Abstract:
A system and method for communicating information using circular multidimensional signal space constellations using uncoded modulation allows increased data rate and bandwidth by eliminating trellis encoding, thus reducing the number of computational cycles required for coding. Furthermore, the use of circular signal space constellations lowers the transmit peak factor, thus consuming less power. Using uncoded modulation with circular constellations allows an approximate 10-20% performance improvement for a given central processor unit. Additionally, circular constellations allow the easy and reliable transmission of special marker symbols such as &#34;End of File&#34;, &#34;Start of Message&#34;, &#34;End of Transmission&#34; or &#34;Increase or Decrease Data Rate&#34;.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims priority to and the benefit of the filing date of copending and commonly assigned provisional application entitled CIRCULAR CONSTELLATIONS FOR UNCODED MODULATION, assigned Ser. No. 60/039,851, and filed Mar. 5, 1997 (Attorney Docket No. 61605-8320) and copending and commonly assigned provisional application entitled CIRCULAR PRECODING AND NONLINEAR ENCODING assigned Ser. No. 60/037,191, and filed Mar. 6, 1997 (Attorney Docket No. 61605-8330) 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 communication using circular constellations with uncoded modulation. 
     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 onedimensional 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, typically both digital data and an analog signal are to be transmitted. The data signal to be transmitted is represented by a sequence of data symbols, where each data symbol is associated with a particular N-dimensional signal point value taken from a signal space. Similarly, the analog signal, which for example can be represented by a voice signal, is processed so that it is mapped into the N-dimensional signal space to provide a voice signal point. This voice signal point defines the magnitude and angle of a voice signal vector about the origin of the signal space. The data symbol and the voice vector are then added together to select a resultant N-dimensional signal point. These N-dimensional signal points are grouped into either square or circular signal space constellations and then transmitted to a far-end modem. 
     Upon reception of the transmitted N-dimensional signal point, the receiver of the far-end modem detects the embedded data symbol and subtracts the data symbol from the received N-dimensional signal point to yield the voice signal vector. This voice signal vector is then used to recreate the voice signal. 
     Because square constellations have a higher peak factor, square constellations typically require more power to transmit a given amount of information than circular constellations. Square constellations also have a greater susceptibility to harmonic distortion. For example, in a 256 point two dimensional circular constellation, the constellation point, or symbol, with the highest power has the x, y coordinates 17, 5 with a peak power of 17 2  +5 2  =314, whereas the highest power point in a square constellation has the x, y coordinates 15, 15 with a peak power Of 15 2  +15 2  =450. As can be seen, the peak power of a circular constellation is 1.6 dB lower than that of a square constellation. 
     The modulation technique used to transmit the signal space constellation can be either coded or uncoded. Coded modulation entails encoding the data signal prior to transmission and decoding the received coded data signal in a receiver. Coded modulation such as coded quadrature amplitude modulation (QAM) as known in the art typically includes various forward error correction (FEC) techniques, such as block coding, convolutional coding and trellis coding. The FEC code acts on a discrete data channel whereby an encoder maps the source data to q-ary code symbols which are modulated and transmitted. During transmission, this signal can be corrupted, causing errors to arise in the demodulated symbol sequence. An FEC decoder attempts to correct these errors and restore the original source data. Trellis coding is presently considered state of the art for coded modulation. Coded modulation, however, consumes power and available bandwidth by requiring additional computational cycles by the system processor to provide the forward error correction code. 
     Previously, circular constellations have been implemented using coded modulation in which trellis coding is employed to reduce the error rate, and square constellations have been implemented using CAP modulation, which uses Tomlinson preceding to reduce the error rate. Transmitting a square constellation increases the peak factor of the transmitted signal, thus causing an increase in power consumption and harmonic distortion. Therefore, it would be beneficial to develop a way in which to transmit a circular signal space constellation in an uncoded modulation environment to maximize processor resources and improve efficiency. 
     SUMMARY OF THE INVENTION 
     Because of the processor resource savings realized by omitting the trellis coding steps, which consume processor cycles, uncoded modulation enables higher data rates, thus making more processor cycles available for the transmission of data. The present invention provides a system and method for modulation in a modem using circular constellations and uncoded modulation. 
     In a preferred embodiment of the present invention, an N bit word is supplied from an ISA bus to a register which separates the N bit word into an N-2 bit word and 2 additional bits. 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-2 bit word is next supplied to a mapper which maps the signal into a multidimensional circular 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. 
     An additional feature of the present invention is the ability to transmit special marker symbols. A marker encoder receives special marker symbols such as &#34;End of File&#34;, &#34;Start of Message&#34;, &#34;End of Transmission&#34;, or &#34;Increase or Decrease Data Rate&#34; and supplies them in the form of an encoded symbol &#34;b&#34;, which is added to a value of 2 N  and supplied to the register along with the N bit word. 
     Next, the signal is operated upon by a phase encoder which is designed to develop a rotation vector using the 2 additional bits supplied by the register. This rotation vector is combined in a rotator with the mapped N-2 bit vector representing the N-2 bit word to form the circular signal space constellation of the present invention and creates a phase rotated signal. Optionally, the phase encoder includes a differential encoder which encodes the 2 additional bits of the N bit word to develop 2 differential bits. These 2 differential bits are added to the 2 additional phase bits 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 uncoded modulation scheme such as uncoded 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 onedimensional 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 circular signal space constellation in a rotator which recovers the mapped N-2 bit vector representing the N-2 bit word. Optionally, the output of the phase slicer is supplied to a differential decoder which develops 2 differential bits in order to recover the 2 additional phase bits of the N bit word. The 2 differential bits are subtracted from the output of the phase slicer and input to 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. 
     If a special marker symbol was included in the transmission, the register supplies the N bit word to a subtractor where a value of 2 N  is subtracted from the N bit word. This output is then supplied to a marker decoder which will separate the special marker symbol from the received N bit word. 
     The multidimensional signal space constellation is then sliced, as is known in the art, in order to recover the mapped N-2 bit word. Lastly, the N-2 bits are combined with the 2 phase bits and, if scrambled, the N bit word is descrambled in order to output an unscrambled 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 uncoded modulation such as uncoded QAM or uncoded 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 enables to use of uncoded modulation, thus reducing processor cycles and improving data speed while requiring reduced processor power. 
     Another advantage of the present invention is that it reduces the transmit peak factor thus reducing susceptibility to harmonic distortion 
     Another advantage of the present invention is that it provides improved shaping gain, thus reducing power required to transmit a given signal (by 0.2 dB.) 
     Another advantage of the present invention is the ability to transmit special marker signals as symbols added to the perimeter of a circular constellation. 
     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. 
     Another advantage of the present invention is that it allows the use of a decision feedback equalizer in a receiver. 
     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. 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; and 
     FIGS. 5A and 5B collectively illustrate a schematic view of the receiver section of the modem of FIG. 3. 
    
    
     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. However, the foregoing software can be stored on any computer-readable medium for use by or in connection with any suitable computer-related system or method. In the context of this document, a computer-readable medium is an electronic, magnetic, optical, or other physical device or means that can contain or store a computer program for use by or in connection with a computer-related system or method. 
     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. 1A. 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. 1B. For simplicity the circular constellation depicted in FIG. 1B contains 64 signal points, 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 uncoded QAM modulation, or uncoded PAM modulation can also benefit from the concepts and features of the present invention. In fact, any uncoded modulation technique can be used. 
     Referring now to FIG. 2, shown is a view illustrating a multipoint communications 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 communications 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 channel 14. Remote location 16 can be a residential, business, or other location served by 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 data using circular constellations with uncoded modulation. While the following preferred embodiment is described with reference to 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 employing the concepts and features of the present invention. Modem 18 contains conventional components as is known in the art of data communications. Central processor 21 controls the operation of the modems&#39; transmitter 30 and receiver through logical interface 23, and contains logic 20 configured to enable transmitter and receiver 40 to communicate using circular signal space constellations and uncoded modulation. The components of the modem connect to communications channel 14 through line interface 22. By employing the concepts and features of the present invention, transmitting a circular constellation in an uncoded modulation scheme reduces the number of computational cycles performed by central processor 21 by 10-20%. This improvement arises from the omission of trellis coding, which consumes valuable processor cycles, and the reduction of the peak factor realized by the implementation of circular signal space constellations, resulting in an approximate 20% data rate increase with a commensurate 20% increase in available bandwidth. 
