Abstract:
A system and method for the transmission of additional special marker symbols in a signal space constellation allows the communication of additional control information with minimal additional power to transmit the additional symbol. Additional symbols can include “Start of Message”, “End of File”, “End of Transmission”, “Increase Data Rate”, “Decrease Data Rate”, “Save State” or “Clear”, or any additional command signal desired to be transmitted.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of copending and commonly assigned patent application entitled SYSTEM AND METHOD FOR TRANSMITTING SPECIAL MARKER SYMBOLS, assigned Ser. No. 08/979,455 and filed on Nov. 26, 1997, the text of which is hereby incorporated by reference, and which claims priority to and the benefit of the filing date of provisional patent application entitled CIRCULAR CONSTELLATIONS FOR UNCODED MODULATION, assigned Ser. No. 60/039,851, and filed Mar. 5, 1997 and copending and commonly assigned provisional patent application entitled CIRCULAR PRECODING AND NONLINEAR ENCODING assigned Ser. No. 60/037,191, and filed Mar. 6, 1997 the text of both provisional applications being hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to data communications, and more particularly, to a system and method for communicating special marker symbols in a signal space constellation. 
     BACKGROUND OF THE INVENTION 
     The field of data communications typically uses a modem to convey information from one location to another. Digital Subscriber Line (DSL) technology now enables modems to communicate large amounts of data. Modems communicate by modulating a baseband signal carrying digital data, converting the modulated digital data signal to an analog signal, and transmitting the analog signal over a conventional copper wire pair using techniques that are known in the art. These known techniques include mapping the information to be transmitted into a multidimensional signal space constellation. In some instances, a one dimensional signal space constellation can be employed, such as in the case of pulse amplitude modulation (PAM). The constellation can include both analog and digital information or only digital information. 
     In the above mentioned communications system it would be beneficial to allow the transmission of additional special marker symbols in a signal space constellation. These special markers can be used to convey a number of command and control functions from one communication device to another. Constellations typically encode exactly N-bits in a constellation with 2 N  points. A need exists for the ability to transmit additional special marker symbols in a signal space constellation. 
     SUMMARY OF THE INVENTION 
     The present invention makes the convenient and efficient transmission of additional special marker symbols possible. The present invention provides a system and method for transmitting a plurality of additional symbols in a signal space constellation. The invention incorporates a marker encoder configured to encode an additional special marker into an additional symbol. This additional symbol, representing any one of a number of additional commands, such as “Start of Message”, “End of File”, “End of Transmission”, “Increase Data Rate”, “Decrease Data Rate”, “Save State” or “Clear” is added to a value of 2 N  and then transmitted in a signal space constellation in accordance with techniques that those skilled in the art will appreciate. The present invention includes a transmitter configured to transmit the additional symbol in a signal space constellation and a receiver configured to receive the signal space constellation containing the additional special symbol. A subtractor configured to subtract the value of 2 N  from the received signal so as to decode the additional symbol is also included in the receiver. A marker decoder configured to decode the additional symbol into the additional special marker is also included. Any number of additional special marker symbols may be transmitted. 
     In a preferred embodiment of the present invention a marker encoder receives special marker symbols such as “End of File”, “Start of Message”, “End of Transmission”, “Increase Data Rate”, “Decrease Data Rate”, or “Clear” and supplies them in the form of an encoded symbol “b”, which is added to a value of 2 N  and supplied as an N+1 bit word to the register alternatively with the N bit word. The N bit word is supplied from an ISA bus to an N+1 bit register which separates the N+1 bit word into N most significant bits (msb&#39;s) and 1 least significant bit (lsb). The encoded symbol “b” occupies the lsb positions such that larger numbers of special marker symbols are easily accommodated. 
     An International Standards Architecture (ISA) bus is an industry standard which eliminates the need for signal interfaces and is well known in the art. Based upon the data rate capacity of the channel, groups of 16 or 32 bit words are converted into frames of N bit words where N is determined by the data rate capacity of the channel. In order to allow the transmission of fractional bit rates as is known in the art of data communications, the register can optionally include a modulus converter or other means, such as constellation switching or shell mapping to enable the transmission of fractional bit rates. The N msb&#39;s are next supplied to a mapper, which maps the signal into a signal space constellation. Optionally, an N bit word is supplied first to a scrambler. The scrambler performs an operation on the N bit word that results in a scrambled N bit word. While in the preferred embodiment the special marker symbols are not scrambled, they can be. 
     Next, the signal is operated upon by a phase encoder which is designed to develop a rotation vector using the 1 lsb supplied by the register. In the case of PAM, only one lsb is phase encoded. This rotation vector is combined in a rotator with the mapped N bit vector representing the N msb&#39;s to form the signal space constellation of the present invention and creates a phase rotated positive or negative signal. Optionally, the phase encoder includes a differential encoder which encodes the 1 lsb of the N+1 bit word to develop 1 differential bit. This differential bit is added to the lsb&#39;s supplied from the register and become part of the rotation vector. 
