Patent Publication Number: US-7225459-B2

Title: Method and system for dynamically adjusting video bit rates

Description:
RELATED APPLICATION 
   This patent application claims priority to U.S. Provisional Patent Application Ser. No. 60/329,863 entitled “Method and System for Dynamically Adjusting Video Bit Rates” filed Oct. 17, 2001. 

   FIELD OF THE INVENTION 
   The present invention generally relates to adjusting a video bit rate and more particularly relates to a method for dynamically adjusting a video bit rate to compensate for changing network conditions. 
   BACKGROUND OF THE INVENTION 
   A computer network is used for a number of different purposes, including sending electronic mail, browsing the Internet, sharing files and conducting videoconferences. The various data transmissions carried by the network cause fluctuations in the available network bandwidth. Each data transmission sent over the network consumes some portion of the network&#39;s total bandwidth, leaving progressively less bandwidth for other transmissions. With respect to videoconferencing, the fluctuation in available bandwidth can be particularly troublesome. For example, if an individual is engaged in a videoconference with another person, an increase in network traffic can degrade the quality of the video or audio. 
   In response to an increase in network traffic, the videoconference data transmission rate may be reduced in order to minimize lag, transmission gaps, or connection loss. However, if additional bandwidth becomes available on the network due to a decrease in network traffic, then continued transmission at the reduced bit rate is unnecessary. If the videoconference system could detect the additional available bandwidth, then the videoconference data transmission rate could be increased to take advantage of the available bandwidth. 
   Some videoconferencing systems reduce the videoconference transmission rate, but do not attempt to increase the transmission rate if additional bandwidth becomes available. Other systems increase and decrease the transmission rate, but do so in a manner that causes the transmission rate to “thrash” or to oscillate between a higher transmission rate and a lower transmission rate. 
   Therefore, there is a need in the art for detecting changes in the available bandwidth and optimizing the bit rate of a videoconference transmission. There is a further need to keep proper statistical and historical data to allow the optimization to be made without thrashing between higher and lower transmission rates. 
   SUMMARY OF THE INVENTION 
   The present invention meets the needs described above by providing a method for dynamically adjusting the transmitted video bit rate. A request to increase or decrease the bit rate is based upon the performance of the network. A videoconference call or call is established between two endpoints. The endpoints are referred to as a sending endpoint and a receiving endpoint for simplicity. The sending endpoint encodes video and audio data and transmits it to the receiving endpoint which decodes the video and audio data and plays back the data. 
   The receiving endpoint maintains information about the call and the network performance as a set of call parameters. The call parameters include variables and counters. The call parameters provide historical and statistical information about the call that can be used by the receiving endpoint to determine whether and when to request an increase or decrease in the bit rate. For example, by maintaining information that indicates the number of intervals that the last increase was maintained, the receiving endpoint can avoid thrashing. If a bit rate increase was requested, but was not maintained for a sufficient period of time, then the endpoint will delay a subsequent request for an increase until the call parameters indicate that the increase will be successful. 
   One aspect of the invention provides a method for setting up a call and dynamically adjusting the bit rate during the call to respond to changing network conditions. The method to dynamically adjust the bit rate can be implemented in either hardware or software associated with the receiving endpoint. The method begins by conducting an available bandwidth test. The available bandwidth test determines the bandwidth available for the call. Once the available bandwidth is determined, then the initial transmission rates for the video and audio are selected and the video setup and the audio setup for the call are completed. In addition, the call parameters are initialized. 
   The call is monitored throughout its duration to determine whether to request a reduction or an increase in the bit rate. The monitoring includes determining both video and audio losses, as well as an estimated received bit rate. The video and audio losses are compared to loss thresholds. The loss thresholds include both predetermined loss thresholds and dynamic loss thresholds. The call parameters are adjusted based upon the measured losses and the comparisons to the loss thresholds. In addition, a request to increase or decrease the bit rate is based upon the loss threshold comparisons. 
   The method supports requests to increase or to decrease the bit rate. Once the bit rate has been reduced, the performance of the network continues to be monitored so that if network conditions improve, then a bit rate increase can be requested. 
   These and other aspects, features and advantages of the present invention may be more clearly understood and appreciated from a review of the following detailed description of the disclosed embodiments and by reference to the appended drawings and claims. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram of a computer network illustrating the operating environment for an exemplary embodiment of the present invention. 
       FIG. 2  is a block diagram of a pair of endpoints in accordance with an exemplary embodiment of the present invention. 
       FIG. 3  is a flow diagram of a method for dynamically adjusting the bit rate of a call in accordance with an exemplary embodiment of the present invention. 
       FIG. 4  is a flow diagram of a method for setting up the video portion of a call in accordance with an exemplary embodiment of the present invention. 
       FIG. 5  is a flow diagram of a method for dynamically increasing the bit rate of a call in accordance with an exemplary embodiment of the present invention. 
   

