Abstract:
Digital impairments in a set of Pulse Code Modulation (PCM) signal levels that are received at a client modem from a server modem are identified by compressing the set of PCM signal levels into a signature. Digital impairments are determined based on the signature. In a preferred embodiment, the PCM signal levels are compressed into a signature by identifying clusters and/or skips in the set of PCM signal levels. In particular, when transmitting PCM signal levels from a server modem to a client modem over a connection that is subject to digital impairments such as Robbed Bit Signaling (RBS) and/or PAD digital impairments and quantization, some adjacent PCM signal levels may become identical or very close to one another. Moreover, other adjacent signal levels may have a difference that is at least approximately twice the difference of other levels. The former phenomenon is referred to as a “cluster” and the latter phenomenon is referred to as a “skip”. By identifying clusters and/or skips in the set of PCM signals that are received at the client modem from the server modem, a signature of the network connection may be obtained. Digital impairments including RBS and/or PAD may be identified using the signature.

Description:
FIELD OF THE INVENTION 
     This invention relates to modems, and more particularly to start-up signals and sequences for modems. 
     BACKGROUND OF THE INVENTION 
     The demand for remote access to information sources and data retrieval, as evidenced by the success of services such as the World Wide Web, is a driving force for high-speed network access technologies. Today&#39;s telephone network offers standard voice services over a 4 kHz bandwidth. Traditional analog modem standards generally assume that both ends of a modem communication session have an analog connection to the Public Switched Telephone Network (PSTN). Because data signals are typically converted from digital to analog when transmitted towards the PSTN and then from analog to digital when received from the PSTN, data rates may be limited to 33.6 kbps as defined in the V.34 transmission recommendation developed by the International Telecommunications Union (ITU). 
     The need for an analog modem can be eliminated, however, by using the Basic Rate Interface (BRI) of the Integrated Services Digital Network (ISDN). A BRI offers end-to-end digital connectivity at an aggregate data rate of 160 kbps, which is comprised of two 64 kbps B channels, a 16 kbps D channel, and a separate maintenance channel. ISDN can offer comfortable data rates for Internet access, telecommuting, remote education services, and some forms of video conferencing. ISDN deployment, however, has been very slow due at least in part to the substantial investment for new equipment. Because ISDN presently is not very pervasive in the PSTN, the network providers have typically tarriffed ISDN services at relatively high rates, which may be ultimately passed on to the ISDN subscribers. In addition to the high service costs, subscribers must generally purchase or lease network termination equipment to access the ISDN. 
     While most subscribers do not enjoy end-to-end digital connectivity through the PSTN, the PSTN is nevertheless mostly digital. Typically, the only analog portion of the PSTN is the phone line or local loop that connects a subscriber or client modem (e.g., an individual subscriber in a home, office, or hotel) to the telephone company&#39;s Central Office (CO). In recent years, local telephone companies have been replacing portions of their original analog networks with digital switching equipment. Nevertheless, the connection between the home and the CO generally has been the slowest to change to digital as discussed in the foregoing with respect to ISDN BRI service. 
     A recent data transmission recommendation issued by the ITU, known as V.90, takes advantage of the digital conversions that have been made in the PSTN. By viewing the PSTN as a digital network, V.90 technology is able to accelerate data downstream from the Internet or other information source to a subscriber&#39;s computer at data rates of up to 56 kbps, even when the subscriber is connected to the PSTN via an analog local loop. 
     To understand how the V.90 recommendation achieves this higher data rate, it may be helpful to briefly review the operation of V.34 analog modems. V.34 modems are optimized for the situation where both ends of a communication session are connected to the PSTN by analog lines. Even though most of the PSTN is digital, V.34 modems treat the network as if it were entirely analog. Moreover, the V.34 recommendation assumes that both ends of the communication session suffer impairment due to quantization noise introduced by analog-to-digital converters. That is, the analog signals transmitted from the V.34 modems are sampled at 8000 times per second by a codec upon reaching the PSTN, with each sample being represented or quantized by an eight-bit pulse code modulation (PCM) codeword. The codec uses 256, non-uniformly spaced, PCM quantization levels defined according to either the μ-law or A-law companding standard (i.e. the ITU G.711 Recommendation). 
     Because the analog waveforms are continuous and the binary PCM codewords are discrete, the digits that are sent across the PSTN can only approximate the original analog waveform. The difference between the original analog waveform and the reconstructed quantized waveform is called quantization noise, which can limit the modem data rate. 
     While quantization noise may limit a V.34 communication session to 33.6 kbps, it nevertheless affects only analog-to-digital conversions. The V.90 standard relies on the lack of analog-to-digital conversions in the downstream path, outside of the conversion made at the subscriber&#39;s modem, to enable transmission at 56 kbps. 
     The general environment for which the V.90 standard was developed is depicted in FIG.  1 . An Internet Service Provider (ISP)  22  is connected to a subscriber&#39;s computer  24  via a V.90 digital server modem  26 , through the PSTN  28  via digital trunks (e.g., T1, E1 and/or ISDN Primary Rate Interface (PRI) connections), through a central office switch  32 , and finally through an analog loop to the client modem  34 . The central office switch  32  is drawn outside of the PSTN  28  to better illustrate the connection of the subscriber&#39;s computer  24  and modem  34  into the PSTN  28 . It should be understood that the central office  32  generally is, in fact, a part of the PSTN  28 . Operation of a communication session between the subscriber  24  and an ISP  22  is best described with reference to the more detailed block diagram of FIG.  2 . 
     Referring to FIG. 2, transmission from the server modem  26  to the client modem  34  will be described first. The information to be transmitted is first encoded using only the 256 PCM codewords used by the digital switching and transmission equipment in the PSTN  28 . These PCM codewords are transmitted towards the PSTN by the PCM transmitter  36  where they are received by a network codec. 
     The PCM data is then transmitted through the PSTN  28  until reaching the central office  32  to which the client modem  34  is connected. Before transmitting the PCM data to the client modem  34 , the data is converted from its current form as either μ-law or A-law companded PCM codewords to Pulse Amplitude Modulated (PAM) voltages by the codec expander (digital-to-analog (D/A) converter)  38 . These PAM voltage levels are processed by a central office hybrid  42  where the unidirectional signal received from the codec expander  38  is transmitted towards the client modem  34  as part of a bidirectional signal. A second hybrid  44  at the subscriber&#39;s analog telephone connection converts the bidirectional signal back into a pair of unidirectional signals. 
     Finally, the analog signal from the hybrid  44  is converted into digital PAM samples by an analog-to-digital (A/D) converter  46 , which are received and decoded by the PAM receiver  48 . Note that for transmission to succeed effectively at 56 kbps, there should be only a single digital-to-analog conversion and subsequent analog-to-digital conversion between the server modem  26  and the client modem  34 . Recall that analog-to-digital conversions in the PSTN  28  can introduce quantization noise, which may limit the data rate as discussed hereinbefore. The A/D converter  46  at the client modem  34 , however, may have a higher resolution than the A/D converters used in the analog portion of the PSTN  28  (e.g. 16 bits versus 8 bits), which results in less quantization noise. Moreover, the PAM receiver  48  preferably is in synchronization with the 8 kHz network clock to properly decode the digital PAM samples. 
     Transmission from the client modem  34  to the server modem  26  follows the V.34 data transmission standard. That is, the client modem  34  includes a V.34 transmitter  52  and a D/A converter  54  that encode and modulate the digital data to be sent using techniques such as Quadrature Amplitude Modulation (QAM). The hybrid  44  converts the unidirectional signal from the digital-to-analog converter  54  into a bidirectional signal that is transmitted to the central office  32 . Once the signal is received at the central office  32 , the central office hybrid  42  converts the bidirectional signal into a unidirectional signal that is provided to the central office codec. This unidirectional, analog signal is converted into either μ-law or A-law companded PCM codewords by the codec compressor (A/D converter)  56 , which are then transmitted through the PSTN  28  until reaching the server modem  26 . The server modem  26  includes a conventional V.34 receiver  58  for demodulating and decoding the data sent by the V.34 transmitter  52  in the client modem  34 . Thus, data is transferred from the client modem  34  to the server modem  26  at data rates of up to 33.6 kbps as provided for in the V.34 standard. 
     Thus, the V.90 standard offers increased data rates (e.g., data rates up to 56 kbps) in the downstream direction from a server to a subscriber or client. Upstream communication still generally takes place at conventional data rates as provided for in the V.34 standard. Nevertheless, this asymmetry is particularly well suited for Internet access. For example, when accessing the Internet, high bandwidth generally is most useful when downloading large text, video, and audio files to a subscriber&#39;s computer. Using V.90, these data transfers can be made at up to 56 kbps. On the other hand, traffic flow from the subscriber to an ISP generally includes mainly keystroke and mouse commands, which are readily handled by the conventional rates provided by V.34. 
     As described above, the digital portion of the PSTN  28  transmits information using eight-bit PCM codewords at a frequency of 8000 Hz. Thus, it would appear that downstream transmission should take place at 64 kbps rather than 56 kbps as defined by the V.90 standard. While 64 kbps is a theoretical maximum, several factors may prevent actual transmission rates from reaching this ideal rate. First, even though the problem of quantization error can be substantially eliminated by using PCM encoding and PAM for transmission, additional noise in the network or at the subscriber premises, such as non-linear distortion and crosstalk, can limit the maximum data rate. Furthermore, the μ-law or A-law companding techniques generally do not use uniform PAM voltage levels for defining the PCM codewords. The PCM codewords representing very low levels of sound have PAM voltage levels spaced close together. Noisy transmission facilities can prevent these PAM voltage levels from being distinguished from one another thereby causing loss of data. Accordingly, to provide greater separation between the PAM voltages used for transmission, not all of the 256 PCM codewords may be used. 
     It is generally known that, assuming a convolutional coding scheme, such as trellis coding, is not used, the number of symbols to transmit a certain data rate is given by Equation 1: 
     