     With reference to FIG. 4, shown is a preferred embodiment of a transmitter 30 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 an N-2 bit word and 2 additional bits. By employing a circular constellation, 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 61/2 bits. For 63/4 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. 
     Another feature of the present invention is the ability to easily and reliable include the transmission of special marker symbols in the circular signal space constellation. In order to transmit special marker symbols, marker encoder 127 supplies special marker symbols such as &#34;End of File&#34; (EOF), &#34;Start of Message&#34; (SOM) or &#34;End of Transmission&#34; (EOT) in the form of an encoded symbol &#34;b&#34;. The encoded symbol is added in adder 128 to a value of 2 N  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. 
     The resulting N-2 bit word, or N-1 bit word if a special marker symbol is sent, on line 123 is supplied to mapper 34 which maps the N-2 bit word into a multidimensional circular signal space constellation, resulting in a mapped N-2 bit word, represented by a 2-dimensional vector, supplied on line 38 to rotator 41. In the case of the addition of special marker symbol b, the N-2 bit word on line 123 becomes an N-1 word. The N-2 bit word is enlarged by b resulting in the possibility of a word larger than N-2 if b is transmitted. By using a single mapper, the N-2 bit word can expand while still allowing the use of a single mapper table. 
     Next, the 2 additional bits on line 111 are operated upon by phase encoder 37. Phase encoder 37 is designed to develop a rotation vector 114 using the 2 additional bits supplied by the register. This rotation vector is output on line 116 and combined in rotator 41 with the mapped N-2 bit word on line 38 to form a phase rotated signal, thus creating the symmetric circular signal space constellation of the present invention. 
     Optionally, phase encoder 37 includes differential encoder 118 which encodes the 2 additional bits of the N bit word to develop 2 differential bits. These 2 differential bits are output on line 119 and combined with the 2 additional bits from register 122 in adder 112 and become part of the rotation vector 114. 
     Rotator 41 performs vector multiplication on the rotation vector on line 116 and the mapped N-2 bit vector word on line 38 to cause a phase rotation, thus producing the final quadrant symmetric circular signal space constellation of the present invention on line 42. The circular constellation on line 42 is supplied to scaler 43. Scaler 43 multiplies the circular constellation by a scale function of the data rate and supplies a complex number comprising X and Y values on line 47 to TX Hilbert filter 46. The scale function allows a single table to be used to implement the mapper at all data rates. TX Hilbert filter 46 operates on the signal to provide a carrierless amplitude/phase modulation (CAP) modulated signal on line 49 to digital-to-analog converter (DAC) 52. In an alternate embodiment of the present invention, the scaled circular 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 and Y components with the output of scaler 43 for input to TX Hilbert filter 46 which provides a bandpass output at a certain frequency range. The concepts and features of the present invention as claimed can be practiced using either CAP modulation or an uncoded modulation technique such as uncoded QAM or uncoded 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 Hilbert 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 of TX Hilbert filter 46 and DAC 52 are computed at the sample rate, which is typically three times that of the symbol rate. 
     Now referring to FIGS. 5A and 5B collectively, shown is a schematic view of the receiver section 40 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 Hilbert filter 64. The filtered signal is output from RX Hilbert filter 64 on line 69. In the case of uncoded QAM 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 Hilbert 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 and Y components representing the values of the symbols in the circular signal space constellation. 
     The normalized output of scaler 81 is supplied to slicer 84, which performs the inverse operation of mapper 34. 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 the 1/scale factor 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 circular signal space constellation to separate the 2 additional bits 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 circular constellation in rotator 92. As in the transmitter, phase decoder 149 optionally includes differential decoder 147 to decode the 2 additional bits if they were differentially encoded in the transmitter. 
     Differential decoder 147 develops 2 differential bits in order to recover the 2 additional bits of the N bit word. The 2 differential bits are subtracted in subtractor 144 from the output of the phase slicer 94 on line 143 and input to register 151. Differential decoder 147 eliminates the need for a trellis decoder, thus reducing processor cycles. In the absence of differential decoder 147, the 2 additional bits are passed through adder 144 on line 143 with nothing subtracted from them, essentially passing them directly to register 151. While uncoded modulation is more susceptible to errors (by approximately 3 dB) the larger bandwidth made available by the elimination of the trellis coder more than compensates for the 3 dB. For example, by doubling the bandwidth only 1/2 as many bits per symbol need be transmitted, thus N is really N/2 for transmitting the same data rate at double the bandwidth. Using N/2, less than half the number of points (order of 4) in the signal space constellation, i.e. removing 2 bits from N, the constellation is reduced by a factor of four, resulting in a 6 dB noise improvement. Reducing N by 1 is a 3 dB noise improvement. The improvement is realized by increased bandwidth is 3N/2 dB. 
     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 and Y values from scaler 81 with the decoded 2 additional bits for rotation into the base constellation subset for input to slicer 97 on line 93. 
     Slicer 97 performs a mathematical operation in that it masks each axis to slice the axis. Slicer 97 then multiplies one of the axes of the constellation by a scale factor, and then adds the other masked axis value to the result, thus forming an index used as an address into a table known as the eye --  slicer table. The output of the table is an integer less than m where for non-fractional bit encoding, m=2 N-2  and the integer is the N-2 bit data that was originally transmitted, which is then combined with the decoded 2 additional bits from phase decoder 149 in register 151 to form the decoded N 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-2) bit data that was originally encoded. 
     If a special marker symbol was included in the transmission, register 151 supplies the N+1 bit word on line 152 to subtractor 153 where a value of 2 N  is subtracted from the N+1 bit word. This output is then supplied to marker decoder 156 which will separate the special marker symbol from the received N+1 word. 
     If scrambler 32 was employed in transmitter 30, the N-2 bit word and the 2 additional 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 30. 
     Another aspect of using circular constellations with uncoded modulation as disclosed herein is the ability to easily and reliably transmit special marker symbols such as End of File, Start of Message and End of Transmission. These special marker symbols are signal points added to the circular signal space constellation. 
     Square constellations, such as that illustrated in FIG. 1A encode exactly N bits in a constellation with 2 N  points. This eliminates the possibility for transmitting any additional symbols. For example, the Tomlinson precoder used in CAP modulation requires square constellations to achieve the precoder modulo operation. Transmission of (1+2 N ) symbols would require a larger modulo, thus increasing the peak factor and dither power loss. 
     Using circular constellations, as disclosed herein and illustrated in FIG. 1B, to transmit B additional special marker symbols requires a constellation with exactly (B+2 N ) points. Special marker symbol 7 is illustrated in FIG. 1B as an End of File symbol, however any special marker symbol can be transmitted. 
     For normal data encoding the encoder uses the N-bit data word on line 31 as an index into the encoder table txencod shown in the program hereinafter set out in detail in appendix A. For any special marker symbol the same table is used and the symbol b is encoded using the index (b+2 N ) where b is any integer between 0 and (B-1) allowing for exactly B special marker symbols. For differential encoding by differential phase encoder 118 the N-bit data word is partitioned into an (N-2) bit index into the table for the coordinates of the subset constellation point and the 2 least significant bits are differentially encoded and define the rotation 0, 90, 180, or 270 degrees to be applied to the subset constellation. Then, for any special marker symbol b, the index into the table is (b/4+2.sup.(N-2)) to identify the subset point which is then rotated by the last state of differential phase encoder 118. The special marker symbols could also be used to drive phase encoder 37. For each set k of 4 or fewer special marker symbols, the subset index is 2.sup.(N-2) where k defines the rotation and is any integer 0, 1, 2, or 3. 
     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 by 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), Start of Message would be assigned index 1, and End of Transmission would be assigned index 2 (highest power index). These special marker symbols may also be passed through the differential encoder or phase bits such that the first 4 markers all have the same power. 
     Referring back to FIG. 1B, shown is a circular constellation including special marker symbols. Included are 4 special marker symbols 7. As can be seen, these special marker symbols are transmitted as extra symbols in an existing circular constellation. 
