Abstract:
A pulse amplitude modulated (PAM) mapper includes a constellation matrix memory which stores indications of a plurality of different constellations, wherein at least one of the different stored constellations is of different dimension than another of the stored constellations. The constellations are used individually or together to support a plurality of different modem data rates. In a preferred embodiment, in addition to the constellation matrix memory, the mapper includes a logic block, a constellation controller, a PAM code generation block, and an output register. The logic block receives incoming bits of information, groups the bits as a function of the desired or agreed upon bit rate as indicated by the constellation controller, and provides a plurality of each group of bits to the PAM code generation block, and one or more sign bits to the output register. The PAM code generation block uses the provided bits to choose at least one point from one of the constellations, and uses each chosen constellation point to generate a seven-bit PAM code (typically μ-law or A-law code value) word. Each seven-bit output is provided to the output register, and together with associated sign bits generates output bytes. Algorithms are provided for choosing multiple points from the 2D and higher dimensional constellations from provided groups of bits.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to data communications equipment. More particularly, the present invention relates to mapping systems and methods having advantageous applications in high speed modems which are coupled to an analog local loop. 
     2. State of the Art 
     With the ever-increasing importance of telecommunications for the transfer of data as well as voice, there has been a strong effort to increase data transfer rates over the telephone wires. Recently, the ITU-T adopted the V.34 Recommendation (International Telecommunication Union, Telecommunication Standardization Sector Recommendation V.34, Geneva, Switzerland 1994) which is hereby incorporated by reference herein in its entirety. The V.34 standard and subsequent amendments define modem operating speeds of 28.8 kbps up to 33.6 kbps, and the vast majority of modems being sold today adhere to the V.34 Recommendation. However, with the explosion in the use of the Internet, even at the V.34 transfer rates, downloading of large files available on the Internet can take long periods of time. Thus, recently, there has been a thrust to provide additional standards recommendations which will increase data transfer rates even further (note the TIA TR-30.1 PAM Modem ad hoc group and the ITU-T Study Group 16). 
     Recognizing that further increases in data rates is theoretically limited where the telecommunication network is an analog system (see C. E. Shannon, &#34;A Mathematical Theory of Communication,&#34; Bell System Technical Journal, 27:379-423, 623-656 (1948)), there have been various proposals to take advantage of the fact that much of the telecommunication network is now digital. For example, U.S. Pat. No. 5,394,437 to Ayanoglu et al., U.S. Pat. No. 5,406,583 to Dagdeviren, and U.S. Pat. No. 5,528,625 to Ayanoglu et al. (all assigned to AT&amp;T/Lucent and all of which are hereby incorporated by reference herein in their entireties) all discuss techniques which utilize the recognition that the network is mostly digital in order to increase data transmission rates to 56 kbps and higher. Similarly, Kalet et al., &#34;The Capacity of PAM Voiceband Channels,&#34; IEEE International Conference on Communications &#39;93, pages 507-511 Geneva, Switzerland (1993) discusses such a system where the transmitting end selects precise analog levels and timing such that the analog to digital conversion which occurs in the central office may be achieved with no quantization error. PCT application number PCT/US95/15924 (Publication WO 96/18261) to Townshend which is hereby incorporated by reference herein in its entirety) discusses similar techniques. All of the disclosures assume the use of PAM (pulse amplitude modulation) digital encoding technology rather than the QAM (quadrature amplitude modulation) currently used in the V.34 Recommendation. The primary difference between the AT&amp;T technology and the Townshend reference is that the AT&amp;T technology suggests exploiting the digital aspect of the telephone network in both &#34;upstream&#34; and &#34;downstream&#34; directions, while Townshend appears to be concerned with the downstream direction only. Thus, systems such as the &#34;x2&#34; technology of US Robotics which are ostensibly based on Townshend envision the use of the V.34 Recommendation technology for upstream communications. 
     As will be appreciated by those skilled in the art, the technologies underlying the V.34 Recommendation, and the proposed 56 kbps modem are complex and typically require the use of high-end digital signal processors (DSPs). One of the complex tasks of the modem is the mapping of digital data into a sequence of digital signals chosen from a constellation which are converted into an analog signal by a D/A converter. Mapping typically includes utilizing a constellation. In the V.34 Recommendation, the preferred constellation is a four-dimensional constellation, whereas in the envisioned 56 kbps modems, the constellation is envisioned as a one dimensional PAM constellation which complies with μ-law (A-law in Europe) requirements. According to μ-law requirements which are set forth in ITU-T Recommendation G.711 which is hereby incorporated by reference herein in its entirety, the total constellation consists of 255 signal levels; 127 positive, 127 negative, and zero. Both the positive portion of the constellation and the negative portion of the constellation include eight sectors with sixteen points each (the constellation being shown in Appendix 1 hereto), with zero being a common point for both portions. As is well known in the art, the minimum distance between points in sector 1 of the constellation is a distance &#34;2&#34;. In sector 2, the minimum distance is &#34;4&#34;, while in sector 3, the minimum distance is &#34;8&#34;. In the eighth sector, the minimum distance is &#34;256&#34;. 
     Using the full PAM μ-law constellation, theoretically, a bit rate of almost 64 kbps can be transmitted over the analog local loop to the digital network. However, the average power of such a constellation would be about -4 dBm, and the minimum distance between points would be a distance of &#34;2&#34;. Such a large average power is undesirable when compared to the present restrictions of an average power of -12 dBm on the network; and such a minimum distance is also undesirable, with minimum distances of at least &#34;4&#34; and preferably &#34;8&#34; being considerably more desirable in reducing errors due to noise. 
     In light of the power restrictions, and minimum distance considerations, the prior art primarily discusses sending data at 56 kbps (i.e., seven bits per symbol at an 8 kHz rate). In order to increase the bit rate to 60 kbps, (e.g., 7.5 bits per symbol), a sequence of symbols could be sent, with every other symbol carrying seven bits and eight bits respectively. However, for reasons set forth above (average power, and minimum distance), the carrying of eight bits per symbol is not feasible. 
