Abstract:
A data communication system is disclosed utilizing a transmitter and one or more receivers. The communication system may increase the data rate without requiring an increase in bandwidth. Additional advantages include an inexpensive encryption property, the incorporation of a simple adaptive synchronization scheme, and the incorporation of an effective error detection and error correction scheme allowing for increased noise and signal degradation.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS  
       [0001]     The present application is a non-provisional patent application claiming priority under 35 U.S.C. 119 to the following U.S. provisional patent applications: 60/159,337 filed Oct. 13, 1999; 60/178,780 filed Jan. 28, 2000; 60/209,646 filed Jun. 6, 2000; and 60/222,354 filed Aug. 1, 2000. The present application incorporates said before mentioned four provisional patent applications by reference herein in their entirety. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates generally to electronic communication, and more specifically to coding schema, synchronization schema, demodulation schema, bandwidth efficiency schema, error detection/correction schema, and encryption schema.  
       BACKGROUND OF THE INVENTION  
       [0003]     Communication systems and methods known to the art utilize a number of digital modulation techniques. Digital modulation techniques known to the art generally encode information by relating the information in different combinations in amplitude, frequency, and phase to a radio frequency carrier. Digital modulation techniques known to the art may include amplitude shift keying, frequency shift keying, phase shift keying, and combinations of the like such as quadrature modulation. In order to decode the modulated signal, receivers need to generate waveform synchronous to the carrier before information can be recovered by applying Fourier expansion/transformation techniques to the modulated signal.  
         [0004]     With differing types of coding/decoding, carrier/symbol synchronization, and error detection/correction, current communication systems and methods may become extremely complex, which in turn, may require very high processing power. In particular, requiring high precision synchrony to the signal carrier and symbol timing by the receivers usually leads to highly complex synchronization circuits.  
         [0005]     Other limitations of current communication systems known to the art is the inability to provide secure communication, free from eavesdropping, without incorporating an encryption system with the system.  
         [0006]     Consequently, it would be advantageous if a system and method of communication existed not requiring specialized circuitry for carrier/symbol synchronization. It would also be advantageous if a system and method of communication existed which required little or minimum circuitry for error detection/correction. It would also be advantageous if a system and method of communication existed which included an inexpensive way to encrypt/decrypt data. Further, it would be advantageous (for the purpose of increasing channel bandwidth efficiency) if a communication system and method existed for which the operations of carrier/symbol synchronization, data extraction, and error detection/correction were all accomplished by essentially one combined operation which were also robust in the presence of noise and signal degradation.  
       SUMMARY OF THE INVENTION  
       [0007]     Accordingly, the present invention is directed to a communication system and method combining carrier/symbol synchronization, data extraction, error detection/correction in essentially one robust operation, thus significantly reducing receiver&#39;s circuit complexity. The system and method of communication of the present invention may include encryption attributes within the system and method.  
         [0008]     It is to be understood, both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention claimed. The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate an embodiment of the invention and together with the general description, serve to explain the principles of the invention. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]     The numerous objects and advantages of the present invention may be better understood by those skilled in the art by reference to the accompanying figures in which:  
         [0010]      FIG. 1  depicts a block diagram of an exemplary embodiment of the communication system of the present invention;  
         [0011]      FIG. 2  depicts an exemplary input signal and an exemplary corresponding output signal from a spike burster of the present invention showing an activation and deactivation region, which are determined and controlled by input signal&#39;s derivative, and the corresponding output voltage spikes from a spike burster;  
         [0012]      FIG. 3  is another exemplary input signal and an exemplary output signal from a spike burster of the present invention showing an activation and deactivation region, which are determined and controlled by input signal&#39;s amplitude, and the corresponding output voltage spikes from a spike burster;  
         [0013]      FIG. 4 ( a ) depicts an exemplary embodiment of a signal&#39;s-derivative-controlled spike burster of the present invention showing a voltage input source, a capacitor, and a non-linear resistive network in series;  
         [0014]      FIG. 4 ( b ) depicts an exemplary current-voltage operating curve for a non-linear resistive network of an exemplary embodiment of signal&#39;s-derivative-controlled spike burster of the present invention shown in  FIG. 4 ( a );  
         [0015]      FIG. 4 ( c ) depicts an exemplary embodiment of a signal&#39;s-derivative-controlled spike burster of the present invention showing a current input source, an inductor, and a non-linear resistive network in parallel;  
         [0016]      FIG. 4 ( d ) depicts an exemplary current-voltage operating curve for a non-linear resistive network of an exemplary embodiment of signal&#39;s-derivative-controlled spike burster of the present invention shown in  FIG. 4 ( c );  
         [0017]      FIG. 5 ( a ) depicts an exemplary embodiment of a signal&#39;s-amplitude-controlled spike burster of the present invention showing a voltage input source, an inductor, and a non-linear resistive network in series;  
         [0018]      FIG. 5 ( b ) depicts an exemplary current-voltage operating curve for a non-linear resistive network of an exemplary embodiment of signal&#39;s-amplitude-controlled spike burster of the present invention shown in  FIG. 5 ( a );  
         [0019]      FIG. 5 ( c ) depicts an exemplary embodiment of a signal&#39;s-amplitude-controlled spike burster of the present invention showing a current input source, a capacitor, and a non-linear resistive network in parallel;  
         [0020]      FIG. 5 ( d ) depicts an exemplary current-voltage operating curve for a non-linear resistive network of an exemplary embodiment of signal&#39;s amplitude-controlled spike burster of the present invention shown in  FIG. 5 ( c );  
         [0021]      FIG. 6  depicts an exemplary embodiment of a derivative-controlled spike burster portion of a receiver of the present invention showing the schematic for an exemplary embodiment of the present invention;  
         [0022]      FIG. 7  depicts an exemplary embodiment of an amplitude-controlled spike burster portion of a receiver of the present invention showing the schematic for an exemplary embodiment of the present invention;  
         [0023]      FIG. 8 ( a ) depicts another exemplary input signal to, and exemplary output signal from, an exemplary embodiment of a signal&#39;s-derivative-controlled spike burster of the present invention as measured utilizing an oscilloscope showing arbitrary-shaped input waveforms;  
         [0024]      FIG. 8 ( b ) depicts another exemplary input signal with noise added to, and exemplary output signal from, an exemplary embodiment of a spike burster of the present invention as measured utilizing an oscilloscope;  
         [0025]      FIG. 9  depicts an exemplary input signal to, and exemplary output signal from, an exemplary embodiment of a spike burster of the present invention as measured utilizing an oscilloscope illustrating actual input to, and output from, an exemplary embodiment of a signal&#39;s-amplitude-controlled spike burster;  
         [0026]      FIG. 10 ( a ) depicts an exemplary embodiment of derivative-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention;  
         [0027]      FIG. 10 ( b ) depicts another exemplary embodiment of derivative-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention highlighting spike burster one&#39;s activation and deactivation region;  
         [0028]      FIG. 10 ( c ) depicts another alternative embodiment of derivative-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention highlighting spike burster two&#39;s activation and deactivation region;  
         [0029]      FIG. 11  depicts an input signal to, and an output signal from, an exemplary embodiment of a four spike burster receiver system of the present invention showing the outputs of the respective spike bursters when the input signal in each&#39;s derivative-controlled activation region and deactivation region;  
         [0030]      FIG. 12 ( a ) depicts an exemplary embodiment of amplitude-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention;  
         [0031]      FIG. 12 ( b ) depicts another exemplary embodiment of amplitude-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention highlighting spike burster one&#39;s activation and deactivation region;  
         [0032]      FIG. 12 ( c ) depicts another alternative embodiment of amplitude-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention highlighting spike burster two&#39;s activation and deactivation region;  
         [0033]      FIG. 13  depicts an input signal to, and an output signal from, an exemplary embodiment of a four spike burster receiver system of the present invention showing the outputs of the respective spike bursters when the input signal in each&#39;s amplitude-controlled activation region and deactivation region;  
         [0034]      FIG. 14 ( a ) depicts an exemplary sinusoid input signal to and an exemplary corresponding output signal from a spike burster of the present invention showing information is coded by the amplitude of the sinusoidal input signal and information is represented by the number of spikes of the output signal when the spike burster is in activation;  
         [0035]      FIG. 14 ( b ) depicts an exemplary sinusoid input signal to and an exemplary corresponding output signal from a spike burster of the present invention showing information is coded by the frequency of the sinusoidal input signal and information is represented by the number of spikes of the output signal when the spike burster is in activation;  