     Set out in detail hereinafter in Appendix A is the program that defines the operation of the present invention. 
     It will be obvious 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 circular constellation and special marker symbols of the present invention are useful in a system that uses trellis coding, and in another alternative, 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. 
     Hereinafter set out in Appendix A is the program that defines the operation of the present invention. 
     
                                           APPENDIX A__________________________________________________________________________Routines to:  1. Initialize modem for transmitting BITS per symbol.  2. Independently sequence and control transmitter and receiver.  3. Control initial training, holdover for polling and polling.  4. Self synchronized scramble/descramble data.  5. Differentially encode/decode constellation.  6. Send and detect specail EOF control signals.  7. Detect active signals and loss of signal.  8. Automatically compensate for 0x0100 dc offset in Tiger CODEC.12/18/96  9. Loopback (LB) is active here &amp; ram init.asm.  10. Kurt&#39;s routines SIM.sub.-- TRAIN ifdef &amp; Equalizer tap preset fordig. loop included  11. 1/2/97 added agc.sub.-- gain preset for digital loop, removedDELAYfrom Tx Seq.  12. Digital loopback now completely controled by SIM.sub.-- TRAIN nochange to ram init.   For the software simulator then also enable asm(&#34; trap20&#34;) in main loop.  13. Send 16000 Hz tone then Phase Reversal &amp; detect for initialtraining.  14. trap 20 NOT active for BTUD sim*****************************************************************************/#define SIMONLY 0 /* 1 FOR SIMULATOR, 0 FOR HARDWARE, not required withSIM TRAIN */#define BITS 8 /* note range 3 to 10 max table 453x4 below */   /* less than 7 requires L$$SRS from rts.lib, -i./ opt. */#define MAXPACKET 1532*8/BITS /* max without header &amp; crc */#define SLICE.sub.-- BITS 8   /* Bits used in slicer */#define SLiCE.sub.-- MAG (1&lt;&lt;SLICE.sub.-- BITS) /* Error free margin is+- SLICE.sub.-- MAG-1*/#define EQ.sub.-- LENGTH 30   /* !!! defined in RAM.ASM as well !! */#define TRNDELAY (EQ.sub.-- LENGTH/3)-DELAY-1  /* Training delay forcentertap */  /* Comment next line out to removeSIM.sub.-- TRAIN mode(for hardware) *//*#define SIM.sub.-- TRAIN 1 /* for short forced train to speed upsimulation*/#ifdef SIM.sub.-- TRAIN  #define DELAY 9 /* DELAY = 9 to use hardware loopback (LB) inRAM.sub.-- INIT.ASM */  #define ST 4    /* Length of initial silent period */  #define TT 20    /* Length of initial tone */ #define CORRDETIME 1 /* Number of successive symbols for tone detectcorrelator */  #define TRNTIME 8 #define TRNHITIME 2#else  #define DELAY 23 /* Tx to Rx Throughput delay for center tap */  #define ST 16000 /* Length of initial silent period */  #define TT 32000 /* Length of initial tone */ #define CORRDETIME 0x80 /* Number of successive symbols for tonedetect correlator */  #define TRNTIME 32000 #define TRNHITIME 100#endif #define TRNLOTIME (TRNTIME-TRNHITIME)/************** EXTERNAL FUNCTIONS AND VARIABLES*************************/extern void baudtiming();extern void constellation();extern void start();  /* variables in asm are .sub.-- eq.sub.-- xout,.sub.-- eq.sub.--yout,.sub.-- eq.sub.-- xerror,.sub.-- eq.sub.-- yerror;*/extern int eq.sub.-- xout,eq.sub.-- yout,eq.sub.-- xerror,eq.sub.--yerror;extern long eq.sub.-- xcoef,eq.sub.-- ycoef;extern int eye.sub.-- slicer[],txencod[];extern int agc.sub.-- beta;extern long dc.sub.-- offset; /* double precision dc offset compensationforADC */extern long agc.sub.-- gain;extern long rcv.sub.-- lvl;extern int *rcv.sub.-- ptr,*xmt.sub.-- ptr,xmt.sub.-- out;extern int corrout;   /*tone detector correlator output */extern int CntrTrib;  /* Control=0, Tributary=1 */extern void init.sub.-- interface(void); /* Host/HPI Initializationroutine */extern void check.sub.-- interface(void); /* Host/HPI Interface routine*//************** FUCTION PROTOTYPES DEFINED HERE IN C********************/void eqinit(void);       /* Equalizer initialization, also instart.asm */void txencode(void);     /* Transmit data mode encoder */void rxdecode(void);     /* Receiver data mode decoder */void rxfreeze(void);     /* Receiver freeze mode decoder */void (*txptr) (void);     /* Pointer for transmitter indirect functioncall */void (*rxptr) (void);     /* Pointer for receiver indirect function call*//************** GLOBAL VARIABLES, DEFINED HERE IN C********************/int bitsperbaud,eyesize,bitmask,rxscale,txscaie;int intflag;       /* for hardware interrupts */int x,y;    /* complex transmit symbol */int ttxd,txd,rxd;int subset,eyeclosure;     /* used to detect loss of signal */int xerror,yerror,peakerrortmp,peakerror,errorcnt; /* diagnosticvariables */int twosecblocks,pollcount,errorfree2sec;             /* Counter for 2 secondblocks, polls */int sparecyclecnt,sparecycles;             /* Counter for spare cyclesper symbol */int txphasebits,oldifencode,oldifdecode,rxphasebits; /* VARIABLES */long int scram,descram,tmp;int seqcntr,seqstate,seqtxcntr,seqrxcntr;    /* sequence statecounter */int eq.sub.-- beta;int corrcnt;int retraincount, retrainflag;/******************** Baud timing variables defined next *********/extern intiphaseReference[];const int*iphaseRefPtr;int  iPhaseError,iPeakPhaseError=0;long intlBPFilter,1Freqoffset,1FreqOffsetLock, 1LoopIntegrator;/*****************Rx &amp; Tx Power Scale Table ******************//* Net is rxscale*txscale = 2**25 expecting Tx scale of &lt;&lt;5 *//* FRCT=1: t *= txscale/2**15, r *= rxcale/2**15, net *= 2**(-5) *//* Expected left shift 5 in the transmitter for unity tx*rx gain *//* Note the 2 bits/baud training uses SLICE MAG&lt;&lt;2 which is 4X larger *//* Error below is for average, not all constellation points */const int rxtxscale[24] = {/* rxsci    txsci RMS  ERROR */3206,    10464,   /*     1.000,          0.00020,               1 subset,                      2 bits/baud(x&lt;&lt;2) */1388,    24167,   /*     3.000,          0.00032,               2 subset,                      3 bits/baud */1792,    18720,   /*     5.000,          0.00024,               4 subset,                      4 bits/baud */2534,    13237,   /*     10.000,          0.00035,               8 subset,                      5 bits/baud */3629,    9245,   /*     20.500,          0.00013,               16 subset,                      6 bits/baud */5124,    6547,   /*     40.875,          0.00023,               32 subset,                      7 bits/baud */7231,    4640,   /*     81.375,          