     SUMMARY OF THE INVENTION 
     It is therefore an object of the invention to provide a PAM mapper for a high speed modem with data rates of up to 60 kbps. 
     It is another object of the invention to provide a PAM mapper which enables data rates of 40 kbps to 60 kbps with fine data rate steps. 
     It is a further object of the invention to provide a PAM mapper and methods utilizing a PAM mapper which optimize signal sets based on desired average power requirements and desired minimum distances between points in the PAM constellations. 
     It is an additional object of the invention to provide a PAM mapper which is simple to implement and which does not require large computing and memory resources. 
     In accord with the invention, a mapper for a PAM encoder is provided and includes means for generating desired μ-law or A-law code levels, and a constellation matrix memory which stores indications of a plurality of different N-dimensional constellations (N being a positive integer), wherein at least one of the different stored constellations is of different dimension than another of the stored constellations. As will become apparent hereinafter, the plurality of different constellations are used individually or together to support a plurality of different modem data (bit) rates. 
     In addition to the means for generating desired code levels and constellation matrix memory, the mapper preferably includes a logic block which receives incoming bits of information, groups the bits as a function of the desired or agreed upon data rate, and provides a plurality of each group of bits (i.e., a subgroup) to the means for generating desired code levels. The means for generating desired code levels uses those bits to choose at least one point from one of the constellations, and uses each chosen constellation point for generating the desired code levels. In one embodiment, the means for generating desired code levels comprises an address computation block and a PAM code memory, where the address computation block chooses a constellation point and that the constellation point is used as a pointer to a location in the PAM code memory which preferably stores a plurality of seven-bit PAM code words. The seven-bit PAM code word chosen from the PAM code memory is then provided as an output with an eighth bit (which is used as the sign bit) which is drawn from one or more of the bits (another subgroup) of the group of bits formed by the logic block. Alternatively, where the desired output code is a PCM code, the means for generating desired code levels is simply the address computation block which chooses a constellation point indication and generates a seven-bit PCM code output from the chosen constellation point indication. 
     According to one embodiment of the invention, in order to provide for data rates in excess of 56 kbps, both one- and two-dimensional constellations are utilized. In using a two-dimensional (2D) constellation, the logic block, which groups incoming bits of information, can group fifteen bits of information together. When fifteen bits are grouped together, two bits are used as the sign bits for two eight-bit output bytes while the thirteen other bits are provided to the address computation block which divides the thirteen bit number by 91 modulo 91 to generate an integer part of a quotient and the remainder. The integer part of the quotient is used to select one of 91 points (representing both positive and negative values) of a predetermined two-dimensional PAM constellation, while the remainder is used to select another of the 91 points of the PAM constellation (it being appreciated that the possible 8281 (91×91) combinations of points is sufficient to cover the 8192 (2 13 ) combinations of thirteen bits). The two selected constellation points are used to generate (e.g., by pointing to two locations in the PAM code memory, or alternatively in the case of PCM, by direct generation) two seven-bit numbers to which the sign bits are added to provide the two eight-bit outputs. 
     If all bits received by the logic block are grouped into groups of fifteen bits, a data rate of 60 kbps can be achieved. According to the preferred embodiment of the invention, however, the bit rate may be chosen at 0.5 kbps increments from 40 kbps (or below, if desired) up to 60 kbps. To achieve all of these rates, indications for four different constellations are stored in the constellation matrix memory. Preferably, each constellation is chosen to obtain the largest separation at a power of about -12 dBm to the extent possible. Thus, for example, a thirty-two point constellation (sixteen positive and sixteen negative points) is provided with a minimum distance of 96, and a power of -12.1 dBm and can be used for the coding of a five-bit input group (one of the five bits being used as a sign bit). Similarly, a sixty-four point constellation is provided with a minimum distance of 36 and a power of -12.2 dBm and can be used for a six-bit input group. A one hundred twenty-eight point constellation is provided with a minimum distance of 16 and a power of -12.1 dBm for use with a seven-bit input group, while the one hundred eighty-two point constellation is provided with a minimum distance of 8 and a power of -8.7 dBm for use with a fifteen point group. In order to obtain different data rates, data frames may be set up which utilize different constellations in the frame, such that the incoming data bits are grouped in groups of different numbers of bits according to the frame. For example, to obtain a data rate of 59.5 kbps, seven groups of fifteen bits would be grouped together for every two groups of seven bits. 
     Where a data rate of 56 kbps or less is chosen, as suggested above, the bits are grouped into five, six, or seven bit groups, with groups of different numbers of bits alternating in a frame to obtain specifically desired rates. In each case, one bit of the group is used as the sign bit for an output byte, and the remaining bits are used by the address computation block of the code generation means to access an indication of a constellation point. The constellation point is then used to generate a seven-bit word (e.g., by selecting a PAM code memory location), and the seven-bit word is output with the sign bit to generate the PAM coded eight-bit byte. 
     As suggested above, by grouping incoming bits into groups of five, six, seven, and fifteen bits, and by storing indications of a plurality of constellations and using the bits to select a constellation point which is used in generating a code level output, a simple mapper for a high speed modem is provided which enables bit rates of up to 60 kbps with 0.5 kbps steps or less. 
     According to another aspect of the invention, higher dimensional constellations (e.g., 3D, 4D, 5D, 6D, . . . ) may be utilized to obtain high bit rates with desired minimum distances and desired power. For example, in a preferred embodiment, 4D and 8D constellations are utilized in conjunction with constellations of other dimensions (2D and 1D) to obtain desired data rates. One of the 4D constellations (which helps permit bit rates in excess of 56 kbps) includes 154 points (77 indications being stored in the 8×16 array), which permits a group of twenty-nine bits to be mapped into four outgoing symbols. With twenty-nine bits, a subgroup of four bits are used as the sign bits, and another subgroup of the remaining twenty-five bits are used to select four of the 77 indications, as 2 25  is less than 77 4 . Similarly, one of the 8D constellations includes 140 points (seventy indications), which permits a group of fifty-seven bits to be mapped into eight outgoing symbols. With fifty-seven bits, a subgroup of eight bits are used as the sign bits, and a subgroup of the remaining forty-nine bits are used to select eight indications of the seventy indications (140 point) constellation. 