       
         bps=R s log 2 N s   EQ. 1 
       
     
     where bps is the data rate in bits per second, R s  is the symbol rate, and N s  is the number of symbols in the signaling alphabet or constellation. To transmit at 56 kbps using a symbol rate of 8000, Equation 1 can be rewritten to solve for the number of symbols required as set forth below in Equation 2: 
     
       
           N   s =2 56000/8000 =128  EQ. 2 
       
     
     Thus, the 128 most robust codewords of the 256 available PCM codewords generally are chosen for transmission as part of the V.90 standard. 
     Successful operation of a V.90 receiver may depend on an accurate identification of the reference PAM signaling levels that are often called the signaling alphabet or the signal constellation. The digital samples that are filtered by a decision feedback equalizer are provided to a slicer/detector where the samples are compared against the signaling alphabet. A determination is made with regard to which member of the alphabet or which point in the constellation the digital sample falls closest to. Once the alphabet member is identified, the PCM code word corresponding to that alphabet member is selected as the symbol transmitted for that digital sample. 
     While a set of ideal signaling levels can be defined for the signaling alphabet, the effective alphabet typically will deviate from these ideal levels because of underlying digital impairments resulting from Robbed Bit Signaling (RBS) and/or digital attenuation PADs. RBS is a mechanism utilized in the digital transport system, such as a T1 trunk, for signal control and status information between network equipment. PAD is similarly found in the digital transport system for the purpose of adjusting signal levels for different analog and digital equipment. Since these impairments will likely be chronic throughout the communication session, it may be more efficient for the modem to learn a new signaling alphabet that takes these impairments into account. 
     Accordingly, the V.90 standard specifies that during Phase 3 of the startup procedure that is carried out after establishing a dialed connection between the client and server modems, digital impairment learning will take place. During digital impairment learning, a plurality of sets of DIL signals, each corresponding to a set of PCM signals, is repeatedly transmitted from a server modem to a client modem during a corresponding plurality of DIL intervals, also referred to as framing intervals. For example, six DIL intervals may be provided during which all or a selected subset of the PCM levels for the constellation are transmitted. The plurality of DIL intervals may be repeated until the RBS and PAD digital impairments are identified. The PAD and RBS digital impairments so identified are then used in the Phase 4 final training procedures for the V.90 modem. 
     Unfortunately, the identification of RBS and PAD digital impairments may be difficult because of the many types of RBS and the many levels of PAD digital impairments that may be present in a telephone network. RBS and PAD identification also may be difficult due to the combinations of one or more PADs and/or RBS that may be present in a given network. 
     For example, RBS can manifest itself when the Least Significant Bit (LSB) of a PCM code word in a particular DIL interval is forced to a one. This operation has the effect of collapsing neighboring PCM code words with even and odd values into the odd value PCM code word. Other types of RBS variations are possible, and different DIL intervals may be subject to different types of RBS. 
     The effect of PADs generally is present in all six DIL intervals. A PAD also can result in multiple PCM code words collapsing into a single code word. Although this may not cause a problem for voice transmission, it may produce great difficulty for data transmission. PADs generally are not standardized and several quantization rules can be used for implementing a given PAD attenuation. 
     Accordingly, it is desirable to provide improved systems, methods and/or computer program products for identifying RBS and PAD digital impairments in the DIL signals that are repeatedly transmitted from a server modem to a client modem during a corresponding plurality of DIL intervals. 
     SUMMARY OF THE INVENTION 
     Systems, methods and computer program products according to the invention can identify digital impairments in a set of Pulse Code Modulation (PCM) signal levels that are received at a client modem from a server modem, by compressing the set of PCM signal levels into a signature. Digital impairments are determined based on the signature. In a preferred embodiment, the PCM signal levels are compressed into a signature by identifying clusters and/or skips in the set of PCM signal levels. A digital impairment in the set of PCM signal levels is determined based on the clusters and/or skips so identified. 
     The invention stems from a realization that when transmitting PCM signal levels from a server modem to a client modem over a connection that is subject to digital impairments such as Robbed Bit Signaling (RBS) and/or PAD digital impairments, and also is subject to quantization, some adjacent PCM signal levels may become identical or very close to one another. Moreover, other adjacent signal levels may have a difference that is at least approximately twice the difference of other levels. The former phenomenon is referred to as a “cluster” and the latter phenomenon is referred to as a “skip”. By identifying clusters and/or skips in the set of PCM signals that are received at the client modem from the server modem, a signature of the network connection may be obtained. Digital impairments including RBS and/or PAD may be identified using the signature. 
     More specifically, according to the invention, clusters and/or skips in the set of PCM signal levels that are received at the client modem from the server modem are counted. The digital impairment then may be determined based on the counts of the clusters and/or skips. A listing of cluster and/or skip counts for a plurality of digital impairment scenarios may be obtained. The clusters and/or skips that are counted in the set of PCM signal levels that are received at the client modem are compared to the listings of cluster and/or skip counts for the plurality of digital impairment scenarios, preferably to identify a closest match. The listings of clusters and/or skips may be obtained by computing cluster counts and/or skip counts for an ideal set of PCM signal levels that is subject to a digital impairment scenario and quantization. 
     In identifying clusters and/or skips, not all the PCM signal levels need be investigated. Rather, only a subset of the set of PCM signal levels may be investigated, wherein the lowest levels may be discarded to reduce the effect of random noise, and the highest levels may be discarded to reduce the effect of nonlinear distortions. Moreover, in identifying a cluster, identical signals need not be identified. Rather, adjacent PCM signal levels that are within a first threshold of one another may be identified. Similarly, in order to identify skips, adjacent signals having a space therebetween that is at least twice the average need not be identified. Rather, adjacent signal levels that are at least a second threshold apart from one another may be identified. 
     In preferred embodiments of the invention, cluster and/or skip counting is performed on a plurality of sets of Digital Impairment Learning (DIL) signals that repeatedly are transmitted from the server modem to the client modem over a corresponding plurality of DIL intervals. The clusters and/or skips may be counted in the plurality of sets of DIL signals and counts for clusters and/or skips for at least two of the DIL intervals may be averaged. 
     In preferred embodiments that can identify RBS and/or PAD digital impairments, the DIL intervals that are not subject to RBS may be determined based on the cluster and/or skip counts. Then, the counts of clusters and/or skips for the DIL intervals that are not subject to RBS may be averaged. PAD impairments then may be determined from the average counts of clusters and/or skips. 
     The present invention can efficiently identify digital impairments because it can base the identification on a compressed signature of the PCM signal levels, that preferably is derived from clusters and/or skips therein, rather than manipulating the entire set of PCM signal levels to identify digital impairments. Moreover, the present invention need not rely on a priori knowledge of a precise network model of the digital impairments. Rather, when an unknown network model is encountered, digital impairments may be identified by identifying the closest known network signature based on clusters and/or skips, and/or by interpolating between a range of known network signatures based on clusters and skips. It also will be understood that the present invention may be provided as modem-related systems, methods and/or computer program products. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a conventional network using client and server modems. 
     FIG. 2 is a more detailed block diagram of a network of FIG.  1 . 
     FIG. 3 is a block diagram of a client modem according to an embodiment of the present invention. 
     FIG. 4 is a flowchart illustrating operations for identifying digital impairments according to an embodiment of the present invention. 