     The phase rotated signal is then modulated using either carrierless amplitude/phase (CAP) modulation or any coded or uncoded modulation scheme such as trellis coding, quadrature amplitude modulation (QAM), or pulse amplitude modulation (PAM), and then transmitted over a communication channel comprising a conventional wire pair. In the case of PAM modulation, the signal space is one dimensional instead of multidimensional as in QAM, however, the concepts of the present invention are equally applicable thereto. At a receiver, the transmitted phase rotated signal is received and demodulated in accordance with techniques that are known in the art of modem communications. A phase decoder which includes a phase slicer operates on the received signal and supplies a signal to a vector rotation operator which provides a derotation vector. The derotation vector is combined with the signal space constellation in a rotator which recovers the mapped N bit vector representing the N msb&#39;s. Optionally, the output of the phase slicer is supplied to a differential decoder which develops 1 differential bit in order to recover the 1 lsb of the N+1 bit word. The 1 differential bit is subtracted from the output of the phase slicer and input to the lsb of a register. 
     The signal space constellation is then sliced, as is known in the art, in order to recover the mapped N msb&#39;s in a register. As in the transmitter, the register can include a device such as a modulus converter, or other means such as constellation switching or shell mapping in order to allow the transmission of fractional bit rates. Lastly, the N msb&#39;s are combined with the lsb and, if scrambled, the N bit word is descrambled in order to output an unscrambled N bit word. 
     The register supplies the N+1 bit word to a subtractor where a value of 2 N  is subtracted from the N+1 bit word. This output is then supplied to a marker decoder which will separate the special marker symbol from the received N bit word. 
     Various modulation techniques may benefit from the concepts and features of the present invention. For example, the present invention will function equally well using carrierless amplitude/phase (CAP) modulation, or any coded or uncoded modulation such as trellis coding, QAM or PAM. 
     The invention has numerous advantages, a few of which are delineated hereafter, as merely examples. 
     An advantage of the present invention is that it permits the transmission of special marker signals as symbols added to a signal space constellation. 
     Another advantage of the present invention is that it provides for seamless data rate changing by designated special symbols. As data rate increases, N increases and unique special marker symbols are retained by adding 2 N . 
     Another advantage of the present invention is that it provides for very fast multi-point synchronization by using a simple designated special Start of Message “SOM” marker to signal the arrival of a new message. The special marker symbols are high power symbols developed by adding 2 N  to a power indexed signal constellation. They have maximum margin for distinguishing them from the idle channel signal which precedes each multi-point transmission, thus making them easy to distinguish. 
     Another advantage of the present invention is that it is simple in design, reliable in operation, and its design lends itself to economical mass production in modems. 
     Other features and advantages of the present invention will become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional features and advantages be included herein within the scope of the present invention, as defined in the appended claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention, as defined in the claims, can be better understood with reference to the following drawings. The drawings are not necessarily to scale, emphasis instead being placed on clearly illustrating the principles of the present invention. 
     FIG. 1A is a graphical representation of a 64 point CAP square signal space constellation; 
     FIG. 1B is a graphical representation of a 64 point CAP circular signal space constellation including special marker symbols; 
     FIG. 1C is a graphical representation of an 8 point PAM constellation including special marker symbols; 
     FIG. 2 is a schematic view of a multipoint communications channel including modems employing the concepts and features of the present invention; 
     FIG. 3 is a schematic view illustrating a modem of FIG. 2 employing the concepts and features of the present invention; 
     FIG. 4 is a schematic view of the transmitter section of the modem of FIG. 3 including the present invention; and 
     FIGS. 5A and 5B collectively illustrate a schematic view of the receiver section of the modem of FIG. 3 including the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention can be implemented in software, hardware, or a combination thereof. In the preferred embodiment, the elements of the present invention are implemented in software that is stored in a memory and that configures and drives a suitable digital signal processor (DSP) situated in the respective modem. 
     The foregoing program, which comprises an ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. In the context of this document, a “computer-readable medium” can be any means 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 readable medium can 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 (electronic) having one or more wires, a portable computer diskette (magnetic), a random access memory (RAM) (magnetic), a read-only memory (ROM) (magnetic), an erasable programmable read-only memory (EPROM or Flash memory) (magnetic), an optical fiber (optical), and a portable compact disc read-only memory (CDROM) (optical). Note that the 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. 