         [0036]      FIG. 14 ( c ) depicts an exemplary sinusoid input signal to and an exemplary corresponding output signal from a spike burster of the present invention showing information is coded by the phase of the sinusoidal input signal and information is represented by the number of spikes of the output signal when the spike burster is in activation;  
         [0037]      FIG. 14 ( d ) depicts an exemplary sinusoid input signal to and an exemplary corresponding output signal from a spike burster of the present invention showing information is coded by the modulated amplitude of the sinusoidal input signal and information is redundantly represented by the number of spikes of the output signal when the spike burster is in activation;  
         [0038]      FIG. 14 ( e ) depicts an exemplary sinusoid input signal to and an exemplary corresponding output signal from a spike burster of the present invention showing information is coded by the modulated frequency of the sinusoidal input signal and information is redundantly represented by the number of spikes of the output signal when the spike burster is in activation;  
         [0039]      FIG. 14 ( f ) depicts an exemplary sinusoid input signal to and an exemplary corresponding output signal from a spike burster of the present invention showing information is coded by the modulated phase of the sinusoidal input signal and information is represented by the number of spikes of the output signal when the spike burster is in activation and during the phase changes;  
         [0040]      FIG. 15  depicts an exemplary sinusoid input signal to and two exemplary corresponding output signals from spike burster(s) of the present invention showing information is coded by the modulated phase of the sinusoidal input signal and information is represented by the burst initiation times of the output signal;  
         [0041]      FIG. 16  depicts an exemplary sinusoid input signal to and two exemplary corresponding output signals from spike burster(s) of the present invention showing information is coded by the modulated amplitude and phase of the sinusoidal input signal and the bit information in phase is represented by the burst initiation times of the output signal;  
         [0042]      FIG. 17  illustrates a 16 state-point quadrature amplitude modulation polar coordinate diagram (QAM constellation) wherein the efficiency of the present invention is illustrated;  
         [0043]     FIGS.  18 ( a ) and  18 ( b ) illustrate more preferred constellations and the increased bandwidth efficiency of some embodiments of the present invention:  
         [0044]      FIG. 19  depicts an exemplary embodiment of a spike burster utilized to create part of a spike burster receiver systems within the present invention;  
         [0045]      FIG. 20  depicts an exemplary embodiment of a coder utilized to code data for transmission within the present invention; and  
         [0046]      FIG. 21  depicts an exemplary embodiment of an adaptive counter circuit of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0047]     Reference will now be made in detail to a presently preferred embodiment of the invention, an example of which is illustrated in the accompanying drawings.  
         [0048]      FIG. 1  generally depicts a block diagram of an exemplary embodiment of the present invention. In  FIG. 1 , a digital number 01010 may be inputted  102  into the system of the present invention. A digital signal representation  104  of the digital sequence 01010 is shown. The digital representation  104  then may enter a modulator/signal generator  106 . The modulator/generator  106  may be constructed to modulate the signal many different ways including amplitude modulation, frequency modulation, phase modulation, frequency shift keying, and the like. The modulated signal may then be transmitted  108  over a particular medium. The particular medium may include wired or wireless transmission. The transmitted modulated signal  108  is received at the receiver(s)  110 . The receiver(s)  110  are designed such that all spike burster activation regions together cover the entire area in which the transmitted modulated signal  108  may lie. When the voltage or current of a signal entering a spike burster lies inside a burst activation region, as defined by the circuitry of the spike burster, the spike burster outputs a pulse stream or spike burst. A spike burster&#39;s activation region is a range of voltages or currents of the input signal or the derivative of the input signal which causes the spike burster to output spikes. By using more than one spike burster, it is possible to decode more than one bit per wavelength. The receiver(s)  110  may convert the transmitted modulated signal to voltage or current spikes  112 . Each spike burster may output a predetermined number of voltage or current spikes when the transmitted modulated signal  108  is within the spike burster&#39;s activation region. For example, the output spike  112  signals may be summed using a summing operational amplifier or the burst timing may be recorded by a threshold or duty cycle timer and then converted to the final number  116  with a digital wave generator or counter  114 .  
         [0049]      FIG. 2  shows an exemplary transmitted modulated signal  202  as a function of voltage in time and the corresponding output voltage spikes  210  from a spike burster. Typical deactivation regions  206  and activation regions  208  of the spike burster are determined by the derivative  204  of the signal  202 . The activation region may be only a fraction of one wavelength in length. Since the transmitted modulated signal  302  may enter more than one activation region every wavelength, more than one bit may be decoded per wavelength. The spike burster may output voltage spikes  210  when the transmitted modulated signal  202  is within the activation region  208 .  FIG. 2  shows the output of voltage spikes  210  while the transmitted modulated signal  202  is in the activation region  208 . Current spikes from the spike burster may also be used.  
         [0050]     The number of voltage spikes  210  outputted by a spike burster may be limited to a particular set of numbers of voltage spikes  210  using, for example, a counter and clipper circuit. Each spike burster may then output a known number of voltage spikes each time the transmitted modulated signal enters the spike burster&#39;s activation region. The output voltage  210  has a near-constant maximum voltage  212  and a near-constant minimum voltage  214  when the transmitted modulated wave  202  is not in the activation region  208  and is in the deactivation region  206  of the spike burster.  
         [0051]      FIG. 3  shows another exemplary transmitted modulated signal  302  and the corresponding output voltage spikes  304  from the spike burster. Again similar to the case of signal&#39;s derivative-controlled spike bursters as of  FIG. 2 , the transmitted modulated signal  302  may enter more than one activation region every wavelength, more than one bit may be decoded per wavelength. An exemplary deactivation region  306  and activation region  308  are shown. The spike burster outputs voltage spikes  304  when the transmitted modulated signal  302  may be located within the activation region  308 , and outputs a near-constant, lower voltage  310  or a near-constant, higher voltage  312  when the transmitted modulated signal  302  is located in the spike burster&#39;s deactivation region  306 . Current spikes from the spike burster may be used, as well as voltage spikes. Since the input signal&#39;s profile (shape, form) is not limited in order to cause a spike burster to output burst of spikes, and since activation and deactivation regions can be arbitrarily specified for a spike burster, information embedded to a transmitting signal may be made secure because only that spike burster may output correct spike bursts representing the message.  
         [0052]      FIG. 4 ( a ) depicts an exemplary circuit type of signal&#39;s-derivative-controlled spike burster. An input voltage source  402  is in series with a capacitor  404  and a non-linear resistive network  406  whose current-voltage operating curve has an exemplary shape of  408 . The load line  410  is controlled by the input source&#39;s derivative. The signal input  402  enters the spike burster&#39;s activation region when the load line  410  cuts across the negative resistant branch of the current-voltage operating curve  408 . The voltage spikes move from point b to point c on  408  when in its upward swing and from point d to point a on  408  when in its downward swing. The current spikes move from point c to point d when in its upward swing and from point a to point b when in its downward swing. Together, the operating point in the voltage and the current move around the cycle abcd during spike burster activation. The signal input  402  enters the spike burster&#39;s deactivation region when the load line  410  cuts across the positive resistant branches of the current-voltage operating curve  408 . When the load line  410  cuts either of the near-vertical branches of  408 , the voltage output reaches either a near-constant maximum value such as  212  or a near-constant minimum value such as  214  of  FIG. 2 .  
         [0053]      FIG. 4 ( c ) depicts another exemplary circuit type of signal&#39;s-derivative-controlled spike burster. An input current source  412  is in parallel with an inductor  414  and in parallel with a non-linear resistive network  416  whose current-voltage operating curve has an exemplary shape of  418 . The load line  420  is controlled again by the input current source&#39;s derivative. The signal input  412  enters the spike burster&#39;s activation region when the load line  420  cuts across the negative resistant branch of the current-voltage operating curve  418 . The voltage spikes move from point c to point d when in its downward swing and from point a to point b when in its upward swing. The current spikes move from point d to point a on  418  when in upward swing and from point b to point c on  418  when in its downward swing. Together, the operating point in the voltage and the current move around the cycle abcd during spike burster activation. The signal input  412  enters the spike burster&#39;s deactivation region when the load line  410  cuts across the positive resistant branches of the current-voltage operating curve  418 . When the load line  420  cuts either of the near-horizontal branches of  418 , the current output reaches either a near-constant maximum value such as  212  or a near-constant minimum value such as  214  of  FIG. 2 .  
