Abstract:
The present invention provides a circuit for detecting and correcting errors in a bit stream. The circuit consists of a plurality of circuit elements, a least one operation circuit means, and at least two logic gates. The logic gates receive inputs from the plurality of circuit elements. The plurality of circuit elements are coupled to receive and store a portion of a bit stream. The operation circuit elements perform bitwise operations on the contents of at least two of the circuit elements. The bitwise operations are dictated by a cyclical redundancy check (CRC) polynomial and are used to perform the CRC error detection division operation. At the end of the division process for the data to be checked, each circuit element corresponds to a bit in a bit error pattern syndrome and the logic gates determine if the contents of the circuit elements match specific bit error patterns. The circuit causes the state of at least one bit in the bit stream to change if the contents of the plurality of circuit elements match one of the specific bit patterns. The circuit is advantageous in that it may detect single bit errors, and double bit errors that may be caused by error duplication characteristic of a scrambler.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a continuation of U.S. patent application Ser. No. 10/147,880, filed on May 20, 2002, the contents of which are incorporated herein by reference. 
     
    
     FIELD OF INVENTION  
       [0002]     This invention relates to the error detection and correction by a 16-bit Cyclic Redundancy Check (CRC-16) generation circuit.  
       BACKGROUND TO THE INVENTION  
       [0003]     Cyclic Redundancy Check (CRC) is an important aspect in the error-detecting capabilities of many protocols, such as the Ethernet local area network, protocol. CRC provides a number of bits (usually 16 or 32) generated from, and appended to the end of, a block of data to provide error detection. A message receiver generates a CRC from the block of data and compares it to the CRC appended to the received message. If the appended CRC matches the generated CRC, then there is a high probability that the received message has not been corrupted.  
         [0004]     One standard 16-bit generator polynomial is represented by x 16 +x 12 +x 5 +1. The polynomial represents the binary number 10001000000100001—a one bit is in positions 16, 12, 5, and 0. The CRC is the remainder after binary (modulo 2) division of the message by the generator polynomial. For Ethernet CRC, the 32-bit generator polynomial is represented by x 32 +x 26 +X 23 +x 22 +x 16 +x 12 +x 11 +x 10 +x 8 +x 7 +x 5 +x 4 +x 2 +x+1. Typically, a 16-bit CRC generator polynomial is used with messages of less than 4 Kbytes. A 32-bit CRC generator is used for messages up to 64 kbytes in length.  
         [0005]     The CRC is usually performed by the data link protocol and a calculated CRC is appended to the end of the data link layer frame. The CRC is calculated by performing a modulo 2 division of the data by a generator polynomial and recording the remainder after division.  
         [0006]     Although this division may be performed in software, it is commonly performed using a shift register and exclusive or X-OR gates. The hardware solution for implementing a CRC is much simpler than a software approach. The CRC-16 is able to detect all single errors, all double errors, and all errors with bursts less than 16 bits in length. The previously-standardized CRC-16 generator polynomials can also detect all odd numbers of errors, at the expense of less detection capability for even numbers of errors.  
         [0007]     On an aside, the CRC is the only field which is by convention sent most significant bit first. To further clarify, the first bit of the CRC-16 to be sent is the bit corresponding to position 16 in the CRC field, the most significant bit (MSB), and the last bit being the bit corresponding to position 0 in CRC field, the least significant bit (LSB).  
         [0008]     As previously mentioned, CRC is pervasive throughout most data traffic. Recently, a protocol, known as the Generic Framing Procedure (GFP), utilizes a CRC-16 for error detection and correction in the frame header and payload. GFP also utilizes an X 43 +1 self-synchronous scrambler, for error protection. The GFP protocol has recently been standardized by the International Telecommunications Union-Telecommunications (ITU-T) as Recommendation G.7041.  
         [0009]     To date, GFP has been implemented as a generic mechanism to adapt traffic from higher-layer signals over a synchronous transport network. There are two types of GFP, the frame-mapped GFP and the transparent GFP. The frame-mapped GFP enables a signal frame to be received and mapped in its entirety into one or more GFP frames. The transparent GFP mapping involves decoding block-coded signal frames and then mapping the decoded signal frames into a fixed-length GFP frame, having only received a block-coded version of the signal frame.  
         [0010]     Prior to transmitting a GFP frame, the payload portion of the GFP frame is normally scrambled. Frames are scrambled to protect a user from other malicious users who may try to cause loss of receiver synchronization at the physical layer. For the SONET/SDH protocol (Synchronous Optical Network/Synchronous Digital Hierarchy), self-synchronized scramblers are utilized to create more physical layer transitions to aid timing recovery at the receiver. The frame-synchronized scrambler was added to make it much more difficult for a malicious user to defeat the effects of the frame synchronous scrambler.  