     Referring now to FIG. 1A, shown is a graphical representation of a 64 point uncoded CAP square signal space constellation  2 . The in-phase and quadrature samples developed by a CAP modulation scheme, as is known in the art, specify a location  3  in the signal space of FIG.  1 A. The set of possible samples that a CAP modulator can produce corresponds to a set of sample points, or a constellation of points. For simplicity, a constellation of 64 points is described, however, as is known in the art, constellations with a larger number of signal points are possible. 
     Referring now to FIG. 1B, shown is a graphical representation of a 64 point uncoded CAP circular signal space constellation  4 . As in a square constellation, the in-phase and quadrature samples developed by a CAP modulation scheme specify a location  6  in the signal space of FIG.  1 B. For simplicity the circular constellation depicted in FIG. 1B contains 68 signal points, including four special marker symbols, however many other configurations are possible. While the following preferred embodiment describes the generation of signal space constellations using uncoded carrierless amplitude/phase (CAP) modulation, other modulation techniques, such as QAM modulation, or PAM modulation can also employ the concepts and features of the present invention. In fact, any modulation technique, including one that uses trellis coding can be used. 
     Referring now to FIG. 1C, shown is a pulse amplitude modulation (PAM) signal constellation in accordance with an aspect of the invention. PAM constellation  8  is an eight point constellation having special marker symbols  7  added thereto, resulting in a  10  point constellation. 
     Referring now to FIG. 2, shown is a view illustrating a multipoint communication channel in which modems  18  and  13  employing the concepts and features of the present invention are used. Remote location  16  is connected to central office location  12  and control modem  13  via communication channel  14 . Channel  14  is typically the copper wire pair that runs between a telephone company central office and a remote residential, business, or any other location. Remote location  16  may contain a plurality of modems  18  connecting a plurality of user devices  17  to communication channel  14 . Remote location  16  can be a residential, business, or other location served by a conventional copper wire pair. By using modems  18  and  13  employing the concepts and features of the present invention, it is possible to transmit and receive additional special marker symbols as points added to the perimeter of a signal space constellation. While the following preferred embodiment is described with reference to remote modem  18 , the concepts and features of the present invention are equally applicable to control modem  13 . 
     Now referring to FIG. 3, shown is a schematic view illustrating a modem  18  of FIG.  2 . Modem  18  contains many conventional components as is known in the art of data communications. Central processor  21  controls the operation of the modems&#39; transmitter  24  and receiver  25  through logical interface  23 , and contains logic  20  configured to enable transmitter  24  and receiver  25  to communicate additional special marker symbols. The components of the modem connect to communications channel  14  through line interface  22 . By employing the concepts and features of the present invention, the transmission of additional special marker symbols using signal space constellations is possible. 
     With reference to FIG. 4, shown is a preferred embodiment of a transmitter  24  of modem  18  employing the concepts and features of the present invention. An ISA bus, a standard computer bus which eliminates the need for interfaces, supplies data, in the form of a data word that can be either 16 or 32 bits for the preferred embodiment, on line  33  to register  122 . This data word is transformed into an N bit word by counting bits and shifting to arrive at a smaller number of bits, in this example, an N bit data word is segmented into a lsb and N−1 additional bits. N can be any number. Optionally, in order to allow the transmission of fractional bit rates as is known in the art of data communications, register  122  can include a modulus converter or other means such as constellation switching or shell mapping. Modulus conversion is a well known technique in the art of communications for allowing the transmission of fractional bit rates, and is described in U.S. Pat. No. 5,103,227. Constellation switching allows the transmission of fractional bit rates by, for example, first transmitting 6 bits in one symbol and 7 bits in the next symbol if it is desired to transmit 6½ bits. For 6¾ bits one would transmit 7 bits per symbol for three symbol cycles and transmit 6 bits per symbol for the fourth symbol cycle. Shell mapping blocks the data into frames and a shell mapping algorithm, such as that described in the V.34 specification, is used to map the frames of data into a constellation of a certain size. 
     Optionally, the N bit word is first input on line  31  to scrambler  32 . Scrambler  32  can be either a self synchronized scrambler or a preset free running scrambler as is known in the art. Depending on the application, the preset scrambler may have some advantage, as in the case of using Reed-Solomon coding. If scrambler  32  is employed, a scrambled N bit word is output on line  33 . Special marker logic  20  allows the easy and reliable transmission of special marker symbols in the signal space constellation of the present invention. In order to transmit special marker symbols, marker encoder  127  supplies special marker symbols such as “End of File” (EOF), “Start of Message” (SOM) “End of Transmission” (EOT), or any other special marker that is desirable to send, in the form of an encoded symbol “b” on line  131 . An example of the output of marker encoder  127  is given in Table 1. Note that the “SOM” and “EOF” special symbols may use the same markers because “SOM” is preceded by an idle channel and “EOF” is preceded by normal data transmission. The N+1 bit word is shown for the example with N=6. 
     