   DETAILED DESCRIPTION 
   The present invention is directed to a method for dynamically adjusting a video transmission rate in response to changing network conditions. Briefly described, information about the performance of the network is maintained and is used by a receiving endpoint to determine when to request an increase or a decrease in the video bit rate. For example, if there are sustained periods of video losses, then the receiving endpoint requests a bit rate reduction. However, if there are sustained periods of low video losses, then the receiving endpoint requests an increase in the bit rate. The information that is maintained includes the number of intervals since the last bit rate increase was attempted and the number of intervals that the last bit rate increase was maintained. By using this information, the receiving endpoint can avoid thrashing. If a bit rate increase has been requested, but has not been maintained for a sufficient period of time, then the endpoint delays a request for an increase until the information indicates that an increase will be successful. 
   Exemplary Operating Environment 
     FIG. 1  and the following discussion are intended to provide a brief, general description of a videoconferencing environment  100  that is a suitable operating environment for the present invention. While the invention will be described in connection with multiple computers that are connected via a network, those skilled in the art will recognize that other, alternative configurations are also possible. 
     FIG. 1  includes three endpoints,  105 ,  110  and  111 . Typically, an endpoint is a computer system that is capable of both sending and receiving videoconferencing data, as well as other types of data. For example, an endpoint can also send and receive electronic messages and files, in addition to videoconferencing data. An endpoint typically include a video camera, a monitor or other display device, a microphone, and a speaker. An endpoint can also include other peripheral devices as well. Additional details of an endpoint are discussed below in connection with  FIG. 2 . Although  FIG. 1  illustrates three endpoints, the present invention can work with more than three endpoints. The endpoints are connected via a network, such as an intranet, the Internet, a local area network (“LAN”), etc. The network can support a single videoconference or multiple videoconferences. 
   Exemplary Endpoints 
     FIG. 2  illustrates an exemplary sending endpoint  105  and an exemplary receiving endpoint  110 . Although endpoints are typically capable of both sending and receiving videoconferencing data, the endpoints illustrated in  FIG. 2  have been labeled as either a sending endpoint or as a receiving endpoint for simplicity. The sending endpoint  105  includes a sending encoder  130 , a sending conference controller  135  and a sending decoder  140 . The receiving endpoint  110  includes a receiving encoder  125 , a receiving conference controller  120  and a receiving decoder  115 . The encoders encode data, such as video or audio data, and transmit the data to a decoder. The decoders receive the transmitted data and decode the data for display or playback at the receiving endpoint. The transmission between a sending endpoint and a receiving endpoint is referred to herein as a “call.” Although shown separately, the encoder and the decoder can be combined into a single block. A combined encoder and decoder is referred to herein as a CODEC (coder/decoder). A CODEC can be implemented in either hardware or software. 
   Typically, a sending encoder is capable of transmitting data using multiple encoding schemes and multiple bit rates simultaneously. An implementation of an encoder using a particular encoding scheme at a particular bit rate is referred to herein as an “engine.” 
   The conference controllers arrange the connection between the endpoints and negotiate the encoding scheme and the bit rate used. The conference controllers also support communications between the endpoints regarding changes in the transmission, such as a request for an increase or a decrease in the transmitted bit rate. Communication between the sending endpoint and the receiving endpoint typically follows a communication standard, such as an ITU standard. 
   Call Parameters 
   The present invention maintains information about each call to determine whether to request an increase or decrease in the bit rate. The information that is maintained includes the number of intervals since the last increase was attempted, the number of intervals that the last increase was maintained, and the number of times an increase was followed by a decrease. In one embodiment, the information is maintained as a number of call parameters. The call parameters include variables and counters. The initial or default values for some of the variables can be stored in a registry, such as the WINDOWS operating system registry. The default values and the minimum and maximum values stored in the registry for one embodiment of the invention are shown below in Table 1. The use of the registry keys is described in more detail in connection with  FIGS. 3–5  below. As will be apparent to those skilled in the art, the values shown in Table 1 are for illustration only. The invention will also work with other values. 
   