     A preferred manner of selecting constellation points of an N-dimensional constellation comprises, taking a group of x bits (where 2 x-N  ≦L N  with L=the number of positive points or indications in the constellation), using the N most significant of the x bits as the sign bits for the N output symbols, and dividing the value represented by the x-N remaining bits by L N-m  (where m is a variable which takes values from 1 to N-1 sequentially) to obtain quotients and remainders. The first quotient is used to select a first constellation point value which is used for generating a first code level output. If N-m equals one, the first remainder is used to select another constellation point. However, if N-m is greater than one, m is increased by one, and the remainder is divided by L N-m  to obtain a second quotient and a second remainder, with the second quotient being used to select a second constellation point value. If the N-m is equal to one, the second remainder is used to select a third constellation point value; otherwise, m is again increased and the remainder divided by L N-m . The process is continued until N-m equals one, and the last remainder is used to select the N&#39;th constellation point value. 
    
    
     Additional objects and advantages of the invention will become apparent to those skilled in the art upon reference to the detailed description taken in conjunction with the provided figures. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a high level block diagram of the PAM modem of the invention. 
     FIG. 2 is a block diagram of the mapper of FIG. 1 according to a first embodiment the invention. 
     FIGS. 3a-3d are functional block diagrams of the four-to-seven bit, the five-to-seven bit, the six-to-seven bit, and the thirteen-to-two-by-seven bit mappers implemented in the mapper of FIG. 2. 
     FIG. 4 is a block diagram of a mapper according to a second embodiment of the invention. 
     Appendix 1 is a prior art chart of the μ-law code. 
     Appendix 2 is a listing of four preferred constellations utilized in the mapper of the embodiment of FIG. 2 of the invention. 
     Appendix 3 is a listing of eighteen preferred constellations utilized in the mapper of the embodiment of FIG. 4 of the invention. 
     Table 1 is a listing of mapping parameters implemented by the mapper of the embodiment of FIG. 2 the invention, including the numbers of fifteen-bit pairs, seven-bit symbols, six-bit symbols, and five bit symbols. 
     Table 2 is a listing representing the mapping of thirteen bit binary combinations into pairs of eight bit outputs. 
     Table 3 is a listing of mapping parameters implemented by the mapper of the embodiment of FIG. 4 of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Turning to FIG. 1, a high level block diagram of a PAM modem 10 is seen. The modem 10 broadly includes a transmitter 20 and a receiver 30. The transmitter includes an interface 32 to a source of digital data (such as a computer), an encoder 34 which includes a mapper 36 and may optionally include a Trellis or convolutional encoder (not shown), and an interface 38. Details of the receiver side of the modem are well known and are not shown in FIG. 1. 
     According to a first embodiment of the invention, and as seen in FIG. 2, the mapper 36 for the PAM encoder 34 preferably includes a constellation matrix memory 40, a logic block 60 for arranging data, a constellation controller 65 coupled to the constellation matrix memory 40 for selecting a constellation from the constellation matrix memory, means for generating output code levels 68 which is coupled to the logic block 60 and to the constellation matrix memory 40, and an output register 75. In one embodiment of the invention, the means for generating output code levels 68 includes an address computation block 70 and a PAM code memory 50. In another embodiment of the invention, and as will be described in more detail hereinafter, the means for generating output code levels 68 includes only the address computation block 70. It should be appreciated that the constellation controller 65, logic block 60, and address computation block 70 can be implemented in a single hardware element, or separate hardware elements, or as software, or as a combination of software and hardware, while the constellation matrix memory 40 (and PAM code memory 50, if utilized) can be implemented in one or more memory elements. The output register 75 may be incorporated in the memory element with the constellation matrix memory and/or PAM code memory, or may be a separate register as desired. 
     The constellation matrix memory 40 stores indications of a plurality of different PAM constellations for a plurality of different bit rates; indications for four different constellations being shown in FIG. 2, with one of the constellations (constellation #1) being a two-dimensional constellation. Preferably, the constellation matrix memory is configured as a plurality (e.g., four) of eight by sixteen-bit blocks such as seen in Appendix 2. Thus, as discussed in more detail below, each block, if desired, can point to all one hundred twenty-eight possible positive or negative μ-law levels (seen in Appendix 1) stored in the PAM code memory 50, with each row of the block pointing to a different μ-law sector, and each bit in the row representing a different level in the sector. 
     For purposes herein, and as will be explained in more detail hereinafter with reference to Appendices 2 and 3, the terms &#34;two-dimensional constellation&#34; or &#34;multi-dimensional constellation&#34; refer to constellations having other than 2 c  points (where c is a positive integer) which are utilized, where a single subgroup of bits is used to select more than one point from the constellation. 
     As seen in Appendix 2, different preferred constellations for the first embodiment of the invention are represented in the constellation matrix memory 40 by setting different values in the matrix. Preferably, and in accord with the invention, the points of the constellation are chosen to maintain a maximum &#34;minimum distance&#34;, as well as to provide a power of nearly -12 dBm. For a thirty-two point constellation, sixteen bits of the eight by sixteen-bit block are set to value 1; it being appreciated that the positive and negative values of the sixteen set values will provide thirty-two desired points. As seen in Appendix 2, in order to maintain a large distance with a power of -12.1 dBm, the constellation points chosen include a single point in sector 2, a single point in sector 3, three points in sector 4, five points in sector 5, and six points in sector 6. By choosing no points in sectors 7 and 8, the power is kept down, and by choosing no points in sector 1, and only a single point in sectors 2 and 3, the minimum distance is made large. Similarly, for the sixty-four point constellation, as seen in Appendix 2, thirty-two bits of another eight by sixteen-bit block are set. Optimally, by choosing one point in sector 1, two points in sector 2, three points in sector 3, five points in sector 4, eight points in sector 5, thirteen points in sector 6, and no points in sectors 7 and 8, the power is kept down, while the minimum distance is a distance of thirty-six. In the one hundred twenty-eight point constellation, sixty-four bits of the block are set as seen in Appendix 2 to obtain a minimum distance of sixteen and a power of -12.1 dBm. Finally, in the one hundred eighty-two point 2D constellation, ninety-one bits (of the possible one hundred twenty-eight bits) are set, and a minimum distance of eight is maintained, while the power is set to -8.7 dBm (which is unavoidably higher than presently desired). 