         [0054]      FIG. 5 ( a ) depicts an exemplary circuit type of signal&#39;s-amplitude-controlled spike burster. An input voltage source  502  is in series with an inductor  504  and a non-linear resistive network  506  whose current-voltage operating curve has an exemplary shape of  508 . The load line  510  is controlled by the input voltage source&#39;s amplitude. The signal input  502  enters the spike burster&#39;s activation region when the load line  510  cuts across the negative resistant branch of the current-voltage operating curve  508 . The voltage spikes move from point c to point d when in its downward swing and from point a to point b when in its upward swing. The current spikes move from point d to point a on  518  when in its upward swing and from point b to point c on  518  when in its downward swing. Together, the operating point in the voltage and the current move around the cycle abcd during spike burster activation. The signal input  502  enters the spike burster&#39;s deactivation region when the load line  510  cuts across the positive resistant branches of the current-voltage operating curve  508 . When the load line  510  cuts either of the near-horizontal branches of  508 , the current output reaches either a near-constant maximum value such as  212  or a near-constant minimum value such as  214  of  FIG. 2 .  
         [0055]      FIG. 5 ( c ) depicts another exemplary circuit type of signal&#39;s-amplitude-controlled spike burster. An input current source  512  is in parallel with a capacitor  514  and in parallel with a non-linear resistive network  516  whose current-voltage operating curve has an exemplary shape of  518 . The load line  520  is controlled again by the input current source&#39;s amplitude. The signal input  512  enters the spike burster&#39;s activation region when the load line  520  cuts across the negative resistant branch of the current-voltage operating curve  518 . The voltage spikes move from point b to point c on  518  when in its upward swing and from point d to point a when in its downward swing. The current spikes move from point c to point d, when in its upward swing and from point a to point b when in its downward swing. Together, the operating point in the voltage and the current move around the cycle abcd during spike burster activation. The signal input  512  enters the spike burster&#39;s deactivation region when the load line  520  cuts across the positive resistant branches of the current-voltage operating curve  518 . When the load line  520  cuts either of the near-vertical branches of  518 , the voltage output reaches either a near-constant maximum value such as  212  or a near-constant minimum value such as  214  of  FIG. 2 .  
         [0056]      FIG. 6  depicts an exemplary embodiment of a circuit which may be utilized as a spike burster portion of a receiver controlled by signal&#39;s derivative. By adjusting the values of the individual components, the activation region and deactivation region of the spike burster may be adjusted. More than one spike burster  600  may be used at the same time to decode a transmitted modulated signal  602 . For example, the input  602  is where a transmitted modulated signal enters the spike burster  600 . The capacitor  604  is connected to the negative input of an operational amplifier  606 . Also connected to the negative input of the operational amplifier is a negative feedback resistor  608 . Again the negative feedback resistor  608  may be adjusted to vary the activation region of the spike burster  600 . The power voltage connected to the positive power input  610  of the operational amplifier  606  defines the amplitude of the output voltage spikes. The value of the power voltage  610  will be the maximum amplitude of the output voltage spikes. The negative power input  612  to the operational amplifier  606  is connected to ground  620 . A positive feedback resistor  614  is connected from the positive input of the operational amplifier  606  to the output  618  of the spike burster  600 . Again the value of the positive feedback resistor  614  may be adjusted to vary the activation region of the spike burster  600 . The ground resistor  616  is connected to the positive input to the operational amplifier  606  and to ground  620 . The output  618  of the spike burster  600  is where the voltage spikes are outputted to the rest of the receiver.  
         [0057]      FIG. 7  depicts an exemplary embodiment of a spike burster circuit which is controlled by signal&#39;s amplitude. The input  702  is where a transmitted modulated signal enters the spike burster  700 . The inductor  704  is connected to the positive input of an operational amplifier  706 . Also connected to the positive input of the operational amplifier is a negative feedback resistor  708 . Again the negative feedback resistor  708  may be adjusted to vary the activation region of the spike burster  700 . The negative power input  712  to the operational amplifier  706  is connected to ground  720 . A positive feedback resistor  714  is connected from the negative input of the operational amplifier  706  to the output  718  of the spike burster  700 . Again the value of the positive feedback resistor  714  may be adjusted to vary the activation region of the spike burster  700 . The ground resistor  716  is connected to the negative input to the operational amplifier  706  and to ground  720 . The output  718  of the spike burster  700  is where the voltage spikes are outputted to the rest of the receiver.  
         [0058]      FIG. 8 ( a ) shows an exemplary screen printout from an oscilloscope with an input wave  802  that includes a combination of distinctly-shaped waves. The input wave to the receiver(s) need not be sinusoidal in character. The corresponding output  804  is shown for a spike burster  600  with the following values: the capacitor  604  is 10 nanofarads; the operational amplifier  606  is National Semiconductor&#39;s part number LM  358 ; the value of the negative feedback resistor  608  is 1000 ohms: the value of the power voltage  610  to the operational amplifier  606  is 1.6 volts; the value of the positive feedback resistor  612  is 10 ohms; the value of the ground resistor  616  is 100 ohms. The activation region  806  of this spike burster is negative edge triggered and lasts until the slope of the input signal  802  is non-negative (either positive or zero slope). The deactivation region  810  is non-negative edge triggered and lasts until the slope of the input signal  802  is negative. The output  804  of this spike burster outputs spikes while the input signal  802  has a negative slope. The output  804  has a constant low voltage when the input signal  802  has a non-negative slope.  
         [0059]      FIG. 8 ( b ) shows the same input signal  802  as in  FIG. 8 ( a ) with noise added to the input  802 . With the present invention, the spike burster will still output the same voltage spikes  812  even with a significant amount of noise added to the input signal  802 . The activation boundary of  808  may be raised or lowered by changing the values of the individual components as shown in  FIGS. 10, 11  and  19 .  
         [0060]      FIG. 9  shows an exemplary screen printout from an oscilloscope with the input wave  902  as a triangular wave. The corresponding output  904  is shown for a spike burster  700  with the following exemplary values; the inductor  704  is 68 millihenrys (mH), the operational amplifier  706  is National Semiconductor part number LM  358 ; the value of the negative feedback resistor  708  is 820 ohms; the value of the power voltage  710  to the operational amplifier  706  is 1.8 volts; the value of the positive feedback resistor  712  is 39 ohms; and the value of the ground resistor  716  is 100 ohms. The activation region  906  of the spike burster  700  is above the activation threshold  908 . The deactivation region  910  is the area below the activation threshold  908 . The output  904  of the exemplary spike burster may output spikes while the signal remains above the activation threshold  908  and within the activation region  906 . Again, the number of output voltage spikes  904  may be limited to a known number of output voltage spikes if more than one spike burster is used, such that the particular number of spikes corresponds to a particular symbol or number. The activation threshold  908  may be raised or lowered by changing the values of the individual components as shown in  FIGS. 12, 13  and  19 .  
         [0061]      FIG. 10 ( a ) shows an exemplary embodiment of signal&#39;s-derivative-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention. Spike burster one&#39;s activation region  1002  includes the area above spike burster one&#39;s activation threshold  1010 . Spike burster one&#39;s deactivation region includes the area below spike burster one&#39;s activation threshold  1010 . Spike burster one&#39;s deactivation region includes spike burster two&#39;s activation region  1004 , spike burster three&#39;s activation region  1006  and spike burster four&#39;s activation region  1008 , as shown by the shaded area in  FIG. 10 ( b ). Spike burster two&#39;s activation region  1004  is between spike burster two&#39;s activation threshold  1012  and spike burster one&#39;s activation threshold  1010 .  
         [0062]     As shown by the shaded area in  FIG. 10 ( c ), spike burster two&#39;s deactivation region may include the area above spike burster one&#39;s activation threshold  1010  and the area below spike burster two&#39;s activation threshold  1012 . Spike burster two&#39;s deactivation region includes spike burster one&#39;s activation region  1002 , spike burster three&#39;s activation region  1006  and spike burster four&#39;s activation region  1008 . Spike burster three&#39;s activation region  1006  is between spike burster two&#39;s activation threshold  1012  and spike burster three&#39;s activation threshold  1014 . Spike burster three&#39;s deactivation region includes the area above spike burster two&#39;s activation threshold  1012  and the area below spike burster three&#39;s activation threshold  1014 . Spike burster three&#39;s deactivation region includes spike burster one&#39;s activation region  1002 , spike burster two&#39;s activation region  1004  and spike burster four&#39;s activation region  1008 . Spike burster four&#39;s activation region  1008  includes the area below spike burster  3 &#39;s activation threshold  1014 . Spike burster  4 &#39;s deactivation region includes spike burster one&#39;s activation region  1002 , spike burster two&#39;s activation region  1004  and spike burster three&#39;s activation region  1006 . Spike burster four&#39;s deactivation includes the area above spike burster four&#39;s activation threshold  1014 .  