     
       
         
             
             
             
             
           
             
               TABLE 1 
             
             
                 
             
             
                 
               Default if not 
                 
                 
             
             
                 
               specified in 
             
             
               Registry Key Name 
               registry 
               Minimum 
               Maximum 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
             
             
          
             
               g711PlusMinBitRate 
               1544000 
               384000 
               1000000000 
             
             
               g711MinBitRate 
               384000 
               128000 
               1000000000 
             
             
               Xinterval 
               3000 
               100 
               30000 
             
             
               YpercentLoss 
               0.02 
               0.002 
               0.15 
             
             
               YpercentAudioLoss 
               0.01 
               0.001 
               0.15 
             
             
               BrateDown 
               0.20 
               0.01 
               0.50 
             
             
               QdecreaseWindow 
               0.50 
               0.1 
               0.9 
             
             
               Pwrroot 
               2.0 
               1.1 
               5.0 
             
             
               Tcoeff 
               24.0 
               1.0 
               100.0 
             
             
               Vroot 
               0.5 
               0.1 
               2.0 
             
             
               Mperfection 
               .001 
               0.0 
               0.01 
             
             
               BrateUp 
               0.20 
               0.01 
               0.50 
             
             
               PPerfect 
               3 
               1 
               20 
             
             
               PFinit 
               1 
               1 
               20 
             
             
               PFincInit 
               2.0 
               1.1 
               10.0 
             
             
               PFdecInit 
               1.5 
               1.1 
               10.0 
             
             
               PFmax 
               60 
               10 
               200 
             
             
               PFmin 
               1 
               1 
               10 
             
             
                 
             
          
         
       
     
   