         [0011]     A frame-synchronized scrambler is one in which the transmitted data is exclusive-ORed bit-by-bit with the output of a pseudo-random sequence generator with the sequence generator being reset to a known state at the beginning of every frame. The frame-synchronized scramblers are very effective in increasing the transition density to an acceptable level for typical traffic. One drawback of a frame-synchronized scrambler is that it is a known, relatively short (2 7 −1) pseudo-random sequence and it is possible for a malicious subscriber to attempt to mimic this pattern within the data he sends. The result is that if the subscriber data lines up with the SONET/SDH scrambler correctly, a long string can occur with no transitions, which in turn can cause the receiver to fail. The phenomenon was observed with early ATM and POS systems and was addressed from the outset with GFP. The solution used for each of these three protocols is a self-synchronous scrambler over the payload region of the cell/frame.  
         [0012]     A self-synchronous scrambler is one in which the data is exclusive-ORed with a delayed version of itself on a bit-by-bit basis. The specific scrambler used for ATM, POS, and GFP exclusive-ORs the input data with scrambler output data after a 43 bit delay termed the scrambler polynomial. The descrambler reverses the process by multiplying the received signal by the same scrambler polynomial. The advantage to such a scrambler in this application is that it is very hard for a malicious user to duplicate due to its never having a known reset point. The value of the scrambler state is a function of the previous data rather than the position of the data within the SONET/SDH frame. The drawback to a self-synchronous scrambler is that any errors occurring on the transmission channel will be duplicated 43 bits later by the descrambler. As a result, an error check code over the data will have to deal with twice the bit error rate as that experienced by the transmission channel.  
         [0013]     The duplicated bit error, hereinafter termed the “double bit error”, requires that the decoded CRC detect the double bit errors, as well as any single bit errors, without compromising the probability of detection. In view of aforementioned shortcomings of the self-synchronous scrambler, the present invention seeks to provide a circuit for detecting and correcting both single bit errors and double bit errors based on a plurality of conditions being met. The present invention further seeks to provide a probability of error detection that is equivalent to the probability of error detection had the double errors not been introduced by the descrambler.  
       SUMMARY OF THE INVENTION  
       [0014]     The present invention provides a circuit for detecting and correcting errors in a bit stream. The circuit consist of a plurality of circuit elements, an least operation circuit means, and at least two logic gates. The logic gates receive inputs from the plurality of circuit elements. The plurality of circuit elements are coupled to receive and store a portion of a bit stream. The operation circuit elements perform bitwise operations on the contents of at least two of the circuit elements. The bitwise operations are dictated by a CRC polynomial and are used to perform the CRC error detection division operation. At the end of the division process for the data to be checked, each circuit element corresponds to a bit in a bit error pattern syndrome, the logic gates determine if the contents of the circuit elements match specific bit error patterns. The circuit causes the state of at least one bit in the bit stream to change if the contents of the plurality of circuit elements match one of the specific bit patterns.  
         [0015]     The present invention is advantageous in that it may detect single bit errors, and double bits errors which may be caused by error duplication characteristic of a scrambler. The circuit utilizes a minimum of logic gates, two AND gates to provide the error detection and correction not known in the prior art.  
         [0016]     In a first aspect, the present invention provides a circuit for detecting and correcting errors in a bit stream, the circuit including at least two logical gates that determine if at least one of a plurality of conditions is present, each one of said plurality of conditions indicating at least one error in said bit stream and activating at least one of the at least two logical gates to change the state of a specific bit in said bit stream.  
         [0017]     In a second aspect, the present invention provides a circuit for detecting and correcting errors in a bit stream, said circuit comprising: 
        a plurality of bit circuit elements coupled to receive and store said bit stream, each bit circuit element corresponding to a specific bit in a bit pattern;     at least one operation circuit element for performing operations between contents of at least two of said bit circuit elements; and     at least two logic gates for determining if contents of said bit circuit elements match specific bit patterns at least one of said at least two logic gate receiving inputs from said bit circuit elements;     wherein an output of said circuit causes a state of at least one bit in said bit stream to change if contents of said bit circuit elements match at least one of said plurality of specific bit patterns; and     wherein said bit patterns correspond to errors that have occurred in the transmitted data.        
 