         [0063]      FIG. 11  shows an input wave  1102 , by way of example only, in one input cycle to the four spike burster system depicted in  FIG. 10 ( a ). As the input wave is within each particular spike burster activation region  1104 ,  1106 ,  1108 ,  1110  each spike burster correspondingly outputs voltage spikes  1112 ,  1114 ,  1116 ,  1118 . When the input wave  1102  is in the spike burster one&#39;s activation region  1104 , spike burster one&#39;s output  1112  outputs voltage spikes. When the input wave  1102  is not in spike burster one&#39;s activation region  1104 , spike burster one&#39;s output  1112  is a constant flat voltage. As the input  1102  passes into spike burster two&#39;s activation region  1106 , spike burster two&#39;s output  1114  outputs voltage spikes. When the input  1102  is not in spike burster two&#39;s activation region  1106 , spike burster two&#39;s output  1114  is a constant flat voltage. When input  1102  lies within spike burster three&#39;s activation region  1108 , spike burster three&#39;s output  1116  outputs voltage spikes. When the input wave  1102  is not in spike burster three&#39;s activation region  1108 , spike burster three&#39;s output  1116  is a constant flat voltage. Finally, when the input  1102  lies within spike burster four&#39;s activation region  1110 , spike burster four&#39;s output  1118  outputs voltage spikes. When the input wave  1102  is not in spike burster four&#39;s activation region  1108 , spike burster four&#39;s output  1118  is a constant flat voltage.  
         [0064]     The present invention may also utilize a natural adaptive timing property. The input wave  1102  does not have to be synchronized with the spike bursters  1104 ,  1106 ,  1108 ,  1110 . When the input wave  1102  is within a particular spike burster&#39;s activation region, that spike burster outputs voltage spikes. When the input signal starts, the output starts. Therefore, when the outputs  1112 ,  1114 ,  1116 ,  1118  from each spike burster  1104 ,  1106 ,  1108 ,  1110  may be summed using, for example, a summing operational amplifier, the data will exit the spike burster system in the same order that the data came into the spike burster system. Using the four spike burster system in  FIG. 10  with four variations of the spike burster in  FIG. 19 , and an amplitude modulator  106  for the coder, increased bandwidth efficiency may be obtained.  
         [0065]      FIG. 12 ( a ) shows an exemplary embodiment of signal&#39;s-amplitude-controlled activation and deactivation regions of an exemplary four spike burster receiver system of the present invention. Spike burster one&#39;s activation region is  1202 . Spike burster two&#39;s activation region is  1204 . Spike burster three&#39;s activation region is  1206 . And spike burster four&#39;s activation region is  1208 . With the signal replacing signal&#39;s derivative in  FIGS. 10 and 11 , the explanation for  FIG. 12  is similar to that of  FIG. 10 .  
         [0066]      FIG. 13  shows an input wave  1302  in one input cycle to the four spike burster system depicted in  FIG. 12 ( a ). Again, with the signal itself replacing signal&#39;s derivative in  FIGS. 10 and 11 , the explanation for  FIG. 13  is similar to that of  FIG. 11 .  
         [0067]      FIG. 14 ( a ) shows an exemplary embodiment of a sinusoid signal  1402  with a fixed frequency but two varying amplitudes onto which information in symbol sequence 0110 is encoded, and an exemplary output  1404  of an amplitude-controlled spike burster of a receiver of the present invention. The spike number sequence that represents the symbol sequence 0110 is  1221  in two varying spike numbers. The output burst is in synchrony with input&#39;s change in amplitude.  
         [0068]      FIG. 14 ( b ) shows an exemplary embodiment of a sinusoid signal  1406  with fixed amplitude but two varying frequencies onto which information in symbol sequence 10010 is encoded, and an exemplary output  1408  of a derivative-controlled spike burster of a receiver of the present invention. The spike number sequence that represents the symbol sequence 10010 is 21121 in two varying spike numbers. The output burst is in synchrony with input&#39;s change in frequency.  
         [0069]      FIG. 14 ( c ) shows an exemplary embodiment of a sinusoid signal  1410  with a fixed frequency but two varying phases taking place during activation onto which information in symbol sequence 011001 is encoded, and an exemplary output  1412  of a derivative-controlled spike burster of a receiver of the present invention. The spike number sequence that represents the symbol sequence 011001 is 122112 in two varying spike numbers. Again, the output burst is in synchrony with input&#39;s change in phase.  
         [0070]      FIG. 14 ( d ) shows an exemplary embodiment of a sinusoid signal  1414  which is an exemplary carrier-modulated wave of the baseband signal  1402  of  FIG. 14 ( a ). Each baseband symbol cycle repeats (in an exemplary embodiment) three times on the carrier to create a modulated symbol cycle. That means the frequency ratio between the carrier cycle and the symbol cycle is 3:1. The symbol sequence 0110 is encoded with two varying modulated amplitudes. An exemplary output  1416  of an amplitude-controlled spike burster of a receiver of the present invention shows a spike number sequence representation 111222222111 with each symbol repeatedly decoded three times, the ratio of carrier frequency to symbol frequency. By decoding a given symbol many times over, errors due to system distortions other than information source error may be detected and corrected. This redundancy is the basis of error detection/correction attribute built into the communication method of the present invention. Also, output bursts are in synchrony with the modulated signal cycles.  
         [0071]      FIG. 14 ( e ) shows an exemplary embodiment of a sinusoid signal  1418  which is an exemplary carrier-modulated wave of the baseband signal  1406  of  FIG. 14 ( b ). Each symbol cycle repeats (in an exemplary embodiment) three times on the carrier. The symbol sequence 10010 is encoded with two varying modulated frequencies. An exemplary output  1420  of an derivative-controlled spike burster of a receiver of the present invention shows a spike number sequence representation 222111111222111 with each symbol repeatedly decoded by the same number of times as the ratio of carrier frequency to symbol frequency. Again, similar to  FIG. 14 ( d ), errors due to system distortions other than information source errors can be detected and corrected. Also, output bursts to modulating cycles are in synchrony.  
         [0072]      FIG. 14 ( f ) shows an exemplary embodiment of a sinusoid signal  1422  which is an exemplary carrier-modulated wave of the baseband signal  1410  of  FIG. 14 ( c ). Unlike the cases of FIGS.  14 ( d ), each symbol represented by varying phase does not repeat with the carrier. For the symbol sequence 011001 carried by the signal, the spike number sequence representation is 331332332331 . . . by an exemplary output  1424  of a derivative-controlled spike burster of the present invention. Each symbol is not decoded redundantly by counting spike number. However, it may be decoded redundantly by an exemplary technique ( FIG. 15 ) wherein the starting time of each burst is used for redundancy symbol decoding. Again, output bursts to modulating cycles are in synchrony.  
         [0073]      FIG. 15  shows an exemplary embodiment phase-modulated sinusoid input signal  1504  and two exemplary spike burst outputs  1506 ,  1508  of a derivative-controlled spike burster(s) of a receiver of the present invention. The sinusoid carrier has a fixed frequency with cycle period denoted by T 0 . The burst activation threshold for a signal  1504  to enter an activation region is exemplarily set at the point its slope changes from positive to negative, that is, at the point the signal  1504  reaches its maximum value. The burst deactivation threshold for a signal  1504  to enter a deactivation region is exemplarily set at the minimum point of the signal  1504  (although it is not necessary to set either point at a special location).  
         [0074]     Signal  1504  encodes an exemplary symbol sequence  1502  with  0  and  1  for the symbols. Each symbol is represented by a phase-modulated wave. One full carrier cycle is set to start at the zero voltage level  1518  in upward moving direction and to end at  1518  in an upward moving direction as well. Output bursts to carrier cycles alone are synchronized periodically T 0  period apart. Symbol  0 &#39;s wave is constructed by deleting a signal segment of a 0  fraction of the period T 0  in time length from a waveform of 3 full carrier cycles. If 0&lt;a 0 &lt;1/4, symbol  0 &#39;s wave results in an advance of burst activation by the amount of a 0 *T 0  in time. In other words, the two consecutive and transitional burst activation times are shortened by a 0 *T 0  units in time such as  1520 .  FIG. 15  is the case with a 0 =1/8. On the other hand. Symbol  1 &#39;s wave is constructed by adding a signal segment of d 0  fraction of the period T 0  to a waveform of 3 full carrier cycles. If 0&lt;d 0 &lt;1/4, this symbol wave results in a delay in burst activation by the amount of d 0 *T 0  in time. In other words, the two consecutive and transitional burst activation times are lengthened by d 0 *T 0  units in time such as  1522 .  FIG. 15  illustrates d 0 =1/8. With 1/4&lt;a 0 &lt;1/2 and/or 1/4&lt;d 0 &lt;1/2, corresponding burst activation shifts may also be obtained similarly. Output waves of  1504  and  1506  may, for example, either be two different outputs in voltage or current of one spike burster or two different outputs of two distinct spike bursters. Denote the burst initiation moment that the signal  1504  crosses the burst activation threshold by . . . τ −2 , τ −1 , τ 0 , τ 1 , τ 2  . . .  1510  with τ 0  the most present moment, τ −1  the moment before τ 0  and τ 1  the moment after τ 0 , and so on. Each burst initiation moment, τ j , may be determined from spike burster outputs  1506 ,  1508  either by a voltage threshold counter or by a cycle timer. For example, a voltage threshold  1512  may be preset between the minimum value of the spikes  1514  and the near-constant deactivation voltage  1516 . Then burst initiation time τ j  may be defined as an average of a time interval during which the output  1506  swings upwards and crosses the voltage threshold  1512 . As for output type  1508 , the burst initiation time τ j  may be defined to be an average moment that the output  1508  becomes active in spiking after a preset long pause of staying near-constant deactivation voltage.  
         [0075]     Having the burst initiation time sequence . . . τ −2 , τ −1 , τ 0 , τ 1 , τ 2  . . .  1510  enables the receiver to decode each symbol by a preset number of time. For the exemplary phase-shift-keyed sinusoid signal  1504 , symbol  0 &#39;s waveform advances the next burst by 1/8 of the carrier period in length, and symbol  1 &#39;s waveform delays the next burst by 1/8 of the carrier period in length. Therefore, the time lapse between consecutive burst initiation times, τ j -τ j-1 , is exactly the period of the carrier (8/8 T 0 ) if it does not occur during a transition between symbols. The time lapse is correspondingly 7/8 of the carrier period for symbol  0  and 9/8 of the carrier period symbol  1  respectively. Having this burst time lapse sequence {τ j -τ j-1 } requires the receiver to remember the last burst initiation time τ j-1 , (a 1-memory receiver). The burst time lapse sequency {τ j -τ j-1 } will exhibit the following exemplary pattern for the symbol sequence . . . 0101 . . . , using 1/8 of the carrier period as the unit of time, 
        . . . 7 8 8 9 8 8 7 8 8 9 8 8 . . . 
 