     FIG. 5 is a flowchart illustrating operations for determining digital impairments based on counts of clusters and/or skips according to an embodiment of the present invention. 
     FIG. 6 is a flowchart illustrating operations for calculating cluster and skip counts in one mapping interval according to an embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like reference numbers signify like elements throughout the description of the figures. 
     As will be appreciated by those skilled in the art, the present invention can be embodied as a method, a digital signal processing system, and/or a computer program product. Accordingly, the present invention can take the form of an entirely hardware embodiment, an entirely software (including firmware, resident software, micro-code, etc.) embodiment, or an embodiment containing both software and hardware aspects. Furthermore, the present invention can take the form of a computer program product on a computer-usable or computer-readable storage medium having computer-usable program code embodied in the medium for use by or in connection with an instruction execution system. In the context of this document, a computer-usable or computer-readable medium can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. 
     The computer-usable or computer-readable medium can be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. More specific examples (a nonexhaustive list) of the computer-readable medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a Random Access Memory (RAM), a Read-Only Memory (ROM), an Erasable Programmable Read-Only Memory (EPROM or Flash memory), an optical fiber, and a portable Compact Disc Read-Only Memory (CD-ROM). Note that the computer-usable or computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory. 
     Computer program code for carrying out operations of the present invention may be written in a high level programming language such as C or C++. Nevertheless, some modules or routines may be written in assembly or machine language to optimize speed, memory usage, or layout of the software or firmware in memory. Assembly language may be used to implement time-critical code segments. In a preferred embodiment, the present invention uses assembly language to implement most software programs. It should further be understood that the program code for carrying out operations of the present invention may also execute entirely on a client modem, partly on a client modem, partly on a client modem and partly on a server modem, or partly in a client modem, partly in a server modem, and partly in the PSTN. 
     High Level Description 
     Referring now to FIG. 3, a block diagram of a client modem  60  according to the present invention is shown. The client modem  60  includes a processor  134 , preferably a digital signal processor, which communicates with a memory  136  via an address/data bus  138 . In addition, the processor  134  can receive and transmit information to external devices via a communication interface  142 , which is accessed through input/output (I/O) bus  144 . The processor  134  can be any commercially available or custom processor, preferably suitable for a real-time intensive embedded application. 
     The memory  136  is representative of the overall hierarchy of memory devices containing the software and data used to implement the functionality of the V.90 client modem  60 . The memory  136  can include, but is not limited to, the following types of devices: cache, ROM, PROM, EPROM, EEPROM, flash, SRAM, and DRAM. As shown in FIG. 3, the memory  136  can include program modules for implementing the functionality of the components of the client modem  60 . Preferably, the memory  136  can include a data rate selector program module  146 , a polyphase interpolator program module  148 , a clock synchronizer program module  152 , a severe error detector program module  154 , an echo canceller program module  156 , a slicer program module  158 , and a Decision Feedback Equalizer (DFE) program module  162 . The slicer program module  158  and the DFE program module  162  preferably include a decision training program sub-module  164  and a reference training program sub-module  166  respectively, which are used for signaling alphabet identification. These program modules and sub-modules can operate independent of the present invention, and need not be described further herein. 
     The memory  136  further includes a startup program module  168  which implements the multi-phase startup protocol defined in the V.90 recommendation. More specifically, the startup program module  168  includes a Phase 1: Network Interaction module  172  and a Phase 2: Channel Probing and Ranging module  174 . These modules are described in the V.90 standard, and need not be described further herein. As also shown in FIG. 3, a Phase 3: Equalizer and Echo Canceller Training and Digital Impairment Learning module  176  is provided. As will be described in detail below, the present invention can provide improved digital impairment learning for the Phase 3 module  176 . Finally, a Phase 4: Final Training module  178  is provided, as is described in the V.90 specification. Other modules also may be included in the startup program  168 , which need not be described in detail herein. 
     The present invention is described with reference to block diagrams and flowchart illustrations of methods, apparatus (systems), and computer program products according to an embodiment of the invention. It will be understood that each block of the block diagrams and flowchart illustrations, and combinations of blocks, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the block or blocks. 
     These computer program instructions may also be stored in a computer-usable or computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-usable or computer-readable memory produce an article of manufacture including instruction means that implement the function specified in the block or blocks. 
     The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions that execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the block or blocks. 
     During startup of a V.90 modem, the analog modem receiver performs signaling alphabet identification. This can be performed, for example, during DIL signal reception, in which pre-specified signal levels are received in each of a plurality, such as six, of DIL intervals. The learned signal levels (and the corresponding ucodes) may be stored in memory for use in determining the combination of digital impairments present in the network. The digital impairments of interest include PADs and RBS impairments. The PAD level and the type of RBS can also be determined. 
     In the digital network, the PAD and RBS impairments can be encountered in a variety of combinations, which can change from connection to connection. In a particular DIL interval, one can encounter no PAD and no RBS, RBS only, PAD only, RBS followed by PAD, PAD followed by RBS, RBS followed by PAD followed by RBS and/or multiple PADs with possible RBS before, between, and/or after PADs. Multiple PADs also are referred to as tandem PADs. Note that typically, PADs affect all six DIL intervals in the same manner, while different RBS types can be present in different DIL intervals. 
     The present invention stems from a realization that clusters and/or skips in the PCM signal levels may be used to provide a compressed signature of digital impairments including RBS and PAD in a connection between a client modem and a server modem. PCM codes and corresponding analog levels used in the telephone network are defined in ITU Standard G.711. Digital impairments generally involve many mapping rules of PCM codes from one level to another. According to the invention, when mapping these codes after digital impairment, some adjacent codes become identical or close to one another to define a cluster, and the spaces between some of the codes are about twice or about three or more times the expected value to define a skip. The present invention uses these clusters and/or skips, and preferably counts of clusters and skips, to define a signature for the digital impairment. 
     For example, Table 1 provides the mapping results of ucodes 1 to 108 with 0 dB (original ucodes), 3 dB and 6 dB PAD. Table 1 shows that there are some spaces that drop to zero, for example between codes 77 and 78 in the 3 dB case, and codes 44 and 45 in the 6 dB case. Moreover, some spaces become twice the normal expectation, for example codes 83 and 84 in the 3 dB case. In Table 1, clusters are identified by brackets to the right of the values, whereas skips are identified by brackets to the left of the values. As shown in Table 1, there are twelve clusters and eleven skips in the 3 dB PAD case, and four clusters and no skips in the 6 dB PAD case from codes 32 to 108. By definition, there are no clusters or skips in the 0 dB case. Thus, different PADs may have different numbers of cluster and/or skip counts. Therefore, the count information may be used to classify the digital impairments in the network. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Ucode level 
                 0 dB 
                 3 dB 
                 6 Db 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 1 
                 8 
                 12┐ 
                 16┐ 
               