     As will be discussed in more detail below, according to the invention, the choice of constellations being used from the constellation matrix memory 40 at any given time is dependent on the chosen data transmission bit rate. Thus, when a bit rate is determined (by any appropriate means or method), the constellation controller 65 chooses appropriate constellations in a sequential fashion. More particularly, as set forth in Table 1, for a bit rate of forty kbps, five-bit symbols (corresponding to a thirty-two bit constellation) can be utilized exclusively, while for a bit rate of forty-eight kbps, six-bit symbols (corresponding to a sixty-four bit constellation) can be utilized exclusively. However, for bit rates between 40 kbps, and 48 kbps, a combination of five-bit and six-bit symbols are required. Thus, for a bit rate of 42.5 kbps, for every five six-bit symbols, eleven five-bit symbols are required. Thus, the constellation controller 65 could interleave the choice of constellations accordingly in a frame; e.g., M4-M4-M3-M4-M4-M3-M4-M4-M3-M4-M4-M3-M4-M4-M3-M4 and repeat the same sequence (frame) to maintain the desired bit rate. Similarly, for other bit rates between forty and forty-eight kbps, other combinations of five-bit and six-bit symbols are required as set forth in Table 1. 
     When the choice of constellation is made by the constellation controller 65, the constellation controller concurrently sends an indication to the logic block 60, so that the logic block can group the incoming bits accordingly. Thus, for example, when the constellation controller chooses the M4 constellation (thirty-two point), a signal is provided to cause the logic block 60 to group five incoming bits together and provides a first of those five bits as a sign bit to a first bit location of the output register 75. The remaining four bits are provided to the address computation block 70 of the code generation means 68 which uses the four bits to choose an indicated constellation point of the M4 constellation (sixteen bits of the sixteen by eight-bit matrix having been set to a value one as seen in Appendix 2). For example, if the four bits used to choose the constellation point have a value of &#34;1011&#34;, the eleventh (1011 base 2=11 base 10) set location in the M4 constellation (e.g., using M4 of Appendix 2, the second level of segment six) would be chosen. The indicated constellation point (having both a sector and level indicator due to its location in the matrix) is then used by the address computation block 70 either to directly generate an output PCM μ-law code (e.g., by subtracting the location of the chosen constellation point indication in the 8×16 bit array from 128 and providing a seven-bit digital output of the difference value), or to generate an output PAM code by using the constellation point indication as a pointer to the PAM code memory 50 (e.g., to sector 6, level 81 of Appendix 1). The seven bit word (e.g., 0101110; the seven least significant bits of the Code of Appendix 1) stored at the PAM code memory location indicated by the constellation point is then provided to the second through eighth bit positions of the output register 75. The seven lsbs, together with the sign bit provided from the logic block 60 provide an eight-bit byte for output to the digital/analog converter. This is seen in functional block diagram 3a, where five data bits are grouped together, and a first of the five bits is used as a sign bit of an output byte, while the other four of the data bits are used to generate the seven additional bits of the output byte. 
     In a similar manner, when the M3 constellation is chosen by the constellation controller 65, the logic block 60 is provided with a signal which causes it to group together six incoming bits. A first of those six bits is used as a sign bit and provided to the first bit location of the output register 75. The remaining five bits are provided to the address computation block 70 which uses the five bits to choose an indicated constellation point of the M3 constellation (thirty-two bits of the sixteen by eight matrix having been set to a value one for the M3 constellation as seen in Appendix 2). The indicated constellation point is then used by the address computation block 70 either as a pointer to the PAM code memory 50, or in a direct manner as discussed above, to generate a seven bit word which is provided to the appropriate bit locations in the output register 75. The seven lsbs, together with the sign bit provided from the logic block 60 provide an eight-bit byte for output to the digital/analog converter. This is seen in functional block diagram FIG. 3b, where six data bits are grouped together, and a first of the six bits is used as a sign bit of an output byte, while the other five of the data bits are used to generate the seven additional bits of the output byte. 
     As suggested by Table 1, in order to generate data rates of between forty-eight and fifty-six kbps, groups of six bits and seven bits are utilized in conjunction with the M3 and M2 constellations. As suggested by FIG. 3c, when seven bits are grouped together, one bit is used as the sign bit, and the remaining six bits are used to generate the seven remaining bits of the output byte. The six bits generate the seven remaining bits by choosing one of the sixty-four set bits of the matrix storing constellation M2, which in turn either points to a PAM code memory location which stores a seven-bit word, or which is used to generate the seven-bit word. 
     Turning back to Table 1 in conjunction with FIGS. 2, 3c, and 3d, the mechanism for generating bit rates of between fifty-six and sixty kbps is slightly different than the previously described mechanisms. In particular, according to the first embodiment of the invention, instead of using a combination of seven- and eight-bit symbols, a combination of seven-bit symbols and fifteen-bit symbol pairs are utilized. For example, to generate a data rate of fifty-eight kbps, four fifteen-bit symbols pairs from the 2D constellation M1 are utilized on conjunction with eight seven-bit symbols from constellation M2 in a repeating four symbol pattern; e.g., M2-M1-M1-M2. The seven-bit symbols are used as set forth above with reference to FIG. 3c. However, according to the invention, the fifteen-bit symbol pairs are generated differently. Thus, when a fifteen-bit pair is indicated by the constellation controller, the two-dimensional M1 constellation is chosen from the matrix memory, and fifteen bits are grouped together by the logic block 60. As indicated by FIGS. 2 and 3d, of the fifteen bits, a subgroup of two bits are used as sign bits for two output bytes which are generated at the output register 75. Thus, one sign bit is sent to a first bit location, and the other sign bit is sent to the ninth bit location of the sixteen-bit output register 75. A subgroup of the remaining thirteen bits are used to select two constellation points from the ninety-one set bits of the M1 constellation matrix (it being noted that M1 is therefore defined as a 2D constellation). According to the preferred embodiment of the invention, in order to select two constellation points or indications, the value of the thirteen bits is divided by ninety-one to obtain a quotient and a remainder. The quotient is used to select a first one of the ninety-one set bits (i.e., indications), and the remainder is used to select another of the ninety-one set bits as suggested by Table 2 (it being noted that where the quotient and remainder are the same, the selected indication from the constellation will be the same). As described above, the selected indications are used either to directly generate seven-bit words or to point to locations in the PAM code memory 50 which store seven-bit words. Regardless, the seven bit words generated are provided to bit locations two through eight and ten through sixteen of the output register 75, and together with the sign bits, generate two eight-bit bytes for output. 