 However, if the decoder uses a 2-memory burst time lapse sequence {τ j -τ j-2 }, the sequence will exhibit the following exemplary pattern for the same symbol sequence, using 1/8 of the carrier period as the unit of time as well, 
    . . . 15 15 16 17 17 16 15 15 16 17 17 16 . . . 
 
 With such an exemplary 2-memory decoder, each symbol is decoded twice. Similarly, a 3-memory burst time lapse sequence {τ j -τ j-1 } looks like 
    . . . 23 23 23 25 25 25 23 23 23 25 25 25 . . . 
 
 decoding each symbol three times in repetition. In general, with a k-memory decoder or the like, so long as k is not greater than the ratio of the carrier frequency to the symbol frequency, then each symbol may be decoded k times redundantly. The signal symbol is in synchrony with burst lapse sequences. 
       
 
         [0079]      FIG. 16  shows an exemplary phase and amplitude modulated sinusoid input signal  1604  and two exemplary spike burst outputs  1606 ,  1608  of a derivative-controlled spike burster(s) of a receiver of the present invention. Output waves  1604  and  1606  may either be two different outputs in voltage or current of one spike burster or two different outputs of two distinct spike bursters. The activation threshold for the signal  1604  to enter the activation region is exemplarily set at the points its slope changes from positive to negative, and the deactivation threshold is set at the minimum points of the signal, all similar to  FIG. 15 . The signal  1604  encodes an exemplary symbol sequence  1602 . Each symbol is a string of two digits in 0 and 1: 00, 01, 10, 11. Each symbol carries two bits of information. The first digit (counted from the right most place, e.g., 0 is the first digit of the symbol  10 ) is represented by a phase shift of the modulating sinusoid carrier of a fixed period T 0 . Digit 0 has an advance shift in burst activation by the amount of 1/8 the carrier period in time, and digit 1 has a delay shift in the burst activation by the amount of 1/8 the period in time.  
         [0080]     The second digit (e.g., 1 of the symbol  10 ) is represented by an amplitude shift of the modulating sinusoid carrier, with the low amplitude for 0 and the high amplitude for 1. Denote the burst initiation moment that the signal  1604  crosses the activation threshold by . . . τ −2 , τ −1 , τ 0 , τ 1 , τ 2  . . .  1610  with τ 0  the most present moment, τ −1  the moment before τ 0  and τ 1  the moment after τ 0 , and so on. Each burst initiation moment, τ j , may be determined from spike burster outputs  1606 ,  1608  either by a voltage threshold counter or by a cycle timer similar to  FIG. 15, 1512 ,  1514 ,  1516 . Thus, similar to  FIG. 15 , the phase shifts of the carrier in burst activation may be detected and the first symbol digit can be decoded. Shifts in carrier amplitude may be detected by either amplitude envelope techniques or by amplitude-controlled spike bursters in addition to the phase shift detecting, derivative-controlled spike bursters. Together, each symbol can be decoded, and each can be synchronized with its corresponding burst initiation time.  
         [0081]      FIG. 17  is an exemplary 16 state-point (data point) quadrature polar coordinate diagram. This diagram shows the 16 available quadrature data points in black circles. These quadrature points occupy one of the 12 phases and 3 amplitude rings.  FIG. 17  also shows an additional set of non-quadrature points which share the same phase and amplitude as the various quadrature points. There are an additional 20 non-quadrature data points available under a preferred embodiment in this example of the present invention ( FIG. 17 , grey circles). This provided a bandwith efficiency gain over the quadrature points alone (ln36/ln2=5.17 bits/s/Hz). Additionally, the diagram also shows an additional 12 corresponding data points ( FIG. 17 , white circles). These corresponding data points both lie on the same amplitude rings as the quadrature points and their phase differences are comparable to the phase differences between quadrature points. By adding these corresponding data points a bandwith efficiency gain may be provided (ln48/ln2=5.85 bits/s/Hz).  
         [0082]     For example, telephone modems utilize quadrature modulation with M-ary signaling. The signal may take the form I*cos(ωt)+Q*sin(ωt) with I the in-phase component and Q the quadrature component, and ω/2*π the carrier frequency. With M states, each state point (I j ,Q k ),j=1,2, . . . , m 1 ; k=1,2, . . . , m 2 ; and m 1 *m 2 =M) carries r=ln(M)/ln2 bits of information, and the bandwidth efficiency factor is r bits/s/Hz. We may rewrite the signal form into I*cos(ωt)+Q*sin(ωt)=A*cos(ωt−P) with A=sqrt(I 2 +Q 2 ), tan(P)=Q/I. A as the amplitude and P as the phase shift. Therefore, the M states (I j ,Q k ) in terms of the phase shift P {jk}  with tan(P {jk} )=Q k /I j , and the amplitude A {jk} . Thus, for large M, there usually are more than sqrt(M) distinct phases P {jk}  and more than sqrt(M) amplitude A {jk} . Denoting the number of distinct phase by N p  and the number of distinct amplitude by N a . The foregoing analysis provides 
 