       
         
               
               
               
               
               
             
           
               
                 Table 1 
               
               
                   
               
               
                 Symbol 
                 b 
                 N + 1 Word 
                 N Word 
                 LSB 
               
               
                   
               
             
             
               
                 SOM 
                 0 
                 1000000 
                 100000 
                 0 
               
               
                 EOF 
                 0 
                 1000000 
                 100000 
                 0 
               
               
                 Dec. Data Rate 
                 1 
                 1000001 
                 100000 
                 1 
               
               
                 Incr. Data Rate 
                 2 
                 1000010 
                 100001 
                 0 
               
               
                 EOT 
                 3 
                 1000011 
                 100001 
                 1 
               
               
                 ISA Data 
                   
                 0MMMMLL 
                 0MMMMMM 
                 L 
               
               
                   
               
             
          
         
       
     
     where L represents the least significant bits and M represents the most significant bits. The encoded symbol is added in adder  128  to a value of 2 N  on line  132  and supplied to register  122  on line  36  alternatively with the output of scrambler  32  through switch  121 . Switch  121  is logically controlled to include the special marker symbol as input to line  35  resulting in N+1 bits input to register  122 . In the case of modulus conversion to a constellation of size 4M, adder  128  would add 4M on line  132 , instead of 2 N , to encoded symbol “b”. 
     The resulting N msb&#39;s on line  123  are supplied to mapper  34  which maps the N msb&#39;s into a signal space constellation, resulting in mapped N msb&#39;s, represented by a 1-dimensional vector, supplied on line  38  to rotator  41 . The N msb&#39;s are enlarged by 2 N−1  resulting in the possibility of a word larger than N bits if “b” is transmitted. By using a single mapper, the N msb&#39;s can expand, as shown by Table 1, while still allowing the use of a single mapper table. Next, the lsb on line  111  is operated upon by phase encoder  37 . Phase encoder  37  is designed to develop a rotation vector  114  using the lsb supplied by register  122 . This rotation vector is output on line  116  and combined in rotator  41  with the mapped N msb&#39;s on line  38  to form a phase rotated signal. Optionally, phase encoder  37  includes differential phase encoder  118  which encodes the lsb&#39;s of the N bit word to develop 1 differential bit. This previous differential bit is output on line  119  and combined with the lsb from register  122  in adder  112  and becomes part of the rotation vector  114 . 
     Rotator  41  performs vector multiplication on the rotation vector on line  116  and the mapped N msb vector word on line  38  to cause a phase rotation, or simply a positive/negative polarity inversion, thus producing the final polarity symmetric signal space constellation used to transmit the information including the additional special marker symbol of the present invention on line  42 . In the case of PAM, the rotator simply inverts the polarity (or sign) of the pulse amplitude. The constellation on line  42  is supplied to scaler  43 . Scaler  43  multiplies the constellation by a scale function of the data rate and supplies a real number comprising X values on line  47  to TX filter  46 . In the case of PAM, a single real number X is supplied on line  47  to TX filter  46 , which may be a simple low pass filter. Alternatively, TX filter  46  may be a Hilbert filter. The scale function allows a single table to be used to implement the mapper at all data rates. TX filter  46  operates on the signal to provide a PAM modulated signal on line  49  to digital-to-analog converter (DAC)  52 . 