0.00008,               64 subset,                      8 bits/baud */10237,    3277,   /*     163.094,          0.00023,               128 subset,                      9 bits/baud */14470,    2318,   /*     325.891,          0.00039,               256 subset,                     10 bits/baud */20467,    1639,   /*     651.969,          0.00027,               512 subset,                     11 bits/baud */28944,    1159,   /*     1303.797,          0.00025,               1024 subset,                     12 bits/baud */-24603,    819,   /*     2607.570,          1.60051,               2048 subset,                     13 bits/baud */} /* END of rxtxscale *//*========================================================================*//*   differential encoder/decoder tables *//* input lookup is y2n y1n y2n-1 y1n-1*//* output is q2n q1n*//*========================================================================*//*differential encoder tables*//* input lookup is q2n q1n y2n-1 y1n-1*//* output is y2n y1n*/const int difc[16] = { /* coded table*/0,  1, 2,   3,1,  2, 3,   0,2,  3, 0,   1,3,  0, 1,   2,} ;/* differential decoder tables *//* input lookup is y2n y1n y2n-1 y1n-1*//* output is q2n q1n*/const int decc[16] = { /* coded table*/0,  3, 2,   1,1,  0, 3,   2,2,  1, 0,   3,3,  2, 1,   0,} ;********************** SUBROUTINES ***********************************//************* SIMPLE UNCODED DIFFERENTIAL ENCODE AND ROTATE**************/void differential.sub.-- rotate(int input,  /* input 2 dif encode bits */int *x,  /* input subset x, output full constellation */int *y)  /* input subset y, output full constellation */{   /* differential encoder input I2,I1 */  int i, temp;  i = oldifencode = difc[((input&amp;0x3)&lt;&lt;2)|oldifencode] ;  while(i!=0) {     /* rotate constellation -90i deg*/   temp = *x ; *x = *y ; *y = - temp   --i ;   }  /* printf(&#34;\ninput %d, %x,%x &#34;,input,*x,*y); getch(); */}/*********** SIMPLE UNCODED DIFFERENTIAL DECODE AND DE-ROTATE**************/const int derotate.sub.-- tb1[4] = { 0, 1, 3, 2 };void differential derotate( /* DECODE FULL CONSTELLATION BACK TO SUBSET*/  int *x,  /* Rx x component */  int *y ) /* Rx y component, both to be rotated to subset */{  int phase,xi,yi,temp ;  xi = *x ; yi = *y ;   /* slice x and y */  xi = (xi&gt;&gt;(SLICE.sub.-- BITS+1)) &amp; 0x1 ; /* get second bit forrotation*/  yi = (yi&gt;&gt;(SLICE.sub.-- BITS+1)) &amp; 0x1  phase = derotate.sub.-- tb1[(xi&lt;&lt;1) + yi] ;  /* get rotation */  rxphasebits = decc[((phase)&lt;&lt;2)|oldifdecode] ; /*differentialdecode */  oldifdecode = phase ;  while(phase!=0) {   /* rotate constellation +90i deg */   temp = *x ; *x = - *y ; *y = temp   --phase ;   }  /* printf(&#34;\n rotate diff %d %x,%x &#34;,rxphasebits,*x,*y);getch();*/}const long iEqXForced[] = { 0x00298BE2, 0xFFFFCBA8, 0x02BC44FC, 0x000077EE, 0x03269536,0x0004C49A, 0x00547D1C, 0x0003589E, 0xF7A92566, 0x000394D4, 0xE76545D0,0x00074352, 0xD5A0A0AE, 0xFFFF55A8, 0x738D897E, 0x0001D7B4, 0xD5A0AA90,0x00048A66, 0xE765ECA0, 0x0000D418, 0xF7A90EA4, 0x0002E9B6, 0x005344CC,0x00033078, 0x032B1006, 0x0001851C, 0x02B9B79E, 0x000072BC, 0x00255592,0x000214AE};const long 1EqYForced[] = { 0xFFF9AC02, 0x00DE73F0, 0xFFE9B29C, 0xFDE72DF2, 0xFFDE8F72,0xF9DA7214, 0xFFDF1876, 0xF59BCA5C, 0xFFE9FBAC, 0xF54A34B6, 0xFFFC3F78,0x06D29B46, 0x000470B8, 0x5E0F1838, 0x000BFE5A, 0XA1C1E802, 0x0015FC2C,0xF976959A, 0xFFFB1B9C, 0x0B68E51E, 0xFFC6BAA8, 0x0AC24398, 0xFF990AE2,0x058BF810, 0xFF98E9AE, 0x00ABE4E6, 0xFFB4B2FC, 0xFD942830, 0xFFEAE72A,0xFEEF0822void vInstantTrain(void){  int  i;  long *plXCoef = &amp;eq.sub.-- xcoef,  *plYCoef = &amp;eq ycoef;  const long  *plInitX = 1EqXForced,  *plInitY = lEqYForced; rcv.sub.-- ptr = xmt.sub.-- ptr; for (i=0; i&lt;EQ.sub.-- LENGTH; i++) {  *plXCoef++ = *plInitX++;  *plYCoef++ = *plInitY++; } agc gain = 0x498000; /* preset agc for digital loop level */  rcv.sub.-- lvl = 0x6000000; agc.sub.-- beta = 0;     /* lock agc */}void eqinit(void) {#ifndef SIM.sub.-- TRAIN  int i;  long *xptr,*yptr;  xptr = &amp;eq.sub.-- xcoef; yptr = &amp;eq.sub.-- ycoef;  for(i=0;i&lt;EQ.sub.-- LENGTH;++i)   *xptr++ = 0x8000;  }  i = EQ.sub.-- LENGTH  while(i--) {   *yptr++ = 0x8000;  }  xptr = &amp;eq.sub.-- xcoef + EQ.sub.-- LENGTH - DELAY*3;  yptr = &amp;eq.sub.-- ycoef + EQ.sub.-- LENGTH - DELAY*3;  if(SIMONLY) {   /* Preset the equalizer for the simulator*/   *xptr++ = 0x40008000; *yptr++ = 0x40008000;   *xptr++ = 0x40008000; *yptr++ = 0xc0008000;   }#endif}/************* CONTROL SEQUENCER and TABLES FOR MODE TRAININGtypedef struct {  int cnt;   /* New sequence state count */  void (*csptr) (void);      /* Pointer to change state routine */  void (*ptr) (void);        /* Pointer for steady state indirectfunction call */} seqtable;seqtable *seqtxtblptr; /* Pointer for tx sequencer indirect functiontable */seqtable *seqtxdataptr; /* Pointer for recall of seqtxtblptr for datamode */seqtable *seqrxtblptr; /* Pointer for rx sequencer indirect functiontable */seqtable *seqrxbase,*seqtxbase; /* Pointer to recall retrain address*//******************** STEADY STATE TRANSMIT MODULATION ROUTINES***************/void txencode(void) {  static int i;/*  i++; txd = i&amp;bitmask ; */  txd = bitmask ;   /* TEST DATA, TRANSMIT MARKS *//*** Byte wise SCBAMBLER, shift input left, x23   x18 ****//*** Note: scrambler uses constant BITS to avoid RTS.LIB low speed ***/  tmp = ( scram&gt;&gt;(18-BITS) ) ( scram&gt;&gt;(23-BITS) )   txd ;  scram = (scram&lt;&lt;BITS ) | bitmask&amp;tmp;  ttxd = bitmask&amp;scram; /* ttxd is the scrambled data *//***** DEBUG code below can be used to send single tones at plus 3 dB*****/     /**************************       bitmask 0 = 4000 Hz and 20000Hz       bitmask 1 = 8000 Hz ( and24000 Hz at -31 dB)       bitmask 2 = 12000 Hz       bitmask 3 = 16000 Hz     **************************//** ttxd = bitmask 0x1; **//*** Next differential phase encode and map x,y outputs */  txphasebits = ttxd&amp;3;  ttxd = ttxd&gt;&gt;2;   /* note this can combine with [] below */  x = txencod[ttxd&lt;&lt;1]*SLICE.sub.-- MAG;/* scale encoder for 2*SLICB.sub.-- MAG-1 margin */  y = txencod[(ttxd&lt;&lt;1)+1]*SLICE.sub.-- MAG;  differential rotate (txphasebits,&amp;x,&amp;y);} /* End txencode */void txsilent(void) {   /* Transmit silence */  x = 0;  y = 0;void tx16000(void) {  x = SLICE.sub.-- MAG&lt;&lt;2;  y = SLICE.sub.-- MAG&lt;&lt;2;/***** Pick code below to send single tones at plus 3 dB *****/     /**************************       bitmask 0 = 4000 Hz and 20000Hz       bitmask 1 = 8000 Hz ( and24000 Hz at -31 dB)       bitmask 2 = 12000 Hz       bitmask 3 = 16000 Hz       3 = 4000 Hz and 20000 Hz       2 = 8000 Hz ( and 24000 Hzat -31 dB)       1 = 12000 Hz       0 = 16000 Hz     **************************//*** Next differential phase encode and map x,y outputs */  differential.sub.