register that is programmed to have a value of 1. Bit 716 is the LSB.
Since the first occurring “1” bit corresponds to the value of register Y1, selection input Last-X1 587 is programmed to have a value of 1, and selection inputs Last-X2 583 and Last-X0 585 are programmed to have a value of 0.
The value of each Last-X selection input determines which input is selected at the corresponding multiplexers to be output from said multiplexers.
Referring back to FIG. 5, since selection input Last-X2 583 has the value 0, multiplexer Mb2 510 and multiplexer Mc2 512 will each select the input line labeled “0” to be their output for a particular cycle. Similarly, since selection input Last-X0 585 has the value 0, multiplexer Mb0 530 and multiplexer Mc0 532 will each select the input line labeled “0” to be their output for a particular cycle.
In contrast, since selection input Last-X1 587 has the value 1, multiplexer Mb1 520 and multiplexer Mc1 522 will each select the input line labeled “1” to be their output for a particular X0 cycle.
In FIG. 5, multiplexer Mout 589 has 4 input lines, namely, A3 546, A2 570, A1 588, A0 591. Since the selection input Last-X1 587 has the value of 1, multiplexer Mout 589 will select A1 588 to be CRC output 534.
Thus, by programming the Y registers and the Last-X selection inputs as described above, the 3-bit capable CRC generator 500 is equivalent to the CRC generator as described in FIG. 2.
5.0 Extensions and Alternatives
In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.

## Claims

1. A cyclic redundancy check generator comprising:
a plurality of shift registers, each shift register corresponding to a coefficient of a general polynomial key word; and
a plurality of programmable registers that are programmed based on a specific polynomial key word,
wherein the specific key word programmed to the plurality of programmable registers is compared to the general polynomial key word to determine which shift registers corresponding to coefficients of the general polynomial key word are to take a predetermined value in order to convert the general polynomial key word into the specific polynomial key word.

2. The cyclic redundancy check generator of claim 1, wherein:
the general polynomial key word has a predetermined bit length; and
the specific polynomial key word has a bit length equal to or less than the predetermined bit length of the general polynomial key word.

3. The cyclic redundancy check generator of claim 2, wherein the general polynomial key word comprises a general Nth order polynomial key word having a bit length of N+1, where N is a positive integer.

4. The cyclic redundancy check generator of claim 3, wherein:
the plurality of shift registers comprises of N+1 shift registers; and
the plurality of programmable registers comprises of N+1 programmable registers.

5. The cyclic redundancy check generator of claim 1, wherein the predetermined value is zero.

6. The cyclic redundancy check generator of claim 1, wherein the plurality of programmable registers are reprogrammable to correspond to a new polynomial key word.

7. A receiver comprising the cyclic redundancy check generator of claim 1.

8. A method for generating a specific polynomial key word through a cyclic redundancy check generator, the cyclic redundancy check generator including a plurality of shift registers, each shift register corresponding to a coefficient of a general polynomial key word, the method comprising:
programming a plurality of programmable registers based on the specific polynomial key word;
comparing the specific key word programmed to the plurality of programmable registers to the general polynomial key word to determine which shift registers corresponding to coefficients of the general polynomial key word are to take a predetermined value in order to convert the general polynomial key word into the specific polynomial key word; and
converting the general polynomial key word to the specific polynomial key word based on the shift registers having the predetermined value.

9. The method of claim 8, wherein:
the general polynomial key word has a predetermined bit length; and
the specific polynomial key word has a bit length equal to or less than the predetermined bit length of the general polynomial key word.

10. The method of claim 9, wherein the general polynomial key word comprises a general Nth order polynomial key word having a bit length of N+1, where N is a positive integer.

11. The method of claim 10, wherein:
the plurality of shift registers comprises of N+1 shift registers; and
the plurality of programmable registers comprises of N+1 programmable registers.

12. The method of claim 11, wherein the predetermined value is zero.

13. The method of claim 8, further comprising reprogramming the plurality of programmable registers to correspond to a new polynomial key word.

14. A cyclic redundancy check generator comprising:
a plurality of shift register means, each shift register means corresponding to a coefficient of a general polynomial key word; and
means for programming a plurality of programmable registers means based on a specific polynomial key word;
means for comparing the specific key word programmed to the plurality of programmable registers means to the general polynomial key word to determine which shift register means corresponding to coefficients of the general polynomial key word are to take a predetermined value in order to convert the general polynomial key word into the specific polynomial key word; and
means for converting the general polynomial key word to the specific polynomial key word based on the shift register means having the predetermined value.

15. The cyclic redundancy check generator of claim 14, wherein:
the general polynomial key word has a predetermined bit length; and
the specific polynomial key word has a bit length equal to or less than the predetermined bit length of the general polynomial key word.

16. The cyclic redundancy check generator of claim 15, wherein the general polynomial key word comprises a general Nth order polynomial key word having a bit length of N+1, where N is a positive integer.

17. The cyclic redundancy check generator of claim 16, wherein:
the plurality of shift register means comprises of N+1 shift register means; and
the plurality of programmable register means comprises of N+1 programmable register means.

18. The cyclic redundancy check generator of claim 14, wherein the predetermined value is zero.

19. The cyclic redundancy check generator of claim 14, wherein the plurality of programmable register means are reprogrammable to correspond to a new polynomial key word.

20. A receiver comprising the cyclic redundancy check generator of claim 14.