     Turning now to FIG. 4 in conjunction with Appendix 3 and Table 3, a second embodiment of the invention is seen. The mapper 136 of FIG. 4 is substantially identical to the mapper 36 of FIG. 2 (with similar elements indicated with similar designation numerals increased by 100), and includes a constellation matrix memory 140, a PAM code memory 150 (as part of a code generation means 168), a logic block 160 for arranging data, a constellation controller 165 coupled to the constellation matrix memory 140 for selecting a constellation from the constellation matrix memory, an address computation block 170 (as part of the code generation means 168) which is coupled to the logic block 160 and to the constellation matrix memory 140 and the PAM code memory 150, and an output register 175. According to the second embodiment of the invention, the constellation matrix memory 140 stores indications of n constellations, including constellations of different dimensions. In the preferred embodiment of FIG. 4, n=18; i.e., indications of eighteen constellations are stored in eighteen 8×16 bit memory blocks, and the eighteen constellations (as shown in Appendix 3) represent 1D, 2D, 3D 4D, 6D and 8D constellations. With indications of 8D constellations stored in the constellation matrix memory 140, it will be appreciated that the output register 175 must be able to accommodate eight eight-bit output symbols; i.e., the output register 175 contains at least sixty-four bits. It will be also appreciated that when using an 8D constellation, eight bits from a large group are first used as sign bits before the remainder of the bits are used to choose eight constellation points as discussed in more detail below. 
     As seen in Table 3, according to the second embodiment of the invention, different bit rates (with different steps) may be obtained using different constellations, or constellation combinations which provide certain minimum distances, certain probabilities F min  of points having the minimum distances, and different powers. The minimum size frame shown is dependent on the dimension of the constellation, the number of constellations used to obtain the desired bit rate, and ratio of frequency of the different constellations utilized. Thus, for example, in accord with the second embodiment of the invention, in order to obtain a bit rate of 57.5 kbps with a minimum distance of 8, as one preferred option, a sixteen symbol frame utilizing the two-dimensional 182-point constellation of Appendix 3 three times, and the one-dimensional 128-point constellation of Appendix 3 ten times (thereby obtaining a F min  of 0.10 and a power of -10.9 dBm) can be provided. As a second preferred option, three utilizations of a four-dimensional 154-point constellation (to obtain twelve symbols) can be interspersed with four utilizations of the one-dimensional 128-point constellation of Appendix 3 (thereby obtaining a F min  of 0.13, but a power of -12.0 dBm). Whenever a 1D constellation is utilized, the grouped bits can be used to directly choose a point in the constellation. However, where the 2D constellation is utilized (in this example), as discussed above with respect to the first embodiment of the invention, thirteen bits are used to choose two points of the 182-point 2D constellation by dividing 2 13  by the ninety-one, and using the quotient to select a first point and a remainder to select a second point. Where the 4D constellation is utilized, in this example, twenty-nine bits are grouped together, with a subgroup of four bits used as signed bits and another subgroup of twenty-five bits used to select four points of the 154-point 4D constellation. According to the invention, the value of the twenty-five bits is divided by 77 3  to provide a quotient which is used to select a first indication (positive point). The remainder of the division is then divided by 77 2  to provide a second quotient which is used to select a second indication. The resulting remainder is then divided by 77 to provide a third quotient which is used to select a third indication, and a remainder which is used to select a fourth indication. As suggested above, all four constellation indications are then used either to select locations in the PAM code memory, with the values in the selected locations of the PAM code memory are used provide seven-bit outputs, or to directly generate four seven-bit outputs, which are sent to the output register. 
     Given the above discussion, it will be appreciated that the method for choosing constellation points in a multidimensional constellation may be broadly stated as follows. First, for an N-dimensional constellation, x bits are grouped together (where 2 x-N  ≦L N  with L=the number of positive points in the constellation). A subgroup of N bits of the x bits are used as the sign bits for the N output symbols. The digital value represented by a subgroup of the x-N remaining bits is then divided by L N-m  (where m is a variable which takes values from 1 to N-1 sequentially) to obtain quotients and remainders. The first quotient is used to select a first constellation point value (indication) which is used to generate a code value output. If N-m equals one, the first remainder is used to select another constellation point indication. However, if N-m is greater than one, m is increased by one, and the remainder is divided by L N-m  to obtain a second quotient and a second remainder, with the second quotient being used to select a second constellation point value. If N-m is equal to one, the second remainder is used to select a third constellation point value; otherwise, m is again increased and the remainder divided by L N-m . The process is continued until N-m equals one, and the last remainder is used to select the N&#39;th constellation point value. 
     Through the use of 2D, 3D, 4D, 6D, and 8D constellations alone, or in conjunction with each other and in conjunction with 1D constellations, as seen in Table 3, many different bit rates can be obtained while maintaining desirable minimum distances and power. It should be noted that Table 3 sets forth the use of all eighteen of the constellations seen in Appendix 3, including the 182-point 2D constellation, the 162-point 3D constellation, the 154-point 4D constellation, the 144-point 6D constellation, the 140-point 8D constellation, the 128-point 1D constellation, the 114-point 6D constellation, 108-point 4D constellation, the 100-point 8D constellation, the 92-point 2D constellation, the 82-point 3D constellation, the 78-point 4D constellation, the 72-point 6D constellation, the 64-point 1D constellation, the 54-point 4D constellation, the 46-point 2D constellation, the 38-point 4D constellation, and the 32-point 1D constellation. It will also be appreciated, that by utilizing constellations of even higher dimension, additional gain may be obtained, albeit at the expense of more complex calculations. 