 N   a   &gt;sqrt ( M ) and  N   p   &gt;sqrt ( M ) 
 
 and the total number of state points in A and P [(A,P)-state points], of which the quadrature points are a part is 
 
 L=N   a   *N   p   &gt;sqrt ( M )* sqrt ( M )= M.  
 
         [0083]     Stated differently, each quadrature point occupies a spot in the phase-amplitude constellation (A,P), but there are more (A,P)-state points not occupied by an M-ary quadrature point. Moreover, an (A,P) state point which is not a quadrature point gives rise to the same signal characteristics as a quadrature does, in particular, in terms of the signal to noise ratio. This means, if the channel allows a quadrature-point signal through, it should allow a non-quadrature (A,P)-state signal through as well. All (A,P)-state signal may also pass through the channel. Also, if two quadrature points are distinguishable at the receiver, so are their amplitudes and phases. Therefore, two (A,P)-state points should be distinguishable at the receiver as well because they share the same amplitude and phases as various quadrature points. The present invention may be utilized to capture these (A,P)-state points (orphan points). Thus, allowing for an increase in the bit efficiency factor (R=ln(L)/ln2 bits/s/Hz) and the gain factor over the quadrature efficient factor 
 
 R/r =ln( L )/ln( M ). 
 
         [0084]     Using conventional Fourier methods to recover the quadrature point (I,Q) does not necessarily recover the phase P=tan −1 (Q/I). Since doing division Q/I or I/Q is tricky, as I, Q may be very small, and round-off errors may be overwhelming, the present invention preferably measures the phase shift of the signal ( FIGS. 15 and 16 ). The practicable measurability is improved by the spike burster of the present invention. The phase shift of the input signal to a derivative-controlled spike burster causes a time shift in the burst activation of the output.  
         [0085]      FIG. 18  shows two exemplary (A,P)-state point constellations. In  FIG. 18 ( a ), there are 4=2 2  amplitude rings spaced apart equally and 8=2 3  phase rays also spaced apart equally. In an exemplary embodiment, each gray point (data point) carries 5 bits of information. We may determine the amplitude A and phase shift P of a symbol signal A cos(ωt−P) ( 1604 ,  FIG. 16 ). In terms of the polar coordinate (A,P), the direction of the phase is along the concentric amplitude circles and the direction of the amplitude is along the equal-phase rays. These directions are orthogonal and representing symbols by varying amplitudes and phases of the sinusoid signal is an example of orthogonal signaling, given that quadrature amplitude modulation is another example of orthogonal signaling. This means that on two distinct rays the phase distance between two points from an inner amplitude ring is the same as two points from an outer amplitude ring. However, in terms of their in-phase and quadrature point signaling, the inner ring points are much closer to each other than the outer ring points. Thus, a quadrature modulation/demodulation scheme which is able to distinguish outer ring (A,P)-points may not necessarily be able to distinguish inner ring (A,P) data points. In other words, which signal characteristics a particular method chooses to measure should strongly effect the method&#39;s utilization of bandwidth. The present invention measures the phase and amplitude independently. Inner ring points are spaced equally apart in phase as outer ring points. Their differences are only in varying amplitude.  
         [0086]      FIG. 18 ( b ) is another (A,P)-point constellation which may be utilized by the present invention. There are 4=2 2  equally spaced amplitude rings and 16=2 4  equally spaced phase rays. Each data point carries 6 bits of information. Compared to the 16-QAM constellation of  FIG. 17  (black points), the signal characteristics are comparable. However, each of the 16-QAM point carries only 4 bits of information. The efficiency gain is (6−4)/4=50%.  
         [0087]      FIG. 19  depicts an exemplary embodiment of a circuit which may be utilized as the spike burster portion in an embodiment of the present invention. By adjusting the values of the individual components in the circuit, the activation region and deactivation region of the spike burster may be adjusted. The input  902  is where the transmitted input signal(s) enter the spike burster circuit. The input resistor, Ri, provides impedance control appropriate for the input signal used in the application.  
         [0088]     Operational amplifiers  904 .  906  are used as voltage followers to buffer the input signal and limit loading on the input line  902 . This allows the impedance to be completely defined by the input resistor, Ri. Since the operational amplifiers are inverting buffers, two are used to return the correct input signal. These operational amplifiers  904 ,  906  could be National Semiconductors part number LM 1458. The next operational amplifiers  912 ,  914  are part of a comparator that sets the active range of the spike burster. The use of this comparator provides control over the upper and lower limits of the spike bursting activity. National Semiconductor part number LM 393 could be used for these operational amplifiers  912 ,  914 . These operational amplifiers ( 912 ,  914 ) usually have their outputs pulled high in operation. This allows for several such comparators to be cascaded as has been done in this circuit. The circuit may be powered by +5 volts and −5 volts as shown at various points in the circuit. This allows for positive and negative input signals to be used entering the circuit at  902 . The lower threshold voltage. V lt ,  908  is defined by the power voltage range multiplied by a particular ratio of the lower threshold resistors R 1  and R 2 . V lt    908  is defined by the circuit as 
 