   The call parameters provide historical and statistical information about the call that can be used by the receiving endpoint to determine whether and when to request an increase or decrease in the bit rate. For example, by maintaining information that indicates the number of intervals that the last increase was maintained, the receiving endpoint can avoid thrashing. If bit rate increases have been requested, but have not been maintained for a sufficient period of time, then the endpoint will delay a request for an increase until the call parameters indicate that the increase will be successful. 
   Method for Dynamic Bit Rate Adjustment 
     FIG. 3  illustrates an exemplary method for setting up a call and dynamically adjusting the bit rate during the call to respond to changing network conditions. In one embodiment, the method to dynamically adjust the bit rate is implemented in software that is associated with the decoder of the receiving endpoint. The method uses call parameters to maintain information about the call. Values for the call parameters can be stored in the registry, as described above in connection with Table 1. The registry key names and parameter names that correspond to the call parameters used in one embodiment are shown herein in parenthesis for illustration purposes. As will be apparent to those skilled in the art, the names and the values can be other than those used herein. 
   The method  300  begins at the start step  302 . From step  302  the method proceeds to set up the call in steps  303 ,  304  and  306 . In step  303 , an available bandwidth test is performed. The available bandwidth test determines the bandwidth available for the call. Typically, the sending endpoint sends data at a given bit rate to the receiving endpoint. The receiving endpoint receives the data and calculates the received bit rate for the data. The receiving endpoint communicates the received bit rate to the sending endpoint. The sending endpoint then determines the bandwidth available for the call. The available bandwidth test does not require that the user specify an initial bit rate for the call, as required by some existing systems. 
   From step  303 , the method proceeds to step  304 . In step  304 , the video portion of the call is setup. The details of setting up the video portion of the call are discussed in more detail below in connection with  FIG. 4 . The audio portion of the call is setup in step  306 . During the audio portion of the call setup, the endpoints negotiate the audio CODEC that will be used for the call. The audio CODEC is selected based upon the results of the available bandwidth test. In one implementation, the received bit rate reported by the receiving endpoint is compared with one or more predefined bit rates to select the appropriate CODEC. Typically, the predefined bit rates are stored in the registry (g711PlusMinBitRate, g711MinBitRate). 
   Once the video and audio portions of the call are set up, then the method proceeds to step  308 . In step  308 , the call parameters used to dynamically adjust the bit rate of the call are initialized. The parameters include both variables and counters. The parameters include a rate increase counter (Lincrease) that indicates the number of consecutive intervals that have elapsed without significant loss. The rate increase counter (Lincrease) is set to an initial value of −1, indicating that there have been no increases. The variable number of sample intervals (F) is set to an initial value specified in the registry (pFinit). In addition, the loss counter (lossCounter) and the loss threshold counter (perfectCounter) are initialized to zero. 
   In step  310 , the call is monitored to determine whether to request a reduction or an increase in the bit rate. The monitoring includes checking both video and audio losses. In one embodiment, the call is sampled and the losses are calculated periodically. The sampling period (Xinterval) can be specified in the registry. In addition to calculating the video and audio losses, the estimated received bit rate is also calculated for each sample interval. The video and audio losses are compared to predetermined loss thresholds. Typically, the predetermined loss thresholds are stored in the registry. For example, to determine whether to request a bit rate reduction, the video loss is compared to a video reduction loss threshold (YpercentLoss) and the audio loss is compared to an audio loss threshold (YpercentAudioLoss). To determine whether to request a bit rate increase, the video loss is compared to a video increase loss threshold (Mperfection). 
   Based upon the measured losses and the comparisons to the loss thresholds, the call parameters are adjusted in step  312 . For example, if the video loss is greater than the video reduction loss threshold (YpercentLoss) or the audio loss is greater than the audio loss threshold (YpercentAudioLoss), then a loss counter (lossCounter) is incremented. The loss counter indicates the number of consecutive intervals that have occurred in which either the video or audio loss exceeded a loss threshold. However, if the video loss is less than the video reduction loss threshold and the audio loss is less than the audio loss threshold, then the loss counter is decremented (but not below 0). In addition, if no rate decrease is needed because the video and audio losses are less than the loss thresholds, then the rate increase counter (Lincrease) remains enabled (Lcountlncrease is true) and the current value of the rate increase counter is maintained. For example, the value of the rate increase counter (Lincrease) is maintained at −1 until the first rate increase occurs. However, if a rate decrease is requested because the video loss or the audio loss exceeds a loss threshold, then the rate increase counter is disabled (by setting LCountIncrease to false) to freeze the rate increase counter (Lincrease) at its current value. 
   In addition, if the video loss is less than or equal to the video increase loss threshold (Mperfection), then a loss threshold counter (perfectCounter) is incremented. The loss threshold counter indicates the number of consecutive intervals that have occurred in which the video loss is less than or equal to the video increase loss threshold. If the video loss is greater than the video increase loss threshold, then the loss threshold counter is reset to zero. 
   From step  312  the method proceeds to step  314 . In step  314  a determination is made as to whether to request a reduction in the bit rate. A reduction in the bit rate is requested if the loss counter (lossCounter) is greater than a dynamic reduction threshold (Zthresh). The dynamic reduction threshold is based, in part, on the maximum estimated received bit rate. In one embodiment, the dynamic reduction threshold (Zthresh) is calculated according to the following formula:
 
 Z thresh=int(( P wrroot** a )+0.5)
 
where  a=t /(( r/ 1000)** v )
 
The int function rounds a value down to the nearest integer. The values for Pwrroot (Pwrroot), t (Tcoeff) and v (Vroot) are predetermined and are typically specified in the registry. The value for r is the maximum estimated bit rate, in bits per second. If the bit rate is lowered, then r is set to the reduced rate, so that subsequent estimated bit rates are compared to this lower rate. The value of the dynamic reduction threshold (Zthresh) increases as the bit rate decreases. This causes higher bit rate calls to request a reduced bit rate before lower bit rate calls. If a sending endpoint is transmitting to multiple receiving endpoints using different bit rates, then adjusting the dynamic reduction threshold causes the bit rates to even out over time instead of allowing a higher bit rate call to continue at a higher bit rate while reducing the bit rate of a lower bit rate call.
 