               
                   
                 2 
                 16 
                 12┘ 
                 16┘ 
               
               
                   
                 3 
                 24 
                 23 
                 32┐ 
               
               
                   
                 4 
                 32 
                 35 
                 32┘ 
               
               
                   
                 5 
                 40 
                 46┐ 
                 48┐ 
               
               
                   
                 6 
                 48 
                 46┘ 
                 48┘ 
               
               
                   
                 7 
                 56 
                 58 
                 64┐ 
               
               
                   
                 8 
                 64 
                 69┐ 
                 64┘ 
               
               
                   
                 9 
                 72 
                 69┘ 
                 80┐ 
               
               
                   
                 10 
                 80 
                 81 
                 80┘ 
               
               
                   
                 11 
                 88 
                 92 
                 96┐ 
               
               
                   
                 12 
                 96 
                 104┐ 
                 96┘ 
               
               
                   
                 13 
                 104 
                 104┘ 
                 112┐ 
               
               
                   
                 14 
                 112 
                 115 
                 112┘ 
               
               
                   
                 15 
                 120 
                 127 
                 128┐ 
               
               
                   
                 16 
                 132 
                 138 
                 128┘ 
               
               
                   
                 17 
                 148 
                 ┌150 
                 144 
               
               
                   
                 18 
                 164 
                 └173 
                 160 
               
               
                   
                 19 
                 180 
                 190┐ 
                 176 
               
               
                   
                 20 
                 196 
                 190┘ 
                 192 
               
               
                   
                 21 
                 212 
                 213 
                 208 
               
               
                   
                 22 
                 228 
                 236 
                 224 
               
               
                   
                 23 
                 244 
                 259┐ 
                 240 
               
               
                   
                 24 
                 260 
                 259┘ 
                 264┐ 
               
               
                   
                 25 
                 276 
                 282 
                 264┘ 
               
               
                   
                 26 
                 292 
                 305┐ 
                 296┐ 
               
               
                   
                 27 
                 308 
                 305┘ 
                 296┘ 
               
               
                   
                 28 
                 324 
                 328 
                 328┐ 
               
               
                   
                 29 
                 340 
                 351 
                 328┘ 
               
               
                   
                 30 
                 356 
                 374┐ 
                 360┐ 
               
               
                   
                 31 
                 372 
                 374┘ 
                 360┘ 
               
               
                   
                 32 
                 396 
                 ┌397 
                 392 
               
               
                   
                 33 
                 428 
                 └443 
                 424 
               
               
                   
                 34 
                 460 
                 ┌466 
                 456 
               
               
                   
                 35 
                 492 
                 └513 
                 489 
               
               
                   
                 36 
                 524 
                 536 
                 521 
               
               
                   
                 37 
                 556 
                 570 
                 553 
               
               
                   
                 38 
                 588 
                 616┐ 
                 585 
               
               
                   
                 39 
                 620 
                 616┘ 
                 617 
               
               
                   
                 40 
                 652 
                 662 
                 649 
               
               
                   
                 41 
                 684 
                 708┐ 
                 681 
               
               
                   
                 42 
                 716 
                 708┘ 
                 713 
               
               
                   
                 43 
                 748 
                 754 
                 745 
               
               
                   
                 44 
                 780 
                 800 
                 793┘ 
               
               
                   
                 45 
                 812 
                 847┐ 
                 793┘ 
               
               
                   