     In an alternate embodiment of the present invention, the scaled constellation on line  47  is modulated using uncoded modulator  48 , using a technique such as uncoded quadrature amplitude modulation (QAM) as is known in the art. Uncoded modulator  48  provides the sine and cosine components of a carrier frequency, or the X and Y values of the carrier frequency as is known in the art, on line  51  to multiplier  126 . Multiplier  126  combines the X component of the carrier frequency with the output of scaler  43  for input to TX filter  46  which provides a bandpass output at a certain frequency range. 
     In the case of PAM, the modulator  48  is generally not used as it would result in conventional amplitude modulation (AM). One of the advantages of PAM is its low frequency bandwidth and resultant lower complexity. 
     The concepts and features of the present invention as claimed can be practiced using either CAP modulation or any coded or uncoded modulation technique such as trellis coding, QAM or PAM. 
     The modulated signal on line  49  is supplied to digital to analog converter  52  for conversion to an analog signal that can be transmitted conventionally at various speeds over communication channel  14  as is known in the art. 
     The operation of the communications system disclosed thus far, i.e., up to TX filter  46 , occurs at the symbol rate of the modem, with the symbol rate equal to the bandwidth of the modem, thus allowing the use of reduced cost components. The output is of TX filter  46  and DAC  52  are computed at the sample rate, which is typically three times that of the symbol rate. In the case of PAM, filter  46  may be eliminated and the sample rate may equal the symbol rate. 
     Now referring to FIG. 5A, shown is a schematic view of the receiver section  25  of the modem of FIG.  3 . The received signal is input from communication channel  14  on line  61  to analog to digital converter (ADC)  62  for conversion to the digital domain as known in the art. The digital received signal is supplied on line  63  to RX filter  64 . RX filter  64  may alternatively be a Hilbert filter. The filtered signal is output from RX filter  64  on line  69 . In the case of uncoded modulation, uncoded demodulator  67  provides the sine and cosine components of the carrier frequency on line  68  to multiplier  157  for combination with the output of RX filter  64 . The demodulated output is provided on line  69  to automatic gain control (AGC) circuit  72 . AGC circuit  72  multiplies the demodulated received signal by gain factor  74 . The AGC compensated signal is then supplied on line  76  to equalizer  78 . Equalizer  78  is a known in the art finite impulse response (FIR) filter with adaptive coefficients. 
     The equalized decoded signal is supplied on line  79  to scaler  81  which operates on the received signal with a 1/scale factor. The 1/scale factor is a function of the data rate depending on the number of points in the constellation. The output of scaler  81  is the normalized X component representing the vector values of the symbols in the signal space constellation. In the case of PAM, the output of scaler  81  is the normalized X component representing the single real value of the symbols. 
     The normalized output of scaler  81  is supplied to slicer  84 , which generates ideal reference vectors as is known in the art. Because the signal is normalized, one slicer can be used for all data rates. 
     The output of scaler  81  is also supplied to adder  93  along with the output of slicer  84 . Adder  93  subtracts the output of scaler  81  from the output of the slicer  84  to obtain an error signal which is supplied on line  88  to update finite impulse response (FIR) filter tap coefficients of equalizer  78 . 
     The output of scaler  81  is also supplied to phase decoder  149  on line  87 . Phase slicer  94  slices the signal space constellation to separate the 1 lsb for input on line  142  to derotation vector operator  141 . Derotation vector operator  141  outputs a derotation vector on line  96  which is combined with the constellation in rotator  92  so as to invert or not invert the polarity of the constellation vector. As in the transmitter, phase decoder  149  optionally includes differential phase decoder  147  to decode the 1 lsb if it was differentially encoded in the transmitter. 
     Differential phase decoder  147  develops 1 differential bit in order to recover the 1 lsb of the N bit word. The 1 differential bit is subtracted in subtractor  144  from the output of the phase slicer  94  on line  143  and input to register  151 . 