   The value of the dynamic reduction threshold (Zthresh) is modified to be equal to (Zthresh*QdecreaseWindow) for a number of intervals (Zthresh intervals) directly following any bit rate increase. Modifying the dynamic reduction threshold (Zthresh) following a bit rate increase ensures that the additional network bandwidth required by a request to increase the bit rate does not cause a reduction in the bit rates of other calls unless the other calls are operating at sufficiently high bit rates. This is accomplished by accepting losses for fewer intervals. In other words, if losses are detected for (Zthresh*QdecreaseWindow) intervals (instead of the usual Zthresh intervals) following an increase, then the endpoint that requested the increase will request a bit rate reduction. Thus, increases that fail are backed off, rather than forcing other endpoints to request reduction. The value of the QdecreaseWindow parameter is typically predetermined and specified in the registry. 
   If the determination in step  314  is to request a bit rate reduction, then the Yes branch is followed to step  324 . In step  324 , the receiving endpoint requests a reduced bit rate that is a predetermined percentage of the estimated received bit rate. In one embodiment, the percentage, (BRateDown) is specified in the registry. In response to receiving a request for a reduced bit rate, the sending endpoint reduces the bit rate. 
   However, if the determination in step  314  is that the loss counter (lossCounter) is less than a dynamic reduction threshold (Zthresh), then the method proceeds to step  316 . In step  316 , a determination is made as to whether the call parameters indicate that an increase in the bit rate should be considered. An increase in the bit rate is considered if the loss threshold counter (perfectCounter), exceeds a dynamic increase threshold (P+F). In one embodiment, P (pPerfect) is a predetermined number of sample intervals and F is a variable number of sample intervals. Typically, the value for P and the values needed to calculate F (pFinit, pFincInit, pFdecInit, pFmax, pFmin) are predetermined and are stored in the registry. 
   If the determination in step  316  is that a bit rate increase should be considered, then the Yes branch is followed to step  326 . In step  326 , additional call parameters are evaluated to determine whether to request a bit rate increase. If the determination is to request an increase in the bit rate, then a request to increase the bit rate is generated. Step  326  is discussed in more detail in connection with  FIG. 5 . 
   However, if the determination in step  316  is that a bit rate should not be considered, then the No branch is followed to step  320 . Step  320  can also be reached from steps  324  and  326 . In step  320 , a determination is made as to whether the call has ended. If the call has not ended, then the No branch is followed to step  310  and steps  310 – 326  are repeated. However, if the call has ended, then the Yes branch is followed to step  328  and the method ends. 
   Although  FIG. 3  illustrates that steps  314  and  316  are performed sequentially, those skilled in the art will appreciate that the steps can be performed in parallel or that the steps can be performed in a different order than that illustrated by  FIG. 3 . 
   Video Call Setup 
     FIG. 4  illustrates the steps of an exemplary method for setting up the video portion of a call.  FIG. 4  corresponds to step  304  of  FIG. 3 . From step  303  of  FIG. 3 , the method proceeds to step  402  and a CODEC is selected. Selecting a CODEC includes selecting an encoding scheme, as well as a bit rate. Typically, the available CODEC&#39;s are prioritized based on bit rate. For example, a particular encoding scheme is associated with a minimum bit rate. If the available bit rate is less than the minimum bit rate, then that encoding scheme is not selected. Once the CODEC is selected, then the method proceeds to step  404 . In step  404  a determination is made as to whether a new engine can be started. Typically, there is a limit to the number of engines that can be running simultaneously at a sending endpoint. The limit is predetermined and is typically stored in the registry. If a new engine can be started, then the Yes branch is followed from step  404  to step  414 . In step  414  a new engine is started using the encoding scheme and the bit rate determined in step  402 . The method then proceeds to step  306  of  FIG. 3 . 
   However, if the determination in step  404  is that a new engine cannot be started, then the No branch is followed to step  406 . In step  406  a determination is made as to whether a current engine is using the encoding scheme selected in step  402 . If a current engine is using the selected encoding scheme, then the Yes branch is followed to step  416 . In step  416  a determination is made as to whether the bit rate selected in step  402  is greater than or equal to the bit rate of the current engine. If the selected bit rate is greater than or equal to the bit rate of the current engine, then the Yes branch is followed to step  422 . In step  422  the current engine begins transmitting to the receiving endpoint using its current bit rate. The method then proceeds from step  422  to step  306  of  FIG. 3 . 