                 46 
                 844 
                 847┘ 
                 857┌ 
               
               
                   
                 47 
                 876 
                 893 
                 857┘ 
               
               
                   
                 48 
                 924 
                 939 
                 921 
               
               
                   
                 49 
                 988 
                 ┌985 
                 985 
               
               
                   
                 50 
                 1052 
                 └1077 
                 1049 
               
               
                   
                 51 
                 1116 
                 ┌1123 
                 1113 
               
               
                   
                 52 
                 1180 
                 └1215 
                 1177 
               
               
                   
                 53 
                 1244 
                 1261 
                 1241 
               
               
                   
                 54 
                 1308 
                 1330 
                 1305 
               
               
                   
                 55 
                 1372 
                 1422┐ 
                 1369 
               
               
                   
                 56 
                 1436 
                 1422┘ 
                 1434 
               
               
                   
                 57 
                 1500 
                 1515 
                 1498 
               
               
                   
                 58 
                 1564 
                 1607 
                 1562 
               
               
                   
                 59 
                 1628 
                 1699┐ 
                 1626 
               
               
                   
                 60 
                 1692 
                 1699┘ 
                 1690 
               
               
                   
                 61 
                 1756 
                 1791 
                 1754 
               
               
                   
                 62 
                 1820 
                 1883┐ 
                 1850┐ 
               
               
                   
                 63 
                 1884 
                 1883┘ 
                 1850┘ 
               
               
                   
                 64 
                 1980 
                 ┌1975 
                 1978 
               
               
                   
                 65 
                 2108 
                 └2160 
                 2106 
               
               
                   
                 66 
                 2236 
                 ┌2252 
                 2234 
               
               
                   
                 67 
                 2364 
                 └2436 
                 2363 
               
               
                   
                 68 
                 2492 
                 ┌2528 
                 2491 
               
               
                   
                 69 
                 2620 
                 └2712 
                 2619 
               
               
                   
                 70 
                 2748 
                 2851┐ 
                 2747 
               
               
                   
                 71 
                 2876 
                 2851┘ 
                 2875 
               
               
                   
                 72 
                 3004 
                 3035 
                 3003 
               
               
                   
                 73 
                 3132 
                 3219 
                 3131 
               
               
                   
                 74 
                 3260 
                 3403┐ 
                 3259 
               
               
                   
                 75 
                 3388 
                 3403┘ 
                 3388 
               
               
                   
                 76 
                 3516 
                 3588 
                 3516 
               
               
                   
                 77 
                 3644 
                 3772┐ 
                 3644 
               
               
                   
                 78 
                 3772 
                 3772┘ 
                 3772 
               
               
                   
                 79 
                 3900 
                 3956 
                 3964 
               
               
                   
                 80 
                 4092 
                 ┌4141 
                 4220 
               
               
                   
                 81 
                 4348 
                 └4509 
                 4477 
               
               
                   
                 82 
                 4604 
                 4693 
                 4733 
               
               
                   
                 83 
                 4860 
                 ┌4878 
                 4989 
               
               
                   
                 84 
                 5116 
                 └5246 
                 5246 
               
               
                   
                 85 
                 5372 
                 5431 
                 5502 
               
               
                   
                 86 
                 5628 
                 5615 
                 5758 
               
               
                   
                 87 
                 5884 
                 5891 
                 6014 
               
               
                   
                 88 
                 6140 
                 6260 
                 6271 
               
               
                   
                 89 
                 6396 
                 6628┐ 
                 6527 
               
               
                   
                 90 
                 6652 
                 6628┘ 
                 6783 
               
               
                   
                 91 
                 6908 
                 6997 
                 7039 
               
               
                   
                 92 
                 7164 
                 7365 
                 7296 
               
               
                   
                 93 
                 7420 
                 7734┐ 
                 7552 
               
               
                   
                 94 
                 7676 
                 7734┘ 
                 7808┐ 
               
               
                   
                 95 
                 7932 
                 8103 
                 7808┘ 
               
               
                   
                 96 
                 8316 
                 8471 
                 8193 
               
               
                   
                 97 
                 8828 
                 ┌8840 
                 8705 
               
               
                   
                 98 
                 9340 
                 └9577 
                 9218 
               
               
                   
                 99 
                 9852 
                 ┌9945 
                 9730 
               
               
                   
                 100 
                 10364 
                 └10683 
                 10243 
               
               
                   
                 101 
                 10876 
                 11051 
                 10755 
               
               
                   
                 102 
                 11388 
                 11420 
                 11268 
               
               
                   
                 103 
                 11900 
                 11973 
                 11780 
               
               
                   
                 104 
                 12412 
                 12710 
                 12293 
               
               
                   
                 105 
                 12924 
                 13447┐ 
                 12806 
               
               
                   
                 106 
                 13436 
                 13447┘ 
                 13318 
               
               
                   
                 107 
                 13948 
                 14184 
                 13831 
               
               
                   
                 108 
                 14460 
                 14921 
                 14343 
               
               
                   
                   
               
             
          
         
       