     Differential phase decoder  147  eliminates the need for a trellis decoder, thus reducing processor cycles. In the absence of differential phase decoder  147 , the 1 lsb is passed through adder  144  on line  143  with nothing subtracted from it, essentially passing it directly to register  151 . 
     Rotator  92  receives the output of scaler  81  on line  82  and the output of derotation vector operator  141  on line  96 . Rotator  92  multiplies the X values from scaler  81  with the derotation vector on line  96  for rotation or polarity inversion into the base constellation subset for input to slicer  97  on line  95 . 
     Slicer  97  performs a mathematical operation in that it masks the axis to slice it. Slicer  97  then multiplies the axis of the constellation by a scale factor, thus forming an index used as an address into a table. The output of the table is an integer less than m where for non-fractional bit encoding, m=2 N−1  and the integer is the (N−1) msb data that was originally transmitted, which is then combined with the decoded lsb from phase decoder  149  in register  151  to form the decoded N bit word, or, in the case of special markers, the N+1 bit word. If fractional rate coding is used then a modulus converter or other method, such as constellation switching or shell mapping is used to convert M integers to the K*N bit data that was originally encoded. 
     The additional symbol, representing the special marker symbol, included in the transmission is supplied in the form of the N+1 bit word by register  151  on line  152  to subtractor  153  where a value of 2 N  on line  154  is subtracted from the N+1 bit word. This output on line  158  is then supplied to marker decoder  156  which will decode the special marker symbol from the received additional symbol. The detection of a special marker symbol is signaled when the value on line  158  is equal to or greater than zero. 
     Now referring to FIG. 5B, if scrambler  32  was employed in transmitter  24 , the original N data bits, which are still scrambled, are supplied to descrambler  99  to be operated on to provide a descrambled N bit word on line  161  to data terminal equipment  103  as is known in the art. Descrambler  99  can be either a self synchronized scrambler or a preset free running scrambler as is known in the art similar to scrambler  32  in transmitter  24 . Descrambler  99  only operates when the value on line  158  is less that zero, i.e., when no special marker symbol was detected. 
     In the receiver, special marker symbols are detected by subtracting a value of 2 N  from the output of slicer  97 . If the result is equal to or greater than zero then a special marker symbol was received and the result is the index of the special marker symbol. 
     Special marker symbols should be chosen with respect to decreasing order of frequency of occurrence. The most common special marker symbol will use the lowest index, which also has the lowest power. This method beneficially reduces overall transmit power. For example, multiple files may be sent before terminating transmission. In this case, the End of File marker would be assigned index  0  (lowest power), and End of Transmission would be assigned index  3  (potentially the highest power index). Start of Message, which precedes transmission can share index  0 . These special marker symbols are passed through the differential encoder or phase bits such that the first 2 markers all have the same power. 
     Referring back to FIG. 1C, shown is a PAM constellation including special marker symbols. Included are two special marker symbols  7 . As can be seen, these special marker symbols are transmitted as extra symbols in an existing linear constellation. 
     It will be apparent to those skilled in the art that many modifications and variations may be made to the preferred embodiments of the present invention, as set forth above, without departing substantially from the principles of the present invention. For example, the constellation and special marker symbols of the present invention are useful in a system that uses trellis coding, and in another alternative embodiment, the equalizer of the present invention can include a decision feedback equalizer. 
     All such modifications and variations are intended to be included herein within the scope of the present invention, as defined in the claims that follow.