   However, if the determination in step  416  is that the selected bit rate is less than the bit rate of the current engine, then the No branch is followed to step  418 . In step  418  the bit rate of the current engine is reduced. If there are multiple engines currently running the selected encoding scheme, then the current engine having the lowest bit rate is the one that is reduced. The method then proceeds to step  422 . 
   If the determination in step  406  is that a current engine is not using the selected encoding scheme, then the No branch is followed to step  408 . In step  408  a determination is made as to whether at least two engines are currently running the same encoding scheme. If at least two engines are running the same encoding scheme, then the Yes branch is followed to step  410 . In step  410 , two of the engines that are using the same encoding scheme are consolidated. In particular, the receiving endpoint(s) for the engine having the next to the lowest bit rate is moved to the engine having the lowest bit rate. By moving the receiving endpoint(s), an engine becomes available and the method proceeds from step  410  to step  414 . The method then proceeds as above from step  414 . 
   If the determination in step  408  is that no two engines are using the same encoding scheme, then the No branch is followed to step  424  and the call is refused. If the call is refused, then the method proceeds to step  328  of  FIG. 3 . 
   Increasing the Bit Rate 
     FIG. 5  illustrates the steps of an exemplary method for increasing the bit rate.  FIG. 5  corresponds to step  326  of  FIG. 3 . If the Yes branch is followed from step  316 , then the method proceeds to step  500 . In step  500 , the rate increase counter (Lincrease) is examined to determine whether it indicates that a bit rate increase should be requested. If the rate increase counter is equal to −1 or is greater than or equal to the dynamic increase threshold (P+F), then the method proceeds to step  502  and the receiving endpoint requests a bit rate increase. The dynamic increase threshold includes a fixed number of intervals and a variable number of intervals. The fixed number of intervals, P, can be specified in the registry (pPerfect). The initial value for the variable number of intervals, F, can also be specified in the registry (pFinit). However, the variable number of intervals is modified during the call, as discussed below. In one embodiment, the increase is a predetermined percentage of the maximum received bit rate. The percentage (BRateUp) is typically stored in the registry. 
   The maximum received bit rate is computed for each sample interval. For example, at the end of the first sample interval, the maximum received bit rate is the estimated received bit rate for the first interval. At the end of the second interval, the maximum received bit rate is the maximum of the estimated received bit rate for the first interval and the second interval. The maximum received bit rate is updated for intervals where the loss is less than the video increase loss threshold (Mperfection). 
   From step  502  the method proceeds to step  504 . In step  504  the sending endpoint makes a determination as to whether all receiving endpoints for the engine have requested an increase. If all the receiving endpoints for the engine have requested an increase, then the method proceeds to step  506 . Otherwise, the method proceeds to step  508 . 
   In step  506  the sending endpoint increases the bit rate. Once the bit rate is increased, then the method proceeds from step  506  to step  508 . In step  508  the relevant call parameters are adjusted. The adjustments depend upon whether an increase occurred or not. For example, if a bit rate increase occurred, then in step  508 , the rate increase counter (Lincrease) is reset to zero, the rate increase counter is enabled (by setting Lcountlncrease to true), and the variable number of intervals (F) is adjusted. If F has reached a maximum (pFmax), then the number of intervals (F) is divided by two (unless pFdecInit is greater than two in which case it is divided by pFdecInit), but not lower than a minimum value (pFmin). Finally, the maximum received bit rate is reset to zero. 
   Dividing the variable number of intervals (F) once it has reached a maximum (pFmax), addresses the situation where the available bandwidth has been severely limited for a long time, but then suddenly bandwidth becomes available. The division of the variable number of intervals reduces the dynamic increase threshold (P+F) and allows the bit rate to be increased sooner. 
   If no bit rate increase takes place, then in step  508 , the rate increase counter is enabled (by setting LcountIncrease to true) to keep counting intervals since the last increase and the variable number of intervals (F) is multiplied by a multiplier (pFincInit). Multiplying F by pFincInit increases the dynamic increase threshold (P+F) so that interruptions in call quality from attempted bit rate increases become rare if there is insufficient bandwidth to honor the increase for a sustained period of time. Once the appropriate call parameters have been adjusted in step  508 , the method proceeds to step  320  of  FIG. 3 . 
   Alternative embodiments will be apparent to those skilled in the art to which the present invention pertains without departing from its spirit and scope. Accordingly, the scope of the present invention is described by the appended claims and is supported by the foregoing description.