     Those skilled in the art will appreciate that demappers according to the invention use techniques corresponding substantially to the opposite of the mapping techniques. 
     There have been described and illustrated herein apparatus and methods for the mapping of data in a high data rate modem. While particular embodiments of the invention have been described, it is not intended that the invention be limited exactly thereto, as it is intended that the invention be as broad in scope as the art will permit. Thus, while the invention has been described with respect to certain hardware, it will be appreciated that various functions can be carried in different hardware and/or software. Indeed, the invention has application to both analog and digital transport types of modems. In addition, while particular constellations and particular numbers of constellations being stored in constellation matrix memory were described as being preferred, it will be appreciated that other, and different numbers of constellations could be utilized. Similarly, different code, such as A-law, can be stored in the PAM code memory. Further, while the apparatus and methods of the invention are described as effectively using up to a sixteen symbol frame to provide the ability to choose bit rates with a step of 0.5 kbps, it will be appreciated that with different size frames, different steps could be generated. For example, finer steps (e.g., 0.25 kbps) can be generated with larger frames (e.g., thirty-two symbols), larger steps with smaller frames, and other different steps (e.g., 2/3 kbps) with different size frames (e.g., twelve symbols). Further, while the invention was described as enabling bit rates of up to 60 kbps using the fifteen-bit symbol pairs (i.e., 2D constellations), it will be appreciated that by using constellations of higher dimension, even higher rates can be obtained. Therefore, it will be apparent to those skilled in the art that other changes and modifications may be made to the invention as described in the specification without departing from the spirit and scope of the invention as so claimed. 
     
         ______________________________________Appendix 1.u-law code (full constellation)Sector Level   Level   Code     Negative                                 Code#     #       Value   12345678 Levels 12345678______________________________________8     127     8031    10000000 -8031  000000008     126     7775    100000018     125     7519    100000108     124     7263    100000118     123     7007    100001008     122     6751    100001018     121     6495    100001108     120     6239    100001118     119     5983    100010008     118     5727    100010018     117     5471    100010108     116     5215    100010118     115     4959    100011008     114     4703    100011018     113     4447    100011108     112     4191    10001111 -4191  000011117     111     3999    10010000 -3999  000100007     110     3871    100100017     109     3747    100100107     108     3615    100100117     107     3487    100101007     106     3359    100101017     105     3231    100101107     104     3103    100101117     103     2975    100110007     102     2847    100110017     101     2719    100110107     100     2591    100110117     99      2463    100111007     98      2335    100111017     97      2207    100111107     96      2079    10011111 -2079  000111116     95      1983    10100000 -1983  001000006     94      1919    101000016     93      1855    101000106     92      1791    101000116     91      1727    101001006     90      1663    101001016     89      1599    101001106     88      1535    101001116     87      1471    101010006     86      1407    101010016     85      1343    101010106     84      1279    101010116     83      1215    101011006     82      1151    101011016     81      1087    101011106     80      1023    10101111 -1023  001011115     79      975     10110000 -975   001100005     78      943     101100015     77      911     101100105     76      879     101100115     75      847     101101005     74      815     101101015     73      783     101101105     72      751     101101115     71      719     101110005     70      687     101110015     69      655     101110105     68      623     101110115     67      591     101111005     66      559     101111015     65      527     101111105     64      495     10111111 -495   001111114     63      471     11000000 -471   010000004     62      455     110000014     61      439     110000104     60      423     110000114     59      407     110001004     58      391     110001014     57      375     110001104     56      359     110001114     55      343     110010004     54      327     110010014     53      311     110010104     52      295     110010114     51      279     110011004     50      263     110011014     49      247     110011104     48      231     11001111 -231   010011113     47      219     11010000 -219   010100003     46      211     110100013     45      203     110100103     44      195     110100113     43      187     110101003     42      179     110101013     41      171     110101103     40      163     110101113     39      155     110110003     38      147     110110013     37      139     110110103     36      131     110110113     35      123     110111003     34      115     110111013     33      107     110111103     32       99     11011111  -99   010111112     31       93     11100000  -93   011000002     30       89     111000012     29       85     111000102     28       81     111000112     27       77     111001002     26       73     111001012     25       69     111001102     24       65     111001112     23       61     111010002     22       57     111010012     21       53     111010102     20       49     111010112     19       45     111011002     18       41     111011012     17       37     111011102     16       33     11101111  -33   011011111     15       30     11110000  -30   011100001     14       28     111100011     13       26     111100101     12       24     111100111     11       22     111101001     10       20     111101011      9       18     111101101      8       16     111101111      7       14     111110001      6       12     111110011      5       10     111110101      4       8      111110111      3       6      111111001      2       4      111111011      1       2      11111110  -2    011111101      0       0      11111111   0    11111111______________________________________ 
    
     
         ______________________________________Appendix 2. PAM CONSTELLATIONS______________________________________1. 182-point 2D Constellation for 7.5 bit per symbol,D.sub.min = 8 (50 points), P = -8.7 dBmS.sub.1 =  0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0!;S.sub.2 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;S.sub.3 =  0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.7 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;2. 128-point 1D Constellation for 7 bit per symbol:D.sub.min = 16 (46 points), P = -12.1 dBmS.sub.1 =  0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0!;S.sub.2 =  0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0!;S.sub.3 =  1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0!;S.sub.4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.7 =  1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;3. 64-point 1D Constellation for 6 bit per symbol:D.sub.min = 36 (6 points), P = -12.2 dBmS.sub.1 =  0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0!;S.sub.2 =  0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1!;S.sub.3 =  0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0!;S.sub.4 =  0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0!;S.sub.5 =  1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0!;S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0!;S.sub.7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;4. 32-point 1D Constellation for 5 bit per symbol:D.sub.min = 96 (8 points), P = -12.1 dBmS.sub.1 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;S.sub.2 =  0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0!;S.sub.3 =  0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0!;S.sub.4 =  0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1!;S.sub.5 =  0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1!;S.sub.6 =  0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0!;S.sub.7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;______________________________________ 
    
     