         [0023]     In a third aspect, the present invention provides a circuit for detecting errors in a bit stream, the circuit comprising: 
        operation means for performing bitwise operations between at least a portion of said bit stream and a bit pattern derived from said bit stream; and     detection means for detecting if a bitwise operation between at least a portion of said bit stream and said bit pattern derived from said bit stream produces a result indicating at least one error in said bit stream;     wherein said operation means implements a bitwise operation corresponding to 
 
 B ( x )= Rem ( D ( x )/ G ( x )) 
    where D(x) is said at least a first portion of said bit stream; 
            G(x) is said bit pattern derived from said bit stream; and     B(x) is a remainder of a division operation between D(x) and G(x);    
            such that said detection means detects when B(x) does not equal 0.       
 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0031]     The present invention will now be described with reference to the drawings, in which:  
         [0032]      FIG. 1  illustrates a known self-synchronous scrambler and descrambler;  
         [0033]      FIG. 2  illustrates a known x 43 +1 self-synchronous scrambler;  
         [0034]      FIG. 3  is a schematic representation of a first circuit for detecting and correcting single and double bit errors according to the present invention;  
         [0035]      FIG. 4  is a schematic representation of a second circuit for detecting and correcting single and double bit errors according to the present invention; and  
         [0036]      FIG. 5  is a block diagram of a circuit for an 8-bit wide parallel implementation according to the present invention. 
     
    
     DETAILED DESCRIPTION  
       [0037]      FIG. 1  illustrates both a x n +1 self-synchronous scrambler  10  and descrambler  20  as discussed in the background to the invention. As previously explained, the x n +1 scrambler  10  receives data in the form of a bit stream at the input  30 . The data is exclusive-ORed  40  with a delayed version of itself. The delayed bits are illustrated as bit circuit elements, D 1 , D 2 , . . . . Dn. The scrambled data is output at  50  by the exclusive-OR operation after an n-bit delay. The scrambler operation is expressed as an x n +1 polynomial.  
         [0038]     In  FIG. 1 , the x n +1 descrambler  20  performs the reverse operation from the scrambler  20 . The descrambler  20  multiplies the received data at the input  60  by the same scrambler polynomial. The descrambler outputs the descrambled data  70  serially after the first set of n bits have been received.  
         [0039]      FIG. 2  illustrates a x 43 +1 self-sychronous scrambler  100  of the prior art. As shown in the x n +1 descrambler of  FIG. 1 , the x 43 +1 self-sychronous scrambler  100  multiplies the received input bit stream by the scrambler polynomial, x 43 +1. The drawback of the self-sychronous scrambler, in general, is that any errors occurring on the transmission channel will be duplicated n bits later in the bit stream. In the case of the x 43 +1 self-sychronous scrambler, any errors are duplicated 43 bits later by the descrambler  100 . A single-bit error is illustrated in a possible output bit stream  120 , whereas a double-bit error is shown in another possible output bit stream  130 . While the descrambler  100  does duplicate any bit errors, a double bit error may not be output within the same data block, or data frame, of descrambled bits. In other words, the first error may be in a preceding data block while the double error is part of the next data block. Furthermore, while it is possible to have double bit errors within a common data block, it is further possible to have triple errors due to bit error placement within the data block. To clarify, in a given data block there may be an error and a duplicate error and in addition, another bit error may occur due to boundary cases. Boundary cases involve triple bit errors from a preceding or successive block, where bit errors from a preceding block are extend across frames into a preceding/successive block. These triple errors, while random, are detectable by the CRC-16.  
         [0040]     Accordingly, the present invention provides a circuit for implementing a CRC-16 polynomial for triple bit error detection with improved single bit error and double bit error detection after descrambling.  
         [0041]      FIG. 3  illustrates a circuit  200  for detecting and correcting single and double bit errors according to a first embodiment of the present invention. The first embodiment is intended for an initial proposed transparent GFP superblock CRC-16. The circuit  200  consists of a plurality of bit circuit elements D 1 , D 2 , D 3 , D 4 , D 5 , D 6 , D 7 , D 8 , D 9 , D 10 , D 11 , D 12 , D 13 , D 14 , D 15 , D 16 , two logic AND gates  210 ,  220 , an OR gate  230 , and a plurality of input bit stream circuit elements D 1 , D 2 , . . . , D 493 , D 494 , . . . , D 536 , as shown in  FIG. 3 . The bit circuit elements may be implemented as bit registers, or other circuit elements such as flip-flops or transistors. The CRC polynomial implemented in the circuit  200  is G(x)=x 16 +x 15 +x 14 +x 12 +x 10 +x 8 +x 7 +X 4 +x 3 +x+1.  
         [0042]     According to the circuit  200  of  FIG. 3 , the input stream is a GFP superblock, essentially a 536 bit block, which is input into circuit elements D 1  through D 536 . On a bit-by-bit basis, the D 1  through D 16  bit circuit elements receive input from the input stream. The circuit elements are coupled to operation circuit elements  240 A,  240 B, . . . ,  240 H,  240 I, which provide bitwise operations dictated by the G(x). The first AND gate  210  receives inputs from bits resulting from bitwise operations between specific selected bits. If the bits at the first AND gate  210  inputs match a predetermined bit pattern then the AND gate  210  is activated. Similarly, the second AND gate  220  receives inputs from bits resulting from bitwise operations between selected bits, specific to the second AND gate  220 . If the bits at the second AND gate  220  inputs match a predetermined bit pattern then the AND gate  220  is activated. The OR gate  230  receives an input from both first AND gate  210  and the second gate  220 . The OR gate is activated by a predetermined output from either or both AND gates  210  and  220 . Upon activation, the OR gate  230  changes a specific bit in the bit stream. In this case, the OR gate  230  would invert the first bit, stored in the D 536  circuit element, to correct the single error. If a positive output is derived from the second AND gate  220 , then a double error has been detected and the bit located 43 bits behind at D 493  is inverted.  
         [0043]     The circuit operation may be expressed as the following equation: 
 