-- rotate(0,&amp;x,&amp;y);} /* End tx16000 */void txtrain(void) {   /* Transmit train mode encoder */  int i,temp;  /* force train 4-phase until count expires */  tmp = (scram&gt;&gt;(18-2) ) (scram&gt;&gt;(23-2) )   0x3  scram = ( scram&lt;&lt;2 ) | ( 0x3 &amp; tmp );  i = txd = 0x3 &amp; scram; /* i is the scrambled data */      /*** Next phase encode and mapx,y outputs ***/  x = SLICE.sub.-- MAG&lt;&lt;2;  y = SLICE.sub.-- MAG&lt;&lt;2;  while(i!=0) {   /* rotate constellation -90i deg*/   temp = x ; x = y ; y = - temp ;   --i   }}void txEOF(void) {  ttxd = eyesize ;  /* TRANSMIT EOF SIGNAL *//*** Next differential phase encode and map x,y outputs */  txphasebits = ttxd&amp;3;  ttxd = ttxd&gt;&gt;2;  /* note this can combine with [] below */  x = txencod[ttxd&lt;&lt;1]*SLICE.sub.-- MAG;  /* scale encoder for 2*SLICE.sub.-- MAG-1 margin */  y = txencod[(ttxd&lt;&lt;1)+1]*SLICE.sub.-- MAG;  differential.sub.-- rotate(txphasebits,&amp;x,&amp;y); /*WARNING, shouldfreezediff encoder */} */ end txEOF *//******************** STEADY STATE RECEIVE DEMODULATION ROUTINES**************/void rxdecode(void) { /* Receiver data mode decoder */  int xi,yi,xri,yri,mask,slice;  mask = -(SLICE.sub.-- MAG&lt;&lt;2)  xi = eq.sub.-- xout;  yi = eq.sub.-- yout;geterror:    /* FIRST SLICE FULL CONSTELLATION FOR ERROR */  xri = (xi &amp; (mask&gt;&gt;1)) + SLICE.sub.-- MAG ;  /* ideal x */  yri = (yi &amp; (mask&gt;&gt;1)) + SLICE.sub.-- MAG ;  /* ideal y */  xerror = xri-eq.sub.-- xout;     /* compute error*/  eq.sub.-- xerror = (xerror+(1&lt;&lt;(eq.sub.-- beta-1)))&gt;&gt;eq.sub.-- beta; /*round &amp; scaleerror for Beta */  if(abs(xerror)&gt;peakerrortmp) peakerrortmp = abs(xerror); /* findpeak */  yerror = yri-eq.sub.-- yout;     /* compute error*/  eq.sub.-- yerror = (yerror+(1&lt;&lt;(eq.sub.-- beta-1)))&gt;&gt;eq.sub.-- beta; /*round &amp; scaleerror for Beta */  if(abs(yerror)&gt;peakerrortmp) peakerrortmp = abs(yerror); /* findpeak *//**** eq.sub.-- xerror = 0; eq.sub.-- yerror = 0; /*** FREEZE &amp; LOCKEQUALIZER TEST***/  differential.sub.-- derotate(&amp;xi,&amp;yi) ; /* slice and counter rotate *//* NEXT SLICE SUBSET CONSTELLATION */  xri = ((xi+SLICE.sub.-- MAG) &amp; mask) + SLICE.sub.-- MAG ; /* ideal x*/  yri = ((yi+SLICE.sub.-- MAG) &amp; mask) + SLICE.sub.-- MAG ; /* ideal y*/  slice = (xri&gt;&gt;(SLICE.sub.-- BITS+2)) - 24*(yri&gt;&gt;(SLICE.sub.-- BITS+2));  slice = slice + ((11*24(+12);  subset = eye slicer[slice]; /* DECODED DATA */  rxd = subset&lt;&lt;2;  rxd += rxphasebits;  /* GET DIFFERENTIAL PHASE DECODED BITS */  if(rxd&lt;eyesize) { /* run scrambler only if rxd&lt;eyesize */   /* Byte wise DESCRAMBLER, shift input left, x23   x18, firstget parity */   tmp = ( descram&gt;&gt;(18-BITS) )   ( descram&gt;&gt;(23-BITS) );   descram = ( descram&lt;&lt; BITS ) | rxd ;   rxd = bitmask &amp; ( rxd   tmp ) ; /* descram out fromdescram LSB */   if(rxd!=bitmask) {   /* test for errors, expect allmarks */    if (errorcnt&lt;32767) ++errorcnt;    } /* end error count if */   if( (!subset)   /* if smallest subset point, testfor closed eye */    &amp;( (abs(eq.sub.-- xout) + abs(eq.sub.-- yout) )&lt;(SLICE.sub.--MAG&gt;&gt;1)) ){if(!(--eyeclosure)) { /* decrement eyeclosure counter */ ++seqrxtblptr;   /* if zero,advance to freeze Rx state */ seqrxcntr = 1; rxptr = rxfreeze; }}   else eyeclosure = 10;  /* reset counter, require 10successive closed bauds */   }  /* end of rxd&lt;eyesize */  else {       /* EOF was detected */   ++seqrxtblptr;     /* advance to freeze Rx state, &amp;scrambler */   seqrxcntr = 1;   rxptr = rxfreeze;} /* end rxdecode */void rxidle (void) {  eq.sub.-- xerror = 0;  /* clear error */  eq.sub.-- yerror = 0;}void rxtrain(void) {   /* Receiver train mode decoder */  int i,temp,x,y;  /* force train 4-phase until count expires */  tmp = (descram&gt;&gt;(18-2) ) (descram&gt;&gt;(23-2) )   0x3 ;  descram = ( descram&lt;&lt;2 ) | ( 0x3 &amp; tmp );  i = rxd = 0x3 &amp; descram;    /* i is the scrambled data */  x = SLICE.sub.-- MAG&lt;&lt;2;  y = SLICE.sub.-- MAG&lt;&lt;2;  while(i!=0) {     /* rotate constellation -90i deg*/   temp = x ; x = y ; y = - temp   --i ;   }  eq.sub.-- xerror = -((eq.sub.-- xout&lt;&lt;0)-x)&gt;&gt;eq.sub.-- beta; /* scaleerror for Beta*/  eq.sub.-- yerror = -((eq.sub.-- yout&lt;&lt;0)-y)&gt;&gt;eq.sub.-- beta;}void rxfreeze(void) { /* Receiver freeze mode decoder */  int xi,yi,xri,yri,mask,slice,savephase;  if(peakerror&gt;=(SLICE.sub.-- MAG-30)) {/*   seqtxtblptr = seqtxbase;  /* Force Tx to send retrain aswell *//*  seqtxcntr = 1; */   retrainflag = 1;   }  mask = -(SLICE.sub.-- MAG&lt;&lt;2)  xi = eq.sub.-- xout;  yi = eq.sub.-- yout;  eq.sub.-- xerror = 0;  /* clear error */  eq.sub.-- yerror = 0;  savephase = oldifdecode;     /* save differentialphase while no signal */  differential.sub.-- derotate(&amp;xi,&amp;yi) ; /* slice and counter rotate */    /* NEXT SLICE SUBSET CONSTELLATION */  xri = ((xi+SLICE.sub.-- MAG) &amp; mask) + SLICE.sub.-- MAG ; /* ideal x*/  yri = ((yi+SLICE.sub.-- MAG) &amp; mask) + SLICE.sub.-- MAG ; /* ideal y*/  slice = (xri&gt;&gt;(SLICE.sub.-- BITS+2)) - 24*(yri&gt;&gt;(SLICE.sub.-- BITS+2));  slice = slice + ((11*24)+12) ;  rxd = eye.sub.-- slicer[slice]&lt;&lt;2 ; /* DECODED DATA */  rxd += rxphasebits;   /* GET DIFFERENTIAL PHASE DECODEDBITS */  if(rxd&lt;(eyesize&gt;&gt;1)) {  /* freeze while rxd&lt;eyesize/2, fordropout recovery */   oldifdecode = savephase;   if(!errorcnt) errorfree2sec=twosecblocks; /* count errorfree seconds */   }  else {   seqrxtbiptr-=2;   /* return to normal Rx data state */   seqrxcntr = 1;   ++pollcount;     /* count polls */   rxptr = rxdecode;/*  peakerror = peakerrortmp; /* copy 2 second peak error *//*  peakerrortmp = 0;   /* clear temporary peak error*/   }} /* end rxfreeze */void rxtonedet(void) { /* Receiver tone detector *//* lFreqOffset = lFreqOffsetLock; /* Hold during silence *//* dc.sub.-- offset = 0; */  if(rcv.sub.-- lvl &gt; 0x1000000)  if(corrout&gt;0x1000) { /* Test tone detector correlator output */   if(++corrcnt&gt;CORRDETIME) {    agc.sub.-- beta = 0x600; /* Wait for tone to set AGC */    #ifdef SIM.sub.-- TRAINagc.sub.