 V   lt =+5−(−5)*( R   2 /( R   1 + R   2 )+(−5). 
 
 Therefore, the lower threshold voltage, V lt    908 , may be positioned by a particular ratio of R 2 /(R 1 +R 2 ) multiplied by the power voltage. For instance, if R 2  was very large in comparison to R 1 , the ratio of R 2 /(R 1 +R 2 ) would be nearly 1 which would make the lower limit voltage V lt    908  very close to 5 volts. If R 1 =R 2  then the lower threshold voltage V lt    908  would be 0 volts. If R 2  were 0, then the lower threshold voltage V lt    908  would be −5 volts. The upper threshold voltage V ut ,  910  is then defined as a particular ratio of the upper threshold resistors R 3 , R 4  multiplied by the power voltages +5 and −5 volts. The particular ratio is defined as 
 
 V   ut =+5−(−5)*( R   4 /( R   3 + R   4 ))+(−5). 
 
 Therefore, the upper limit voltage V ut    910  may, be manipulated by the same changes in R 3  and R 4  as were shown with the lower threshold voltage V lt    908 , using R 1  and R 2 . The operational amplifier  916  acts as a derivative detector circuit. It detects the negative slope of the analog input waveform. It does this by imposing a lag time on the input to the circuit, R 5  and C 1  define the lag time coefficient 
 
τ= R   5 * C   1 . 
 
 The lag time coefficient τ should be less than 1% of the period of the analog waveform to insure that the spike burst occurs in a timely manner. Therefore, on the rising portions of the input waveform, the positive input will always be less than the negative input. This keeps the output of the operational amplifier  916  low, thereby disabling the transistor  918 . This also keeps the rest of the circuit from outputting spike bursts. If the input signal voltage entering the circuit at  902  is greater than the lower threshold limit V lt    908  and less than the upper threshold limit V ut    910 , and the signal has a negative slope, the comparator will enable the spike burster through the transistor  916 . In the exemplary embodiment, the resistor R 5  was set at 500 ohms so that the signal traveling to the transistor  916  is TTL or CMOS compatible. The spike burster operational amplifier  920  is part of the circuit that functions as a variable duty multivibrator or spike burster. 
 
         [0089]     When enabled, the amplifier  920  outputs a pulse stream or spike burst. The NPN transistor  916  enables or disables the rest of the circuit. The part of the circuit below the transistor is very much like the spike burster in  FIG. 4 . So the transistor  916  enables or disables the spike burster. The transistor  916  could be a National Semiconductor part number 2N2222. The positive feed back resistor, R 6  and the positive feedback to ground resistor R 7  set the multivibrator threshold. For simplicity we set R 6 =R 7 . The ratio between the negative feedback resistor R 8  and the transistor resistor R 9  sets the duty cycle output from the multivibrator. Setting R 8 =R 9  creates an equal on and off cycle for the spikes within the spike burst stream. The transistor  916  and the diode  918  control the charge and discharge cycles for the capacitor C 1 . These components, along with R 8  and R 9  control the on and off times for the multivibrator. The diode  918  and R 8  assures that there will be no partial spikes outputted. The on time T on , for the multivibrator is defined by 
 
 T   on   =R   8 * C   1 *ln(1+((2 *R   6 )/ R   7 ). 
 
         [0090]     Since T on  is the cycle time, the frequency of the spike bursts is 1/T on . The off time T off , of the multivibrator is defined by 
 
 T   off   =R   9 * C   1 *ln(1+((2 *R   6 )/ R   7 ). 
 
 Therefore, if R 8 =R 9 , then the multivibrator will have an equal on and off time. If the transistor is turned off, then the transistor resistor R 9 , effectively becomes infinite and T off  therefore becomes infinite and the multivibrator remains disabled. The last pair of operational amplifiers  924 ,  926  form another pair of voltage followers as did  906  and  908 , and function as a buffer pair. This again limits the load on the output of the spike burster operational amplifier  922 . 
 
         [0091]     Again, two are used to get the correct sign on the signal as it travels out of the circuit. The output impedance resistor R 10  sets the output impedance for the spike burster. The value of R 10  must be coordinated with the circuitry downstream from the spike burster. The output of spike bursts exits the circuit at  928 . So using this circuit, the lower threshold voltage V lt    908  and the upper threshold voltage V ut    910  can easily be set as shown in  FIGS. 10 and 11 . By using more than one spike burster, the various different activation regions can be created as in  FIGS. 10 and 11 .  
         [0092]     The output is evenly spaced apart spikes because of R 8 =R 9 , and there are no partial spikes because of the diode  918  and the resistor R 9 . A counter such as Texas Instruments part number 74HC4040 may be used to count the spikes and output the number of spikes counted to a processor, thereby completing the decoding of the transmitted signal.  
         [0093]      FIG. 20  depicts an exemplary embodiment of a circuit that may be used as a coder for the present communication system. The first capacitor C 1  separates this circuit from the rest of the system and provides instantaneous charge current for circuit operation. This circuit takes digital inputs at  1002  and  1004 . Low voltage or “0” should be inputted at  1002  and high voltage or “1” should be inputted at  1004 . The bilateral switches will transfer an analog or digital signal bidirectionally regardless of polarity once the switch is enabled. The enable connection for the bilateral switch is shown in the figure at the bottom of each switch. When the enable is activated the switch will transfer a signal bidirectionally. The invertors  1006 ,  1008 ,  1010 ,  1012  are used to enable the switched 180 degrees out of phase with each other. When switch  1006  is enabled, switch  1008  is disabled. When switch  1008  is enabled, switch  1006  is disabled. The same applies for switches  1010  and  1012 . Bilateral switch  1006  controls the charging of the capacitor C 2 . Bilateral switch  1010  controls the charging of the capacitor C 3 . The capacitor C 1  should be much greater than the values of C 2  and C 3 . The bilateral switch may be Texas Instruments part number 74HC4066. Capacitors C 2  and C 3  should have different values as this will affect the amplitude of the outgoing analog wave. The greater the value of the capacitor, the greater the amplitude of the outgoing wave. In this way the amplitude of the analog wave corresponding to a “0” will be different (lesser) than the amplitude of the analog wave corresponding to a “1” (greater).  
         [0094]     Whenever C 2  or C 3  is not being discharged, it is being charged and prepared for its next discharge cycle. This allows the piecewise assembly of an analog waveform that corresponds to the 0&#39;s and 1&#39;s of the input digital wave. Once C 2  and C 3  are charged, the circuit can be forced to discharge either C 2  or C 3  to ground through the resistor R 1  by either inputting a 0 or 1 in at  1002  and  1004  respectively. This circuit will also take inputs of neither a 1 or a 0 or both.  
         [0095]     Therefore, this circuit may encode up to 4 different logic numbers, 00, 0, 1, and 01. Circuits similar to the one depicted in  FIG. 19  may be designed to decode all four of these different type of bits, thereby increasing the data rate without increasing bandwidth. The operational amplifiers  1014  and  1016  again form a buffer that allows the output impedance to be defined by R 2 . The operational amplifiers may be National Semiconductor part number LM1458. The power to these amplifiers should be plus and minus 12 volts so that the output wave will not be clipped. The output of this circuit exits at  1018 . The output of this circuit will look similar to a saw-tooth waveform. The capacitors will charge rapidly and discharge at a rate according to the equation 
 
 T   d =5 e   −(t/(50+R2)*C2)  
 
 for the portion of the coder that codes the digital 0, where T d  is the discharge time. 
 