     
     FIG. 4 is a flowchart illustrating overall systems, methods and computer program products for identifying digital impairments according to an embodiment of the invention. Although the digital impairments may be identified in any set of PCM signals that are received at a client modem from a server modem, they preferably are identified in a plurality of sets of DIL signals that are repeatedly transmitted from the server modem to the client modem over a corresponding plurality of DIL intervals. 
     As shown at Block  410 , the number of clusters and/or skips in the received DIL levels are counted or accumulated. In particular, the spacing between points in the G.711 curves may be identified in all six DIL intervals. All of the DIL levels may be analyzed. However, preferably, codes of less than 32 and of more than 108 may be discarded so as not to consider codes that are unduly affected by noise or nonlinear distortion, respectively. When analyzing the spacing between adjacent DIL levels, it can be determined when the spacing suddenly drops to close to zero, which can cause the cluster count to increment, and when the spacing suddenly jumps to about twice or more the normal spacing, which can cause the skip count to increment. The spacing may suddenly drop to close to zero because two G.711 points collapse on top of one another due to a digital impairment such as a PAD. The spacing suddenly may become twice or more the normal spacing due to one or more missing G.711 points, for example due to a digital impairment. 
     Then, referring to Block  420 , the digital impairment is determined based on the counts of clusters and/or skips. More specifically, a small set of lists or tables with skip and cluster counts may be computed based on noise-free compression of the G.711 curve, for example corresponding to single and tandem PADs with 0.25 dB spacing from 0 to 12 dB, and all permutations of PADs from 2 to 6 dB with 1 dB spacing. Examples of these lists or tables will be shown below. Examination of these tables indicates that when PADs increase by 0.25 dB steps, there generally is only a small change in the skip and cluster count values. Stated differently, a “continuum” may be produced. Accordingly, if a PAD is encountered somewhere between the 0.25 dB spaced table entries, an interpolation or other technique may be used to determine the closest PAD. Thus, the skip counts and/or cluster counts may be less sensitive to variations between adjacent PAD levels compared to distance-based approaches for determining unknown PADs. The reason the skip and/or cluster counts may be less sensitive to these variations may be due to compressing the G.711 curve into a signature. As the curve is compressed with one PAD, for example 2.8 dB and compared to an ideal model skip and cluster count for 3 dB, it may be found that the signatures are quite close compared to, for example, a 5 dB or 6 dB PAD. 
     Each of the DIL intervals, for example six DIL intervals, can have its own associated skip and cluster count. Thus, the skip and cluster counts in the DIL intervals may be compared to one another. When two intervals have identical skip and cluster counts, an averaging function can average these two intervals together. If more than two intervals have identical skip and cluster counts, all of them can be averaged together, which can reduce the noise or variance in the DIL levels. A detailed approach for combining the skip and/or cluster counts in the received DIL intervals will be described below. 
     A more detailed description of operations to count the number of clusters and/or skips in the received DIL levels (Block  410  of FIG. 4) now will be provided. In particular, although all of the received DIL levels may be examined in order to determine a count of clusters and/or skips, preferably only a subset of the DIL levels are processed to identify clusters and/or skips. In particular, due to noise in the network, codes can be distorted so that two PCM codes may become closer or farther apart than the ideal case. The small (lower value) PCM codes may be relatively more sensitive to noise, so that cluster and/or skip values may be less indicative of the signature of the digital impairments and more indicative of noise. Accordingly, a lower bound of PCM code may be set to reduce and preferably eliminate those PCM codes that may be unduly influenced by noise. 
     At the upper PCM codes, distortions may be introduced due to saturation over the network. Moreover, these codes may be used sparingly. Accordingly, an upper bound preferably also is set to reduce and preferably eliminate these upper codes that may be unduly influenced by saturation or other factors. In a preferred embodiment, an upper limit u of 108 and a lower limit 1 of 32 may be set. 
     Referring now to FIG. 5, more detailed operations for determining digital impairments based on counts of clusters and/or skips (Block  420  of FIG. 4) now will be described. As shown in FIG. 5, at Block  510 , a table of expected cluster and skip counts is constructed for various PAD values. Then at Block  520 , RBS and non-RBS intervals are determined. At Block  530 , cluster and skip counts are averaged for the non-RBS intervals. Finally, at Block  540 , the cluster and skip counts are compared to the values in the table, in order to determine the digital impairment. Each of Blocks  510 - 540  now will be described in greater detail. 
     Referring again to Block  510 , a table of expected cluster and/or skip counts is constructed for various PAD values. It will be understood that the table may be constructed offline and the resulting tables may be stored in the modem. 
     Alternatively, tables may be constructed in the modem as needed. The table may be constructed using the following processing: 
     select PAD range (PAD_start to PAD_end) and step size (PAD_step) 
     initialize x_lin=all PCM codes from G.711 
     for P=PAD_start to PAD_end increment PAD_step { 
     transmit x_lin to new PCM code with pad P, 
     x_new=x_lin*10{circumflex over ( )}(−P/20) 
     quantize the resulting PCM code to the nearest PCM code, 
     x_output=Quant(x_new) 
     compute counts of cluster and skip in the final PCM code between upper and lower limits. 
     } 
     Table 2 illustrates ideal cluster counts of a single PAD with no RBS, from 0.25 dB to 12 dB in 0.25 dB increments: 
     
       
         
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 PAD Range 
                 Cluster Counts (0.25 dB increments) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0.25-3 db 
                  5 
                  5 
                  6 
                  5 
                  8 
                  9 
                 10 
                 11 
                 10 
                 13 
                 11 
                 12 
               
               
                 3.25-6 Db 
                 14 
                 11 
                 11 
                 11 
                 10 
                  9 
                 10 
                  8 
                  7 
                  6 
                  4 
                  4 
               
               
                 6.25-9 dB 
                  4 
                  5 
                  6 
                  8 
                 10 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 15 
               
               
                 9.25-12 db 
                 16 
                 16 
                 16 
                 16 
                 15 
                 15 
                 15 
                 14 
                 13 
                 13 
                 13 
                 12 
               
               
                   
               
             
          
         
       
     
     Table 3 illustrates ideal skip counts of single PAD with no RBS, from 0.25 dB to 12 dB in 0.25 dB increments: 
     
       
         
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 PAD Range 
                 Skip Counts (0.25 dB increments) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0.25-3 db 
                  4 
                  4 
                 6 
                  4 
                 7 
                 7 
                 9 
                 10 
                 9 
                 12 
                 9 
                 11 
               
               
                 3.25-6 Db 
                 12 
                 10 
                 9 
                 10 
                 8 
                 7 
                 8 
                  6 
                 5 
                  3 
                 0 
                  0 
               
               
                 6.25-9 dB 
                  0 
                  1 
                 1 
                  2 
                 4 
                 4 
                 4 
                  5 
                 6 
                  6 
                 7 
                  6 
               
               
                 9.25-12 db 
                  7 
                  7 
                 6 
                  7 
                 5 
                 5 
                 5 
                  4 
                 2 
                  3 
                 2 
                  1 
               
               
                   
               
             
          
         
       
     
     Table 4 illustrates ideal cluster counts of a tandem PAD with no RBS, from 2 dB to 6 dB in 1 dB increments: 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 2 
                 3 
                 4 
                 5 
                 6 dB 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 2dB+ 
                 19 
                 15 
                 15 
                 12 
                 12 
               
               
                   
                 3dB+ 
                 18 
                 18 
                 15 
                 16 
                 15 
               
               
                   
                 4dB+ 
                 16 
                 17 
                 19 
                 15 
                 15 
               
               
                   
                 5dB+ 
                 15 
                 18 
                 18 
                 17 
                 15 
               
               
                   
                 6dB+ 
                 16 
                 17 
                 17 
                 14 
                 11 
               
               
                   
                   
               
             
          
         
       
     
     Table 5 illustrates ideal skip counts of tandem PAD with no RBS, from 2 dB to 6 dB in 1 dB increments: 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 2 
                 3 
                 4 
                 5 
                 6 dB 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 2dB+ 
                 17 
                 13 
                 11 
                 6 
                 5 
               
               
                   
                 3dB+ 
                 17 
                 15 
                 10 
                 10 
                 7 
               
               
                   
                 4dB+ 
                 13 
                 12 
                 13 
                 8 
                 6 
               
               
                   
                 5dB+ 
                 10 
                 11 
                 10 
                 7 
                 5 
               
               
                   
                 6dB+ 
                 8 
                 9 
                 8 
                 4 
                 0 
               
               
                   
                   
               
             
          
         
       