-- beta = 0;  /* Lock for simulator */    #endif    seqrxcntr = 1;  /* set counter to 1, end this stateon next symbol */    ++seqrxtblptr;  /* advance pointer to detect end oftone */    }  }  else corrcnt = 0;}void rxprevdet(void) { /* Receiver phase reversal detector */  if(corrout&lt;0) {   /* Test tone detector output for phasereversal */   seqrxcntr = 1;  /* set counter to 1, end this state onnext symbol */  }}/************* TX State Transition Routines *************/void stxinit(void) {    scram = 0;    oldifencode = 0;    txscale = rxtxscale[1]; /* scale for 4 point train */}void stxprev(void) {    oldifencode += 2;   /* 180 degree phase reversal*/    oldifencode &amp;= 0x3;    /* mask result */}void stxtodata(void) {    retrainflag = 0;   /* end of train, clear flag */    txscale = rxtxscale[1+((bitsperbaud-2)&lt;&lt;1)];    seqtxdataptr = seqtxtbiptr; /* save pointer forreturn to data mode */}void stxdata(void) {   if(retrainflag) {    seqtxtbiptr = seqtxbase; /* restart full training */    seqtxcntr = 1;    }   else seqtxtbiptr = seqtxdataptr+1; /* restore pointer,return to data mode */}         /* +1 to skip stxtodataseqtxcntr reload */void stxrepeat(void) {    --seqtxtblptr;    /* Decrement pointer tolock in this state */}void stxend(void) {  seqtxcntr = 16;    /* reload sequence counter */  --seqtxtblptr;    /* lock pointer at end of table */}/************* RX State Transition Routines **************/void srxeqinit(void) {    eq.sub.-- beta = 2;   /* agc.sub.-- beta = 0x600; /** Removed, too much gain on BTUDpilot **/    descram = 0;    oldifdecode = 0;    rxscale = rxtxscale[0]; /* scale for 4 point train */    eqinit();    corrout = 0;    corrcnt = 0;}void srxbetal(void) {    agc.sub.-- beta = 0;    eq.sub.-- beta = 6;}void srxscale(void) {    rxscale = rxtxscale[(bitsperbaud-2)&lt;&lt;1]; /* set nextbaud eq scale */    agc.sub.-- beta = 0;}void srxtodata(void) { sparecycles = 32767; /* initialize minimum spare cycle count */    errorcnt = 0;    /* clear error count */    peakerror = 0;    /* clear peak error */    peakerrortmp = 0;   /* clear temporary peak error*/    twosecblocks = 0;    /* Clear 2 second blockcounter */}void srx2sec(void) {    eq.sub.-- beta = 5;     /* equalizer */    peakerror = peakerrortmp;  /* copy 2 second peakerror *//*   peakerrortmp = 0;    /* clear temporary peakerror */    --seqrxtbiptr;      /* Decrementpointer to lock in this state */    ++twosecblocks;      /* Count 2 secondblocks */}void srxretrain(void) {  lFreqOffsetLock = lFreqoffset; /* Hold during silence */  seqrxtbiptr=seqrxbase;   /* Point to initial start-up state*/  seqrxcntr = 1;/* seqtxtbiptr = seqtxbase;  /* Force Tx to send retrain as well*//* seqtxcntr = 1; */  retrainflag = 1;   /* set flag, force Tx to return retrain */  ++retraincount;}void srxtone(void) {  retrainflag = 1;   /* No tone for 2 sec, set retrain flag *//* lFreqoffsetLock = lFreqoffset; /* Hold during silence *//* seqrxtblptr=seqrxbase; /* went too far back to Continue initialstart-up state *//* seqrxcntr= 1; */  /* this would clear corrcnt when srxeqinitran */  --seqrxtblptr;      /* Continue initial start-up state*/  agc.sub.-- beta = 0x600;     /* Release AGC */void srxrepeat(void) {    eq.sub.-- beta = 5;      /* equalizer */    --seqrxtblptr;      /* Decrementpointer to lock in this state */}void srxend(void) {  seqrxcntr = 16; /* reload sequence counter */  --seqrxtbiptr;    /* lock pointer at end of table */void seqnop(void) {/************* CONTROL SEQUENCER TABLES FOR MODEN TRAINING*************/ /*** The count is pre-decremented,the count is ***/ /*** the true number of symbols forthe state. ***/seqtable seqtx[] = {/** COUNT, CHANGE STATE, STEADY STATE **/{   ST,       stxinit,               txsilent                    },                      /* SendSilence */{   TT,       seqnop, tx16000 },/* Send Tone */{   8,        stxprev,               tx1600 }, /*Send Phase Reversal in Tone */{   TRNTIME,     stxinit,            txtrain },                      /* for now,2 second training */{   1,        stxtodata,               txencode                    },{   32000,    seqnop, txencode                      }, /*normal data mode */{   1,        seqnop, txEOF                      }, /*send EOF signal, freeze data */{   DELAY,    seqnop, txsilent                      }, /*send silence, freeze data */{   1,        seqnop, txEOF                      }, /*send EOF signal, return to data */{   MAXPACKET, stxdata,            txencode                 }, /* return to datamode */{   32000,    seqnop, txencode                      },{   32000,    stxrepeat,               txencode                    },{   1,        stxend, txencode                      }  /*Reset ptr, prevent leaving table! */} ;seqtable seqrx[] = {/** COUNT, CHANSE STATE, STEADY STATE **/{   32000,    srxeqinit,               rxtonedet                    },                      /* WaitDELAY + silence time */{   32000,    srxtone,               rxtonedet                    , /* Wait fortone */{   CORRDETIME, seqnop,               rxidie }, /*Wait for agc to settle */{   TT,       seqnop, rxprevdet                      }, /*Wait DELAY + silence time */{   8+2,  seqnop,   rxidle }, /*Wait for 8 prev&#39;s &amp; center tap */{   TRNLOTIME, seqnop,               rxtrain                      }, /*Train Equalizer */{   TRNHITIME-1,srxbetal,            rxtrain },                      /* ChangeEqualizer Beta */{   1,        srxscale,               rxtrain                      },{   32090,    srxtodata,               rxdecode                    },                      /* normal Rxdata mode */{   MAXPACKET-99,srx2sec,            rxdecode                 }, /* repeat datamode, measure error/* rxdecode will detect EOF and advance to the freeze state */{   8000, seqnop,   rxfreeze                    },                      /* repeatfreeze mode, until EOF */{   1,        srxretrain,               rxfreeze                    },                      /* after .25sec silence, retrain */{   1,        srxend,                rxdecode                      }  /*Reset ptr, prevent leaving table! */} ;/************* END OF CONTROL SEQUENCER TABLES*************************//******************* BEGIN MAIN PROGRAM********************************/void main() {  int i=0,ttxd,xi,yi,xri,yri,mask,slice; start();#ifdef SIM.sub.-- TRAIN vInstantTrain();#endif/************* Initialize Control Sequencers *************/ seqtxtblptr = seqtxbase = seqtx-1; /* initialize seqencer pointer totable base */ seqtxcntr = 1; /* execute first state one symbol time */ seqrxtblptr = seqrxbase = seqrx-1; /* initialize seqencer pointer totable base */ seqrxcntr = 1; /* execute first state one symbol time */ txptr = txencode;  /* set normal data mode */ rxptr = rxdecode;/************ Initialize Baud Timing *************/ iphaseRefptr      = &amp;iPhaseReference[0]; /* Initialize BaudTiming */ iPhaseError      = 0; lBPFilter = 0; lFreqOffset      = 0; lFreqOffsetLock = 0; lLoopIntegrator      = 0;/************* Initialize Data Variables *************/ intflag = 0;   /* for hardware interrrupts */ bitsperbaud = BITS; eyesize = 1&lt;&lt;bitsperbaud; bitmask = eyesize -1; rxscale = rxtxscale[(bitsperbaud-2)&lt;&lt;1]; txscale = rxtxscale[1+((bitsperbaud-2)&lt;&lt;1)]; dc.sub.