         [0096]     Therefore, the discharge time of the capacitor is directly proportional to the value of the capacitor. Therefore, the amount of time it takes for the output analog signal to discharge from peak voltage to a steady low voltage depends directly on the size of the capacitor C 2 . In this way the amount of time the output analog signal spends in a particular activation region can be controlled by the sizes of the capacitors used in this circuit. The same may be done for the portion of the circuit that creates the analog signal that corresponds to the digital 1 by varying the value of C 3 . The circuit in  FIG. 19  will output spikes while the analog wave from this circuit has a negative slope and is within the particular activation region of a circuit similar to the one in  FIG. 19 . Even in this simple example, more than one bit per wavelength is achieved if the analog wave outputted from this circuit is allowed to descend through more than one activation region of circuits like the one in  FIG. 19 .  
         [0097]      FIG. 21  is a schematic of an adaptive counter circuit which may be utilized in a preferred embodiment of the present invention. The input to U 1 A is the USB signal. In an exemplary embodiment the waveform represents a three spike burst. It is not ground referenced and the characteristics of the individual pulses are arbitrary for illustrative purposes only. U 1 A is an inverting unity gain buffer which acts to prevent the circuit from distorting the waveform. This preserves the purity of the waveform. R 3  and C 1  function as an averaging circuit. The change on C 1  provides a rolling average of the inverted signal. A representation of the change on C 1  follows. Note, the sense of this voltage is an inversion from the incoming signal. This voltage is also utilized later for comparison. The first part of this circuit cleans up an analog signal and ground references it, later converting it to a TTL compatible logic signal, U 1 B is an inverting amplifier. Two inversions put the signal back on the positive side of ground. The gain of this amplifier is held to about −1.1. This provides a slight offset from the actual average. This is done to prevent false triggering in the comparator. It raises the reference voltage slightly.  
         [0098]     The output from the comparator is a ground referenced TTL compatible logic signal. It takes the form of a series of pulses with amplitudes of nearly five volts. This becomes the USB′ signal that is fed back into U 3 , the retriggerable monostable multivibrator. The retriggerable feature is important because it allows the counter to be adaptable. U 3  retriggers on each pulse. It times out after waiting 150% of a gap width. The Q output then drops to a low level. The Q signal rises at the end of the time out period. This signal is fed to U 4 , U 4  is sensitive to the rising edge of the signal, U 4  is also a monostable multivibrator but it is not retriggerable, U 4  output is a very narrow pulse. The USB′ pulse train has been fed to the counter U 6 , U 6  is a twelve stage ripple counter. This pulse, the output of U 4 , latches the count to U 5  from U 6 . This pulse also sets the data flag “DATA” by latching the flip flop U 7 .  
         [0099]     U 8  is an inverter pack and is used here to provide a propagation delay. After being delayed, the pulse resets the counter, in preparation for the next burst. The delay prevents resetting the counter before the count is latched to the register U 5 . Thus, it protects the validity of the count.  
         [0100]     In practice, the USB signal is fed to the input. The “DATA” line is tied to a processor interrupt line. The presence of data interrupts whatever processor is monitoring this circuit. That processor reads data on lines D 0 →D 7  by pulling the “OE” line low. It does this in its interrupt handling routine. After reading the data, it clears the data flag by pulling the “CLR” line low. The D 0 →D 7  bus is eight bits wide and conveniently interfaces with a processor bus. The “OE”, “CLR” and “DATA” lines provide the necessary handshaking for the interface. The circuit can be adjusted by changing the timing resistors and capacitors. R 3  and C 1  control the timing of the averaging circuit. Basically, this is done with the consideration that τ=RC where R is in Ohms and C is in Farads. The units of τ are seconds.  
         [0101]     R PXT  and C PXT  on U 3  control the timeout period for the multivibrator by the equation t w =0.37 RC. T w  should be set to 150% of the longest gap width between pulses. In a present exemplary embodiment this circuit is currently wired for 0.001 sec pulses and gaps.  
         [0102]     R P  and C P  on U 4  provide the width of the latching pulse. Current component choices have set this pulse width to be 100 nsec. The pulse width is given by the equation T w =0.7 R e C e .  
         [0103]     U 8  provides a propagation delay. A series of four inverters provides this delay. An even number of inverters was chosen to preserve the logical sense of the pulse. A delay of about 14 nsec per gate is assumed. The inverter string, then, provides a delay of 56 nsec.  
         [0104]     The present invention provides a method of communication that may increase data rates without a corresponding increase in bandwidth. More than one spike burster may be used to decode a signal. A spike burster&#39;s activation region is determined by the circuitry of the particular spike burster. These spike bursters may be designed such that each spike burster has a separate and distinct activation region, and all activation regions together cover the entire region in which the transmitted signal may lie. Each spike burster may output a predetermined number of voltage spikes when the transmitted wave is within the spike burster&#39;s activation region. Preferably, voltage spikes may only be outputted by one spike burster at a time. The voltage spikes from the individual spike bursters may be added together, creating distinct, separate spike burst patterns in a voltage spike signal. Then, a digital signal may be created from the pattern of voltage spikes (or their time shift in burst activation). In this way, more than one bit per wavelength may be transmitted and decoded. Therefore, more data may be transmitted and decoded utilizing essentially the same amount of bandwidth.  
         [0105]     The present invention provides a secure method of communication by coding a spike number by a seemingly arbitrary signal going through arbitrarily preset activation and deactivation regions of a spike burster ( FIGS. 2, 3 ,  8 ,  9 ). It may also do so by coding the activation bursts with arbitrarily preset activation and deactivation thresholds of a spike burster. The present invention gives rise to a method of communication which may measure the phase shift of a modulated sinusoid signal by timing the bursts from an output of a spike burster (see, e.g.,  FIGS. 15 and 16 ). Such a method may detect orphan data points of a QAM constellation as in  FIG. 17 , or data points of an (A,P)-constellation as in  FIG. 18 . This facilitates bandwidth efficiency where signal characteristics are comparable to a QAM constellation of a smaller number of states. The present invention provides a method of communication which may be utilized to reduce transmission error rate. This may be accomplished by making use of a modulated sinusoid carrier for redundant symbol retrieving as illustrated ( FIGS. 14, 15 , and  16 ). The present invention also provides a method of control which may use spike burster&#39;s input-output control methodology for purposes of synchronization, error detection/correction, data storage, pattern recognition, image segmentation, artificial intelligence of neural networks.  
         [0106]     It is believed that the present invention and many of its attendant advantages may be understood by the foregoing description, and it will be apparent that various changes may be in the form, construction, and arrangement of the components thereof, without sacrificing all of its material advantages. The form herein described being merely an explanatory embodiment thereof, it is the intention of the following claims to encompass and include such changes.