     
     Other tables may be constructed as appropriate. 
     Referring again to FIG. 5, at Block  520  RBS and non-RBS intervals are determined. In particular, with the tables from the ideal model, thresholds may be set for determination of RBS and non-RBS intervals based on the cluster and/or skip counts for each interval. For example, when using PCM codes from 108 to 32 as described above, an interval may be considered to be an RBS interval if its cluster counts are greater than 21 or its skip counts are greater than 19. These large cluster and/or skip counts may be caused by RBS because RBS can change the structure of a data segment(s) in the ucode. 
     Referring to Block  530 , cluster and skip count averages are then determined for intervals without RBS. In Block  540 , the digital impairments are determined utilizing the averages calculated in Block  530 . In particular, search intervals for both cluster (c) and skip (s) are determined by adding one to and subtracting one from the average cluster count (c_cnt) and average skip count (s_cnt), i.e., c=(c_cnt−1, c_cnt+1) and s=(s_cnt−1, s_cnt+1) to take noise into consideration. If c=0 and s=0 then the PAD interval=(0, 0.25). Otherwise, all single PAD intervals are found which are within a threshold, e.g., 2, of c and s simultaneously and reported. Final single PAD intervals which are +/−0.25 dB of the reported single PAD intervals are identified. All tandem PADs are found which are within a threshold, e.g., 2, of c and s simultaneously. 
     A more detailed description of an embodiment for computing cluster and skip counts from PCM codes 108 to 32, corresponding to Block  410  of FIG. 4 above, now will be described. There are 128 PCM codes defined in G.711, divided into 8 data segments. Each segment has 16 PCM codes and therefore has 15 spaces. A space is defined as the distance between two adjacent PCM codes. All spaces in one data segment are the same. Let S(j) and S(j−1) be the spaces of data segment j and its next smaller data segment j−1, and Bj be the boundary space in the two data segments. Then S(j)/S(j−1)=1/2 and B(j)/S(j)=3/4 according to G.711: Space between two consecutive PCM codes in the same data segment may be used to calculate counts. Since the smaller PCM codes may be more sensitive to noise, the calculation may be performed from the larger PCM code (108) to the smaller one (32) so that the space information in one data segment (larger) can be used as guidance for the calculation of space in a next data segment (smaller). Another issue in the calculation of cluster and skip counts is the boundary location of each data segment. Spaces and boundaries may be calculated as follows: 
     
       
         
               
             
           
               
                   
               
             
             
               
                 for mapping interval 1 to 6 { 
               
               
                  compute space within the G.711 segment which contains PCM code 108 
               
               
                  PCM code = 108 to PCM code 32{ 
               
               
                   determine space type (normal, cluster, skip, or boundary) for the 
               
               
                   space between current PCM code and the next smaller one 
               
               
                   increment space, cluster and skip counts accordingly 
               
               
                   if a boundary is found { 
               
               
                    compute base (the largest number) of the next data segment 
               
               
                    compute space within the next data segment 
               
               
                   } 
               
               
                  } 
               
               
                 } 
               
               
                   
               
             
          
         
       
     
     FIG. 6 is a flowchart of an embodiment for calculating cluster and skip counts in one mapping interval, corresponding to Block  410  of FIG.  4 . In FIG. 6, c denotes cluster counts, s denotes skip counts, and S_Count denotes space counts in the data segment. 
     Referring now to FIG. 6, variable i, which is a pointer to the current ucode, is set to 108 as the initial ucode to be processed at Block  602 , and at Block  604 , the component “find space” (described in detail below) is executed. At Block  606 , cluster count c is set to 0, skip count s is set to 0 and space count S_Count is set to 15. At Block  608 , a distance measurement is defined where the distance is the distance between ucode(i) and ucode(i−1). 
     At Block  614 , a test is made as to the space type based on the processing described in detail below. At Block  616 , if it is a cluster, the cluster count is incremented and the variable i is decremented at Block  618 . If i is 32 at Block  612 , then c and s are output at Block  610  and operations end. If not, then a new distance measurement is computed at Block  608 , and a test again is made at Block  614 . 
     If the test at Block  614  determines that a normal boundary is present, then the space count is decremented at Block  620 . As long as the space count is 0 or more, processing continues at Block  618 . 
     Referring again to Block  614 , if the test at Block  614  determines that a boundary is present, then the variable i is decremented at Block  628  and a test is made at Block  630  as to whether i is 32. If i is 32, then the cluster count and skip count are output at Block  656  and operations end. On the other hand, if i is not 32 at Block  630 , then the “find space” operation is again performed at Block  632  and a base is computed at Block  634 . The space count then is incremented by 15 at Block  636  and a distance measurement is made at Block  638 . 
     Referring now to Block  640 , a test again is made as to the space type. If a cluster, then the cluster count is incremented and the variable i is decremented at Blocks  642  and  646 , and if the variable i is equal to 32, the cluster count and skip count are output at Block  656 . If the variable i is not 32 at Block  654 , then the distance measurement is performed again at Block  638  and the space type is identified again at Block  640 . 
     If the space type is normal, then the space count is decremented at Block  644 . If the space count is less than 0 at Block  648 , then the variable i is decremented at Block  628  and processing continues. On the other hand, if the space count is not less than 0 at Block  648 , then the variable i is decremented at Block  646 . 
     Referring again to Block  640 , if the space type is a boundary, then the variable i is decremented at Block  628  and operations continue. On the other hand, if the space type is k skips at Block  640 , then k is added to the number of skip counts at Block  650  and the space count is decremented by k+1 at Block  652 . Accordingly, cluster and skip counts are computed. 
     An embodiment for finding a space (Blocks  604  and  632  of FIG. 6) now will be described. Let S(j), S(j−1), and B(j) are defined as above. If a boundary or skip is found in the first 6 spaces from PCM codes 108 to 102, then the space, S, of the PCM curve segment containing PCM code 108 can be set accordingly. The space can be determined as a boundary or skip based on three consecutive non-cluster spaces, say d 1 , d 2 , d 3 : 
     if d 1 /d 2 =3/4 and d 2 /d 3 =2, then d 1 =B(j), d 2 =S(j−1)+S(j−1), and d 3 =S(j−1), S=d 2   
     if d 1 /d 2 =4/5 and d 2 /d 3 =5/2, then d 1 =S(j), d 2 =B(j)+S(j−1), d 3 =S(j−1), S=d 1   
     if d 1 /d 2 =8/9, then d 1 =S(j)+S(j), d 2 =S(j)+B(j)+S(j−1), d 3 =S(j−1), S=d 1 / 2   
     if d 1 /d 2 =4/3, then d 1 =S(j), d 2 =B(j), S=d 1   
     if d 1 /d 2 =3/2, then d 1 =B(j), d 2 =S(j−1), S=2*d 2   
     if d 1 /d 2 =2, then d 1 =S(j)+S(j), d 2 =S(j), S=d 1 / 2   
     if d 1 /d 2 =9/4, then d 1 =S(j), d 2 =S(j)+B(j)+S(j−1), S=d 1   
     if d 1 /d 2 =5/2, then d 1 =B(j)+S(j−1), d 2 =S(j−1), S=2*d 2   
     if d 1 /d 2 =7/2, then d 1 =S(j)+B(j), d 2 =S(j−1), S=2*d 2   
     } 
     Note that due to the noise in the network, the ratio of d 1 /d 2  generally will not be exactly the ideal case. The mid point of the two adjacent numbers may be set as the cut off point for the decision of the ratio. 
     If the PCM code is not in the PCM curve segment containing PCM code  108 , or no boundary or skip is found in the space between PCM code  108  to  102   
     