-- offset = 0;   /* double precision dc offset compensation forADC */ eq.sub.-- beta = 6; pollcount = 0;   /* clear poll counter */ retraincount = 0; twosecblocks = 0;   /* clear count of 2 sec blocks of actualRx data */ errorfree2sec = 0;  /* store twosecblocks here until first error */ sparecycles = 32767; /* initialize minimum spare cycle count */ /* PUT CALL TO HPI.sub.-- DP INTERFACE INITIALIZATION FUNCTION HERE JQC*/#ifndef SIM TRAIN init.sub.-- interface();#endif   /* also, initialized in srxtodata toskip init time */while (1) {  /* continuous loop */    /* PUT CALL TO HPI.sub.-- DP HERE JQC */#ifndef SIM.sub.-- TRAIN   check.sub.-- interface ();#endif/*********** GENERATE 3 INTERRUPT SAMPLES, EQ RUNS WITH tx.sub.-- hil*****/  if(SIMONLY) {  asm(&#34; trap  20&#34;);    }/********** CODE ASOVE FOR SIMULATOR, BELOW FOR HARDWARE **********/  else {#ifdef SIM.sub.-- TRAIN/*******/ asm(&#34; trap  20&#34;); /******** NEEDED FOR TI EVM BOARD FOR INTERRUPT***/#endif    sparecyclecnt = 0;  while(!intflag) sparecyclecnt+=10; /* Count spare cycles persymbol. */    /* 40,000/16 = 2500 cycles persymbol. */    /* Each count is 10 cycles inwait loop. */  if (sparecyclecnt&lt;sparecycles) sparecycles=sparecyclecnt;  intflag=0;    }/************** ABOVE FOR HARDWARE INTERRUPTS ***************/  baudtiming();  if(iPhaseError&lt;iPeakPhaseError) iPeakPhaseError=iPhaseError;/*********** NEW TX SEQUENCE CONTROLLER *********************/  if(!(--seqtxcntr))  /* if counter decrements to zero, changestate */    {    ++seqtxtblptr;       /* advance to nextstate */    seqtxcntr = seqtxtblptr-&gt;cnt;   /* reload the counter */    txptr =  seqtxtblptr-&gt;ptr;   /* reload steady statepointer */    (*(seqtxtblptr-&gt;csptr)) ();    /* call change stateroutine +//*********** NEW RX SEQUENCE CONTROLLER *********************/  if(!(--seqrxcntr))  /* if counter decrements to zero, changestate */    {    ++seqrxtbiptr;       /* else, advanceto next state */    seqrxcntr = seqrxtblptr-&gt;cnt;   /* reload the counter */    rxptr =  seqrxtblptr-&gt;ptr;   /* reload steady statepointer */    (*(seqrxtblptr-&gt;csptr)) ();    /* call change stateroutine */    }/************ TRANSMIT ENCODER *************************/ (*txptr) ();    /* call transmit encoder *//************ ENCODE ABOVE, DECODE BELOW *****************/ (*rxptr) ();    /* call receive decoder */ } /* END OF WHILE(1) */}    /* END OF MAIN *//************** CONSTANT LOOK UP TABLES**************************************/ /* POWER INDEXED 4-D SUBSET */const int cye.sub.-- slicer[576] = { 0,  0,  0,  0,  0,  0,  0,  0, 441, 420, 408, 396, 394, 400, 414, 427,0,  0,  0,  0,  0,  0,  0,  0, 0,  0,  0,  0,  0,  0, 429, 398, 375, 349, 339, 329, 326, 335, 347, 359,386, 416, 451,  0,  0,  0,  0,  0, 0,  0,  0,  0,  0, 412, 371, 340, 314, 290, 279, 269, 265, 273, 281,302, 322, 353, 390, 430,  0,  0,  0,  0, 0,  0,  0,  0, 401, 357, 318, 282, 257, 236, 224, 216, 212, 218, 228,247, 270, 298, 337, 378, 424,  0,  0,  0, 0,  0,  0, 406, 350, 306, 266, 234, 206, 185, 173, 164, 162, 170, 181,197, 220, 253, 288, 327, 379, 431,  0,  0, 0,  0, 421, 360, 310, 263, 226, 193, 165, 146, 133, 123, 121, 125, 137,154, 179, 207, 242, 289, 338, 391, 452,  0, 0, 447, 384, 324, 277, 229, 189, 156, 131, 110,  96,  87,  83,  92, 100,117, 140, 172, 208, 254, 299, 354, 417,  0, 0, 418, 355, 294, 243, 201, 160, 126,  98,  79,  64,  58,  54,  62,  71, 90, 112, 141, 180, 221, 271, 323, 387,  0, 0, 392, 330, 274, 222, 177, 435, 102,  77,  55,  41,  35,  31,  37,  48, 65,  91, 118, 155, 198, 248, 303, 361, 428,448, 380, 316, 255, 203, 158, 119,  84,  60,  39,  24,  17,  15,  20,30,  49,  72, 101, 138, 182, 230, 283, 348, 415,439, 367, 304, 244, 194, 148, 108,  75,  50,  28,  13,  6,  4,  8,  21,38,  63,  93, 127, 171, 219, 275, 336, 402,432, 362, 296, 238, 186, 142, 103,  69,  43,  22,  9,  1,  0,  5,  16,32,  56,  85, 122, 163, 213, 267, 328, 395,437, 365, 300, 240, 190, 144, 106,  73,  45,  25,  11,  3,  2,  7,  18,36,  59,  88, 124, 166, 217, 272, 331, 397,445, 372, 307, 251, 199, 152, 113,  80,  52,  33,  19,  12,  10,  14,26,  42,  66,  97, 134, 174, 225, 280, 341, 409, 0, 388, 320, 261, 210, 167, 128,  94,  67,  47,  34,  27,  23,  29,  40, 57,  81, 111, 147, 187, 237, 291, 351, 422, 0, 410, 343, 284, 232, 183, 149, 115,  89,  68,  53,  46,  44,  51,  61, 78,  99, 232, 168, 209, 258, 315, 376, 442, 0, 433, 369, 311, 259, 214, 175, 139, 116,  95,  82,  74,  70,  76,  86,104, 129, 157, 195, 235, 285, 342, 399,  0, 0,  0, 403, 345, 292, 249, 205, 176, 150, 130, 114, 107, 105, 109, 120,136, 161, 191, 227, 268, 319, 373, 434,  0, 0,  0, 443, 382, 332, 287, 250, 215, 184, 169, 153, 145, 143, 151, 159,178, 202, 231, 264, 308, 358, 413,  0,  0, 0,  0,  0, 425, 377, 333, 293, 260, 233, 211, 200, 192, 188, 196, 204,223, 245, 278, 312, 352, 404,  0,  0,  0, 0,  0,  0,  0, 426, 383, 346, 313, 286, 282, 252, 241, 239, 246, 256,276, 295, 325, 363, 407,  0,  0,  0,  0, 0,  0,  0,  0,  0, 444, 405, 370, 344, 321, 309, 301, 297, 305, 317,334, 356, 385, 423,  0,  0,  0,  0,  0, 0,  0,  0,  0,  0,  0,  0, 435, 411, 389, 374, 366, 364, 368, 381, 393,419, 449,  0,  0,  0,  0,  0,  0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 446, 438, 436, 440, 450,  0,  0,0,  0,  0,  0,  0,  0,  0};  /*     Power indexed encode table (x,y).  */const int txencod[906] = {/* 0*/1, 1,     -3, 1,          1, -3,               -3, -3,/* 4*/1, 5,     5, 1,          -3, 5,               5, -3,/* 8*/5, 5,     -7, 1,          1, -7,               -7, -3,/* 12*/-3, -7,     -7, 5,          5, -7,               1, 9,/* 16*/9, 1,     -3, 9,          9, -3,               -7, -7,/* 20*/5, 9,     9, 5,         -11, 1,               1,-11,/* 24*/-7, 9,    -11, -3,          9, -7,               -3,-11,/* 28*/    -11, 5,     5,-11,          9, 9,               1, 13,/* 32*/13, 1,    -11, -7,          -7,-11,               -3, 13,/* 36*/13, -3,     5, 13,          13, 5,              -11, 9,/* 40*/9,-11,     -7, 13,          13, -7,              -15, 1,/* 44*/1,-15,    -15, -3,          -3,-15,              -11,-11,/* 48*/9, 13,     13, 9,         -15, 5,               5,-15,/* 52*/    -15, -7,     -7,-15,          1, 17,              -11, 13,/* 56*/17, 1,     13,-11,          -3, 17,               17, -3,/* 60*/    -15, 9,     9,-15,          5, 17,               17, 5,/* 64*/-7, 17,     13, 13,          17, -7,              -15,-11,/* 68*/    -11,-15,    -19, 1,          1,-19,               9, 17,/* 72*/17, 9,    -19, -3,          -3,-19,              -19, 5,/* 76*/5,-19,    -15, 13,          13,-15,              -11, 17,/* 80*/    -19, -7,     17,-11,          -7,-19,               1, 21,/* 84*/    -19, 9,     21, 1,          9,-19,               -3, 21,/* 88*/21, -3,    -15,-15,          13, 17,               17, 13,/* 92*/5, 21,     21, 5,         -19,-11,              -11,-19,/* 96*/-7, 21,     21, -7,         -15, 17,               17,-15,/*100*/9, 21,     21, 9,         -19, 13,              -23, 1,/*104*/13,-19,     1,-23,         -23, -3,               -3,-23,/*108*/    -23, 5,     5,-23,         -11, 21,               21,-11,/*112*/17, 17,    -23, -7,          -7,-23,              -19,-15,/*116*/    -15,-19,     13, 21,          21, 13,              -23, 9,/*120*/9,-23,     1, 25,          25, 1,               -3, 25,/*124*/25, -3,     5, 25,         -19, 17,               25, 5,/*128*/    -23,-11,     17,-19,         -11,-23,              -15, 21,/*132*/21,-15,     -7, 25,          25, -7,              -23, 13,/*136*/13,-23,     9, 25,          25, 9,              -19,-19,/*140*/17, 21,     21, 17,         -27, 1,               1,-27,/*144*/    -27, -3,     -3,-27,         -11, 25,               25,-11,/*148*/    -27, 5,    -23,-15,         -15,-23,               5,-27,/*152*/    -27, -7,     -7,-27,          13, 25,               25, 13,/*156*/    -19, 21,     21,-19,         -27, 9,               9,-27,/*160*/    -23, 17,     17,-23,          1, 29,               29, 1,/*164*/-3, 29,    -15, 25,          29, -3,              -27,-11,/*168*/25,-15,    -11,-27,          5, 29,               29, 5,/*172*/21, 21,     -7, 29,          29, -7,              -23,-19,/*176*/    -19,-23,    -27, 13,          13,-27,               17, 25,/*180*/25, 17,     9, 29,          29, 9,              -27,-15,/*184*/    -15,-27,    -11, 29,         -31, 1,               29,-11,/*188*/1,-31,    -23, 21,         -31, -3,               21,-23,/*192*/-3,-31,    -19, 25,         -31, 5,               25,-19,/*196*/5,-31,     13, 29,          29, 13,              -31, -7,/*200*/-7,-31,    -27, 17,          17,-27,              -31, 9,/*204*/9,-31,    -23,-23,         -15, 29,               21, 25,/*208*/25, 21,     29,-15,         -31,-11,              -11,-31,/*212*/1, 33,     33, 1,         -27,-19,              -19,-27,/*216*/-3, 33,     33, -3,          5, 33,               33, 5,/*220*/17, 29,     29, 17,         -31, 13,               13,-31,/*224*/-7, 33,     33, -7,         -23, 25,               25,-23,/*228*/9, 33,    -27, 21,          33, 9,               21,-27,/*232*/    -31,-15,    -15,-31,         -19, 29,               29,-19,/*236*/    -11, 33,     33,-11,         -35, 1,               1,-35,/*240*/    -35, -3,     -3,-35,          25, 25,              -31, 17,/*244*/    -35, 5,     17,-31,          5,-35,               13, 33,/*248*/33, 13,    -27,-23,         -23,-27,              -35, -7,/*252*/-7,-35,     21, 29,          29, 21,              -35, 9,/*256*/9,-35,    -15, 33,          33,-15,              -31,-19,/*260*/    -19,-31,    -35,-11,         -11,-35,              -27, 25,/*264*/25,-27,     1, 37,         -23, 29,               37, 1,/*268*/29,-23,     -3, 37,          17, 33,               33, 17,/*272*/37, -3,     5, 37,         -35, 13,               37, 5,/*276*/13,-35,    -31, 21,          21,-31,               7, 37,/*280*/37, -7,     9, 37,         -19, 33,               37, 9,/*284*/    -35,-15,     33,-19,         -15,-35,              -27,-27,/*288*/25, 29,     29, 25,         -11, 37,               37,-11,/*292*/    -31,-23,    -23,-31,         -35, 17,               17,-35,/*296*/    -39, 1,     1,-39,          21, 33,               33, 21,/*300*/    -39, -3,     -3,-39,          13, 37,               37, 13,/*304*/    -39, 5,     5,-39,         -27, 29,              -39, 7,/*308*/29,-27,     -7,-39,         -31, 25,              -35,-19,/*312*/25,-31,    -19,-35,         -15, 37,               37,-15,/*316*/    -39, 9,     9,-39,         -23, 33,               33,-23,/*320*/    -39,-11,    -11,-39,          17, 37,               37, 17,/*324*/    -35, 21,     21,-35,          1, 41,               29, 29,/*328*/41, 1,     -3, 41,         -39, 13,               41, -3,/*332*/    -31,-27,    -27,-31,          13,-39,               5, 41,/*336*/41, 5,     25, 33,          33, 25,               -7, 41,/*340*/    -19, 37,     41, -7,          37,-19,              -39,-15,/*344*/    -15,-39,    -35,-23,         -23,-35,               9, 41,/*348*/41, 9,    -11, 41,         -31, 29,               41,-11,/*352*/29,-31,     21, 37,          37, 21,              -39, 17,/*356*/17,-39,    -27, 33,          33,-27,               13, 41,/*360*/    -35, 25,     41, 13,         -43, 1,               25,-35,/*364*/1,-43,    -43, -3,          -3,-43,              -43, 5,/*368*/5,-43,    -39,-19,         -19,-39,              -23, 37,/*372*/    -43, -7,     37,-23,          -7,-43,              -15, 41,/*376*/41,-15,    -31,-31,          29, 33,               33, 29,/*380*/    -43, 9,     9,-43,         -35,-27,              -27,-35,/*384*/    -39, 21,     21,-39,          17, 41,               41, 17,/*388*/    -43,-11,    -11,-43,          25, 37,               37, 25,/*392*/    -43, 13,     13,-43,          1, 45,               45, 1,/*396*/-3, 45,     45, -3,         -19, 41,               41,-19,/*400*/5, 45,    -31, 33,          45, 5,              -39,-23,/*404*/33,-31,    -23,-39,         -35, 29,               29,-35,/*408*/-7, 45,     45, -7,         -43,-15,              -15,-43,/*412*/    -27, 37,     37,-27,          9, 45,               45, 9,/*416*/21, 41,     41, 21,         -43, 17,               17,-43,/*420*/    -11, 45,    -39, 25,          45,-11,               25,-39,/*424*/33, 33,    -35,-31,         -31,-35,               13, 45,/*428*/45, 13,    -23, 41,          29, 37,               37, 29,/*432*/    -47, 1,    -43,-19,          41,-23,              -19,-43,/*436*/1,-47,    -47, -3,          -3,-47,              -47, 5,/*440*/5,-47,    -15, 45,          45,-15,              -39,-27,/*444*/    -27,-39,    -47, -7,          -7,-47,              -43, 21,/*448*/    -47, 9,     21,-43,          9,-47,               25, 41,/*452*/41, 25    /* 453*4 = 1812 point full constellation */         };__________________________________________________________________________