         ______________________________________Appendix 3 PAM CONSTELLATIONS______________________________________1. 182-point 2D Constellation for 7.5 bit per symbol,Dmin = 8 (50 points = 0.27), P = -8.7 dBmz1 =  0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0!;z2 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;z3 =  0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z7 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;2. 154-point 4D Constellation for 7.25 bit per symbol,Dmin = 8 (26 points = 0.17), P = -12.0 dBmS.sub.1 =  0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0!;S.sub.2 =  0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0!;S.sub.3 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1!;S.sub.4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.7 =  1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;3. 128-point 1D Constellation for 7 bit per symbol:D.sub.min = 16 (46 points = 0.36), P = -12.1 dBmS.sub.1 =  0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0!;S.sub.2 =  0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0!;S.sub.3 =  1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0!;S.sub.4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.7 =  1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;4. 108 4D Constellation for 6.75 bit per symbol:Dmin = 16 (12 points = 0.11), P = -11.9 dBmS.sub.1 =  0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0!;S.sub.2 =  0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0!;S.sub.3 =  0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1!;S.sub.4 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;S.sub.5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.7 =  1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;5. 92-point 2D Constellation for 6.5 bit per symbol,Dmin = 32 (54 points = 0.58), P = -12.0 dBmS.sub.1 =  0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0!;S.sub.2 =  0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0!;S.sub.3 =  0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0!;S.sub.4 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;S.sub.5 =  0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;S.sub.7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;6. 78-point 4D Constellation for 6.25 bit per symbol,Dmin = 32 (20 points = 0.26), P = -12.0 dBmh1 =  0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0!;h2 =  0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0!;h3 =  0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0!;h4 =  1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1!;h5 =  0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1!;h6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0!;h7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;h8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;7. 64-point 1D Constellation for 6 bit per symbol:D.sub.min = 36 (6 points = 0.09), P = -12.2 dBmS.sub.1 =  0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0!S.sub.2 =  0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1!S.sub.3 =  0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0!S.sub.4 =  0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0!S.sub.5 =  1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0!S.sub.6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0!S.sub.7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!S.sub.8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!8. 54-point 4D Constellation for 5.75 bit per symbol:Dmin = 60 (4 points = 0.07), P = 11.9 dBmh1 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1!;h2 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1!;h3 =  0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1!;h4 =  0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1!;h5 =  0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0!;h6 =  1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0!;h7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;h8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;9. 46-point 2D Constellation for 5.5 bit per symbol:Dmin = 64 (16 points = 0.36), P = -12.0 dBmz1 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z2 =  1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z3 =  1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0!;z4 =  0,1,0,0,1,0,0,0,0,1,0,0,0,0,1,0!;z5 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;z6 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;z7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;10. 38-point 4D Constellation for 5.25 bit per symbol:Dmin = 72 (4 points = 0.11), P = -12.0 dBmz1 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z2 =  0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z3 =  0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0!;z4 =  0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0!;z5 =  1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1!;z6 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0!;z7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;11. 32-point 1D Constellation for 5 bit per symbol:D.sub.min = 96 (8 points = 0.25), P = -12.1 dBmz1 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z2 =  0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0!;z3 =  0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0!;z4 =  0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1!;z5 =  0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1!;z6 =  0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0!;z7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;12. 140-point 8D constellation:Dmin = 12 (16 points = 0.11), P = -11.3 dBmz1 =  0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1!;z2 =  0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1!;z3 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;z4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z7 =  1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0!;z8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;13. 100-point 8D constellation for 6.625 bit per symbol (53 kbps):Dmin 24 (16 points = 0.16), P = -11.9 dBmh1 =  0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0!;h2 =  0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0!;h3 =  0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0!;h4 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;h5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;h6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;h7 =  1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;h8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;14. 162-point 3D constellation for 7.333 bit per symbol (58.667 kbps),Dmin = 8 (50 points = 0.31), P = -12.0 dBmz1 =  0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0!;z2 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;z3 =  0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;z7 =  1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0!;z8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;15. 144-point 6D constellation for 7.1666 bit per symbol (57.333 kbps),Dmin = 8 (14 points = 0.10), P = -12.2 dBmh1 =  0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0!;h2 =  0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0!;h3 =  1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1!;h4 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;h5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;h6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;h7 =  1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0!;h8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;16. 72-point 6D constellation for 6.1666 bit per symbol (49.333 kbps),Dmin = 32 (12 points = 0.17), P = -12.0 dBmz1 =  0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0!;z2 =  0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0!;z3 =  0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0!;z4 =  0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1!;z5 =  0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1!;z6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0!;z7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;z8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;17. 82-point 3D constellation for 6.3333 bit per symbol (50.667 kbps);Dmin = 32 (28 points = 0.34), P = -12.1 dBmh1 =  0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0!;h2 =  0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0!;h3 =  0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0!;h4 =  0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0!;h5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1!;h6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0!;h7 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;h8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;18. 114-point 6D constellation for 6.8333 bit per symbol (54.667 kbps),Dmin = 16 (26 points = 0.23), P = -12.0 dBmh1 =  0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0!;h2 =  0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0!;h3 =  0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1!;h4 =  0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1!;h5 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;h6 =  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1!;h7 =  1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;h8 =  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0!;______________________________________ 
    
     