 B ( x )= Rem ( D ( x )/ G ( x ) 
        where D(x) is said at least a portion of the 536 bit block;     G(x) is a bit pattern derived from the bit stream according to the polynomial;     B(x) is a remainder of a division operation between D(x) and G(x); and     Rem is the remainder from the modulo division of D(x) by G(x); 
 
 such that the circuit detects when B(x) does not equal 0. 
       
 
         [0048]     The operation may be designed as a nested IF/THEN loop 
        If Rem (D(x)/G(x))=a double bit error pattern then flip bit  1  AND flip the bit which is n bits behind bit  1      If Rem (D(x)/G(x))=a single bit error pattern then flip bit  1 .     where n is derived from the scrambler polynomial, X n +1.        
 
         [0052]     According to an embodiment of the present invention, n may be 43 if the X 43 +1 scrambler polynomial is utilized in conjunction with the circuitry of the present invention.  
         [0053]     In  FIG. 3 , the CRC-16 polynomial G(x) dictate the bitwise operation over the 536 bit GFP superblock. According to limitations of the CRC-16 error detection, the best possible error detection capability of the CRC-16 polynomial is triple error detection. With triple error detection capability, single error correction is also possible. In order to preserve the triple error detecting capability, the CRC-16 generator polynomial must have no common factors with the payload scrambler polynomial. The x 43+1  payload scrambler polynomial factors into: 
 
 x   43 +1=( x+ 1)( x   14   +x   11   +x   10   +x   9   +x   8   +x   7   +x   6   +x   5   +x   4   +x   3 + 1 )( x   14   +x   12   +x   10   +x   7   +x   4   +x   2+ 1)( x   14   +x   13   +x   11   +x   7 +x 3   +x+ 1) 
 