       
         
               
             
           
               
                   
               
             
             
               
                 { 
               
               
                  calculate space in current data segment by 
               
               
                 { 
               
               
                   select all space if u*S(j) &lt;= d &lt;= 1*S(j) where S(j) the space in 
               
               
                 previous data segment and S(j)= 1000 
               
               
                    if PCM code = 108), and (u, 1)=(0.55, 0.45) for PCM != 108 
               
               
                 and (u, 1)=(0.8, 0.2) if PCM =108 
               
               
                   set space to be average of all selected spaces 
               
               
                   } 
               
               
                 } 
               
               
                  Detailed processing for determining whether a space is normal cluster, 
               
               
                 skip or boundary (Blocks 614 and 640 of FIG. 6) now will be provided: 
               
               
                 if the PCM curve segment contains PCM code 108 { 
               
               
                  let d = the space between two consecutive PCM codes 
               
               
                  calculate d/S 
               
               
                  determine space type as described below 
               
               
                 else if the PCM curve segment does not contain PCM code 108 
               
               
                  let d = the space between the PCM code and the base of the data 
               
               
                 segment − (15-space counts) * space 
               
               
                  calculate d/S 
               
               
                  determine space type as described below. 
               
               
                 Space type may be determined using the following operations: 
               
               
                  cluster if d/S=0, d=0 
               
               
                   increment cluster count by 1 
               
               
                  normal if d/S=1, d=S(j) 
               
               
                   if S_Count == 0 
               
               
                    reset S_Count to 15 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   else 
               
               
                    decrement S_Count by 1 
               
               
                   end 
               
               
                  normal if d/S=3/4, d=B(j) 
               
               
                    if S_Count == 0 
               
               
                    reset S_Count to 15 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   else 
               
               
                    decrement S_Count by 1 
               
               
                   end 
               
               
                  1 skip if d/S=2, d=S(j)+S(j) 
               
               
                    increment skip count by 1 
               
               
                    if S_Count &lt;= 1 
               
               
                    set S_Count = 14+S_Count 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   else 
               
               
                    decrement S_Count by 2 
               
               
                   end 
               
               
                  1 skip if d/S=7/4, d=S(j)+B(j) or 2 skip, d=B(j)+S(j−1)+S(j−1) 
               
               
                    if S_Count == 1 
               
               
                    increment skip count by 1 
               
               
                    reset S_Count to 15 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   elseif S_Count == 0 
               
               
                    increment skip count by 2 
               
               
                    reset S_Count to 13 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   elseif S_Count &gt;= 2 
               
               
                     increment skip count by 1 
               
               
                    decrement S_Count by 2 
               
               
                    end 
               
               
                  1 skip if d/S=5/4, d=B(j)+S(j−1) 
               
               
                   if S_Count == 0 
               
               
                     increment skip count by 1 
               
               
                    reset S_Count to 14 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   else 
               
               
                    decrement S_Count by 1 
               
               
                   end 
               
               
                  2 skips if d/S=3, d=S(j)+S(j)+S(j) 
               
               
                    increment skip count by 2 
               
               
                   if S_Count &lt;= 2 
               
               
                    set S_Count = 13+S_Count 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   else 
               
               
                    decrement S_Count by 3 
               
               
                   end 
               
               
                  2 skips if d/S=11/4, d=S(j)+S(j)+B(j) 
               
               
                    increment skip count by 2 
               
               
                   if S_Count &lt;= 2 
               
               
                    set S_Count = 13+S_Count 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   else 
               
               
                    decrement S_Count by 3 
               
               
                   end 
               
               
                  2 skips if d/S=9/4, d=S(j)+B(j)+S(j−1) 
               
               
                   if S_Count == 1 
               
               
                    increment skip count by 2 
               
               
                    set S_Count =13+S_Count 
               
               
                    calculate space S 
               
               
                    calculate base 
               
               
                   else 
               
               
                    increment skip count by 1 
               
               
                    decrement S_Count by 2 
               
               
                   end 
               
               
                 } 
               
               
                   
               
             
          
         
       
     
     Note that due to the noise in the network, the ratio of d/S generally will not be exactly the ideal case. The mid point of the two adjacent numbers may be set as the cut off point for the decision of the ratio. 
     The present invention can be relatively insensitive to a precise network model being known a priori. Although the present invention may not exhibit the accuracy of digital impairment detection techniques using a priori knowledge of a network model, it may not exhibit gross errors when an unknown network model is encountered, such as tandem PADs or a type of transcoding between Alaw and μlaw. An accuracy of about 0.5 dB to about 1.0 dB may be obtained. 
     The present invention can be less sensitive than techniques based on a priori knowledge of a network because there generally is a smooth overlap or continuum across various cluster counts from a PAD value of 0 dB increasing to a PAD value of about 12 dB. Similarly, for tandem PAD combinations such as 6 dB and 6 dB in the network, an approximate PAD estimation of 11 to 12 dB may be obtained. In sharp contrast, approaches based on a priori knowledge of a network model may be confused by tandem PADs unless the precise tandem PAD combination is known a priori. As such, if a priori knowledge of an unusual network scenario, such as tandem PADs is not known, a network model approach based on a priori knowledge of the network model may determine that the two 6 dB PADs in tandem are just one 6 dB PAD, and the power boost may be 6 dB lower than desired. 
     The present invention also can handle unusual uchord spacings that may violate G.711 rules. One example of this is a 3 dB type F PAD found in Raleigh and Cary, N.C. The lowest six uchords is the normal G.711 spacing, but the top chords are separated in a manner inconsistent with G.711. The present invention can recalibrate the predicted spacing between points in determining skip and cluster counts at each uchord boundary. Thus, the present invention can find an approximate PAD value of around 3 dB. In contrast, an a priori technique may identify a 4 dB or 5 dB PAD. 
     Finally, the present invention can be computationally efficient because it only needs to compare signatures rather than comparing an entire range of PCM codes for each DIL level. High speed modem initialization thereby may be provided. 
     The flow charts of FIGS. 4,  5  and  6  illustrated the architecture, functionality and operation of a possible implementation of the Phase 3 Digital Impairment Learning software  176 . In this regard, each block can represents a module, segment, or portion of code, which can comprise one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. 
     In the drawings and specification, there have been disclosed typical preferred embodiments of the invention and, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention being set forth in the following claims.