         [0054]     All of the known standard CRC-16 generator polynomials, have x+1 as a factor, and would therefore suffer degraded performance due to duplicate errors. In order to also provide double error detecting capability the CRC generator polynomial must have a factor that is a primitive polynomial with a degree of at least 10. To further provide a triple bit error detection, a CRC-16 generator polynomial with triple error detection capability was utilized. According to the present invention, it was determined that various CRC-16 generator polynomials met both the double error detection and the no common scrambler factors criteria. The CRC polynomial G(x) of  FIG. 3 , and that of  FIG. 4 , are examples of CRC polynomials which met the above criteria.  
         [0055]     As explained in the background, each single transmission error will result in either one or two superblock errors in the descrambled data. Due to the feedback tap on the x 43 +1 descrambler, a second error is always created exactly 43 bit after the bit affected by the transmission bit error. If both of these errors fall within the data of the same superblock, then the CRC-16 must cope with two errors. It is possible, however, for the two errors to occur around a superblock boundary where one of the errors appears in each superblock. Errors occurring at boundaries is discussed in detail in a technical paper T1X1.5/2001-094, “Impact of x43+1 Scrambler on the Error Detection Capabilities of Ethernet CRC,” standards contribution from Norival Figueira, Nortel Networks, March 2001, which incorporated herein by reference. A more rigorous theoretical analysis is to be found in “Analysis of the Interaction Between CRC Error Detecting Polynomials and Self-Synchronous Payload Scramblers”, Steven S. Gorshe, PhD Dissertation, Oregon State University, USA, 2002.  
         [0056]     In general, single error correction is possible with a linear cyclic code as long as each possible error pattern leads to a unique syndrome at the decoder. For a CRC, the syndrome created by the bit error pattern is the remainder calculated in the division of the data block by the CRC generator polynomial. A remainder other than zero indicates the presence of an error. In order to preserve the capability of correcting single transmission errors, the syndromes (remainders) must be unique for each possible single error and 43-bit-spaced double error pattern. The unique syndromes allow the decoder to know the original error pattern, which is what makes the correction possible. For each of the CRC-16 polynomials that met the above triple error detecting criteria, bit error patterns were calculated for each possible single error and 43-bit-spaced double errors.  
         [0057]     The following are the single-bit error patterns and double-bit error patterns which met the following criteria.  
         [0058]     According to  FIG. 3 , single-bit error patterns and double-bit error patterns are detected by the first and second AND gates to determine whether single-bit errors and double-bit errors have occurred.  
         [0059]     The single-bit error patterns (Syndrome A) and the double bit patterns (Syndrome B) are as follows:  
         [0000]     Syndrome A  
         [0000]    
       
          0000000000000001  
          0000000000000010  
          0000000000000100  
          0000000000001000  
          0000000000010000  
          0000000000100000  
          0000000001000000  
          0000000010000000  
          0000000100000000  
          0000001000000000  
          0000010000000000  
          0000100000000000  
          0001000000000000  
          0010000000000000  
          0100000000000000  
          1000000000000000  
          1001010000011111  
          1011110000100001  
          1110110001011101  
          0100110010100101  
          1001100101001010  
          1010011010001011  
          1101100100001001  
          0010011000001101  
          0100110000011010  
          1001100000110100  
          1010010001110111  
          1101110011110001  
          0010110111111101  
          0101101111111010  
          1011011111110100  
          1111101111110111  
          0110001111110001  
          1100011111100010  
          0001101111011011  
          0011011110110110  
          1101111011011000  
          0010100110101111  
          0101001101011110  
          1010011010111100  
          1101100101100111  
          0010011011010001  
          0100011011010001  
          0100110110100010  
          1001101101000100  
          1010001010010111  
          1101000100010001  
          0011011001111101  
          0110110011111010  
          1101100111110100  
          0010011111110111  
          1100001101010001  
          0001001010111101  
          0010010101111010  
          0100101011110100  
          1001010111101000  
          1011111111001111  
          1110101110000001  
          0100001100011101  
          1000011000111010  
          1001100001101011  
          1010010011001001  
          1101110110001101  
          0010111100000101  
          0101111000001010  
          1011110000010100  
          1110110000110111  
          0100110001110001  
          1001100011100010  
          1010010111011011  
          1101111110101001  
          0101011010011010  
          1010110100110100  
          1100111001110111  
          0000100011110001  
          0001000111100010  
          0010001111000100  
          0100011110001000  
          1000111100010000  
          1000010100011111  
          1000000001100001  
          1001010011011101  
          1011110110100101  
          1110111101010101  
          0100101010110101  
          1011111011001011  
          1110100110001001  
          0100011100001101  
          1000111000011010  
          1000100000101011  
          1000010001001001  
          1001110010001101  
          1010110100000101  
          1100111000010101  
          0000100000110101  
          0001000001101010  
          0010000011010100  
          0100000110101000  
          1001001010111111  
          1011000101100001  
          1111011011011101  
          0111100110100101  
          0111100110100101  
          1111001101001010  
          0111001010001011  
          1110010100010110  
          0101111000110011  
          1011110001100110  
          1110110011010011  
          0100110110111001  
          1001101101110010  
          1010001011111011  
          1101000111101001  
          0110111110011010  
          1101111100110100  
          0010101001110111  
          0101010011101110  
          1010100111011100  
          1100011110100111  
          0101010011101110  
          1010100111011100  
          1100011110100111  
          0001101101010001  
          0011011010100010  
          0010000100001111  
          0100001000011110  
          1000010000111100  
          1001110001100111  
          1010110011010001  
          1100110110111101  
          0000111101100101  
          0001111011001010  
          0011110110010100  
          0111101100101000  
          1111011001010000  
          0111100010111111  
          1111000101111110  
          0111011011100011  
          1110110111000110  
          0100111110010011  
          1001111100100110  
          1010101001010011  
          1100000010111001  
          0001010101101101  
          0101010110110100  
          1010101101101000  
          1100001011001111  
          0001000110000001  
          0010000110000010  
          0100011000000100  
          1000110000001000  
          1000110000001111  
          1000110000000001  
          1000110000011101  
          1000110000100101  
          1000110001010101  
          1000110010110101  
          1000110101110101  
          1000111011110101  
          1000100111110101  
          1000011111110101  
          1001101111110101  
          1010001111110101  
          1101001111110101  
          0011001111110101  
          0110111111101010  
          1100111111010100  
          0000101110110111  
          0001011101101110  
          0010111011011100  
          0101110110111000  
          1011101101110000  
          1110001011111111  
          1010001111000010  
          1101001110011011  
          0011001100101001  
          0110011001010010  
          1100110010100100  
          0000110101010111  
          0001101010101110  
          0011010101011100  
          0110101010111000  
          1101010101110000  
          0011111011111111  
          0111110111111110  
          1111101111111100  
          0110001111000111  
          0101100001011110  
          1011000010111100  
          1111010101100111  
          0111111011010001  
          1111110110100010  
          0110111101011011  
          1101111010110110  
          0010100101110011  
          0101001011100110  
          1101111110000111  
          0010101100010001  
          0101011000100010  
          1010110001000100  
          1100110010010111  
          0000110100110001  
          0001101001100010  
          0011010011000100  
          0110100110001000  
          1101001100010000  
          0011001000111111  
          0110010001111110  
          1100100011111100  
          0000010111100111  
          0000101111001110  
          0001011110011100  
          0010111100111000  
          0101111001110000  
          1011110011100000  
          1110110111011111  
          0100111110100001  
          1001111101000010  
          1010101010011011  
          1100000100101001  
          0001011001001101  
          0010110010011010  
          0101100100110100  
          1011001001101000  
          1111000011001111  
          1110101100000010  
          0100001000011011  
          1000010000110110  
          1001110001110011  
          1010110011111001  
          1100110111101101  
          0000111111000101  
          0001111110001010  
          0011111100010100  
          0111111000101000  
          1111110001010000  
          0110110010111111  
          1101100101111110  
          0010011011100011  
          0100110111000110  
          1001101110001100  
          1010001100000111  
          1101001000010001  
          0011000000111101  
          0110000001111010  
          1100000011110100  
          0001010111110111  
          0010101111101110  
          0101011111011100  
          1010111110111000  
          1100101101101111  
          0000001011000001  
          0000010110000010  
          0000101100000100  
          0010110000010000  
          0101100000100000  
          1011000001000000  
          1111010010011111  
          0111110100100001  
          1111101001000010  
          0110000010011011  
          1100000100110110  
          0001011001110011  
          0010110011100110  
          0101100111001100  
          1011001110011000  
          1111001100101111  
          0111001001000001  
          1110010010000010  
          0101110100011011  
          1011101000110110  
          1110000001110011  
          0101010011111001  
          1010100111110010  
          1100011111111011  
          0001101111101001  
          0011011111010010  
          0110111110100100  
          1101111101001000  
          0010101010001111  
          0101010100011110  
          1010101000111100  
          1100000001100111  
          0010100110100010  
          0101001101000100  
          1010011010001000  
          1101100100001111  
          0010011000000001  
          0100110000000010  
          1001100000000100  
          1010010000010111  
          1101110000110001  
          0010110001111101  
          0101100011111010  
          1011000111110100  
          1111011111110111  
          0111101111110001  
          1111011111100010  
          0111101111011011  
          1111011110110110  
          0111101101110011  
          1111001110100110  
          0111001101010011  
          1110011010100110  
          0101100101010011  
          1011001010100110  
          1111000101010011  
          0111011010111001  
          1110110101110010  
          0100111011111011  
          1010111111110011  
          1100101111111001  
          0000001111101101  
          0000011111011010  
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          0110100000010000  
          1101000000100000  
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          0101111000101110  
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          1110110010100111  
          0100110101010001  
          1001101010100010 
 
 Syndrome B 
 
          0100110110100011  
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          0000000100100001  
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          1000101101111011  
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          1001000111001101  
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          0110001000110101  
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          0111001100101100  
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          1111001010110010  
       
     
         [1045]     The above explanation of the present invention, as embodied in circuit  200  of  FIG. 3 , has assumed that positive logic is utilized. Positive bit logic was applied in detecting and correcting errors based on the outputs derived from both bitwise operations and bit logic operations. For example, a binary output of 1 at an AND gate indicates an error. However, if negative logic is utilized in the circuit  200 , a binary output of O at the AND gate  210  would indicate an error as well.  
         [1046]      FIG. 4  illustrates a circuit  300  for detecting and correcting single and double bit errors according to a second embodiment of the present invention. The second embodiment is intended for a final version transparent GFP superblock CRC-16. The circuit  300  differs from that of  FIG. 3 , in that bitwise operations are dictated by a different G(x) polynomial. The CRC polynomial implemented in this circuit  300  is G(x)=x 16 +x 15 +x 14 +x 12 +x 10 +x 4 +X 3 +x 2 +X+1.  
         [1047]     It should be mentioned that while the circuits of  FIGS. 3 and 4  detect double bit errors generated by a descrambler, the circuits of the present invention detect single bit, double bit, and triple bit errors derived from any number of other sources. The 536 bit block need not be derived from a descrambler, such as is used on a GFP CRC-16. The circuit of the present invention may derive a 536-bit superblock, prior to processing by the circuit of the present invention. Furthermore, the art that the present invention may be embodied in other circuitry. For example, additional AND gates may be utilized to perform error detection in both circuits  200  and  300  of  FIGS. 3 and 4 .  
         [1048]      FIG. 5  is a block diagram of a circuit  400  for an 8-bit wide parallel implementation according to a third embodiment of the present invention. As compared to the serial bit implementation of  FIGS. 3 and 4 , the error detection logic  410  outputs an 8-bit wide output to the OR gate  420 . In an 8-bit wide parallel implementation, errors are detected for an 8-bit wide block. The single and double errors are corrected in the same manner as in the implementation of  FIG. 4  with the advantage that operating on 8-bit data blocks allows the circuit to operate at ⅛ the data path clock speed of a serial implementation such as in  FIGS. 3 and 4 . The data path clock speed reduction is a significant advantage for high-speed data transmission.  
         [1049]     In  FIG. 5 , the process implemented by the circuit  400  is similar to that of  FIGS. 3 and 4 . The parallel CRC-16 generator consists of a bit circuit elements which are coupled to sequentially receive and store a sequential 16 bits derived from an 8-bit wide input stream  450 . The generator  440  performs bitwise operations on the 16 stored in the bit circuit elements. The bitwise operation, again, is dictated by the CRC polynomial selected. Upon completion of the bitwise operations, the generator  440  outputs the generated 16 bits to the bit pattern generation logic  410 . If the single error output  450  indicates a single bit error, then the OR gate  420  enables the errorred bit within the last 8 bits in the bit circuit element D 67  to be corrected. If the double error output  450  indicates a 43-bit spaced double error, then the exclusive-OR logic gates  470 A,  47 B enable the bit error which is 43 bits behind the first bit to be corrected. The bits of the errored byte to be corrected are stored in two bit circuit element, D 61  and D 62 . The first 3 bits, of the errorred byte, are stored in the D 61  bit stream circuit element. The last 5 bits are stored in the bit stream circuit element D 62 .  
         [1050]     Based on the circuit implementation shown in  FIGS. 3, 4 , and  5 , the present invention is not limited to a single CRC polynomial. Rather, the present invention provides single error and double error detection and correction capabilities for both serial and parallel bit streams, in which a number of CRC polynomials may be utilized. The above bit error patterns are not exclusive to the GFP protocol. Any protocol which utilizes a fixed-length block may utilize the specific bit patterns to detect errors in portions of the block bit stream.