                                           TABLE 1__________________________________________________________________________   # of 15-bit        # of 7-bit             # of 6-bit                  # of 5-bit   pairs in        symbols in             symbols in                  symbols in                       Basic PCMBit Rate    Bit per   the frame        the frame             the frame                  the frame                       Constellationskbps    Symbol   N1   N2   N3   N4   Size                           D.sub.min                              F.sub.min                                 P.sub.dBm__________________________________________________________________________60  7.5 8    0         --   182  8 0.27                                 -8.759.5    7.4375   7    2    --   --   182/128                            8 0.24                                 -9.059  7.375   6    4    --   --   &#34;   &#34;  0.20                                 -9.558.5    7.3125   5    6    --   --   &#34;   &#34;  0.17                                 -10.058  7.25   4    8    --   --   &#34;   &#34;  0.14                                 -10.557.5    7.1875   3    10   --   --   &#34;   &#34;  0.10                                 -10.957  7.125   2    12   --   --   &#34;   &#34;  0.07                                 -11.556.5    7.6025   1    14   --   --   &#34;   &#34;  0.03                                 -11.956  7   0    16   --   --   128 16 0.36                                 -12.155.5    6.9375   --   15   1    --   128/64                           16 0.34                                 -12.155  6.875   --   14   2    --   &#34;   &#34;  0.32                                 -12.154.5    6.8125   --   13   3    --   &#34;   &#34;  0.29                                 -12.154  6.75   --   12   4    --   &#34;   &#34;  0.27                                 -12.153.5    6.6875   --   11   5    --   &#34;   &#34;  0.25                                 -12.153  6.625   --   10   6    --   &#34;   &#34;  0.23                                 -12.152.5    6.5625   --   9    7    --   &#34;   &#34;  0.20                                 -12.152  6.5 --   8    8    --   &#34;   &#34;  0.18                                 -12.151.5    6.4375   --   7    9    --   &#34;   &#34;  0.16                                 -12.151  6.375   --   6    10   --   &#34;   &#34;  0.14                                 -12.150.5    6.3125   --   5    11   --   &#34;   &#34;  0.12                                 -12.150  6.25   --   4    12   --   &#34;   &#34;  0.09                                 -12.149.5    6.1875   --   3    13   --   &#34;   &#34;  0.07                                 -12.249  6.125   --   2    14   --   &#34;   &#34;  0.05                                 -12.248.5    6.0625   --   1    15   --   &#34;   &#34;  0.02                                 -12.248  6   --   0    16   --   64  36 0.09                                 -12.247.5    5.9375   --   --   15   1    64/32                           36 0.09                                 -12.247  5.875   --   --   14   2    &#34;   &#34;  0.08                                 -12.246.5    5.8125   --   --   13   3    &#34;   &#34;  0.08                                 -12.246  5.75   --   --   12   4    &#34;   &#34;  0.07                                 -12.245.5    5.6875   --   --   11   5    &#34;   &#34;  0.06                                 -12.245  5.625   --   --   10   6    &#34;   &#34;  0.06                                 -12.244.5    5.5625   --   --   9    7    &#34;   &#34;  0.05                                 -12.244  5.5 --   --   8    8    &#34;   &#34;  0.05                                 -12.143.5    5.4375   --   --   7    9    &#34;   &#34;  0.04                                 -12.143  5.375   --   --   6    10   &#34;   &#34;  0.04                                 -12.142.5    5.3125   --   --   5    11   &#34;   &#34;  0.03                                 -12.142  5.25   --   --   4    12   &#34;   &#34;  0.03                                 -12.141.5    5.1875   --   --   3    13   &#34;   &#34;  0.02                                 -12.141  5.125   --   --   2    14   &#34;   &#34;  0.01                                 -12.140.5    5.0625   --   --   1    15   &#34;   &#34;  0.01                                 -12.140  5   --   --   0    16   32  96 0.25                                 -12.1__________________________________________________________________________ 
    
     
                                           TABLE 2__________________________________________________________________________   N - Decimal          Example of13-bit Binary   Number        Pairs of                        8-bit OutputInput   of the Input          N/91   7-bit Output                        CombinationsCombinations   Combinations          (modulo 91)                 Combinations                        (X &amp; Y - sign digits)__________________________________________________________________________0000000000000   0      00 00  P.sub.0 P.sub.0                        X1111101 Y11111010000000000001   1      00 01  P.sub.0 P.sub.1                        X1111101 Y11110000000000000010   2      00 02  P.sub.0 P.sub.2                        X1111101 Y11100110000001011010   90     00 90  P.sub.0 P.sub.90                        X1111101 Y00011100000001011011   91     01 00  P.sub.1 P.sub.0                        X1111000 Y11111010000001011100   92     01 01  P.sub.1 P.sub.1                        X1111000 Y11110000000010110100   180    01 89  P.sub.1 P.sub.89                        X1111000 Y00011110000010110101   181    01 90  P.sub.1 P.sub.90                        X1111000 Y00011100000010110110   182    02 00  P.sub.2 P.sub.0                        X1110011 Y11111010000010110111   183    02 01  P.sub.2 P.sub.1                        X1110011 Y11110000000100010000   272    02 90  P.sub.2 P.sub.90                        X1110011 Y00011100000100010001   273    03 00  P.sub.3 P.sub.0                        X1110011 Y11111010000100010010   274    03 01  P.sub.3 P.sub.1                        X1110011 Y11110001111111111101   8189   89 90  .sub. P.sub.89 P.sub.90                        X0001111 100011101111111111110   8190   90 00  P.sub.90 P.sub.0                        X0001110 111111011111111111111   8191   90 01  P.sub.90 P.sub.1                        X0001110 11111000__________________________________________________________________________ 
    
     
                                           TABLE 3__________________________________________________________________________Mapping Parameters                   Basic PAMBit Rate    Bit per    Sequence of           Minimum Frame                   Constellationskbps    Symbol    Constellations           Size    Size                       D.sub.min                           F.sub.min                              P.sub.dBm__________________________________________________________________________60  7.5  1x2D   2       182 8   0.27                              -8.759.5    7.4375    7x2D + 2x1D           16      182/128                       8   0.24                              -9.059.5     6x2D + 1x4D           16      182/154                       8   0.19                              -9.059  7.375    3x2D + 2x1D           8       182/128                       8   0.20                              -9.559       2x2D + 1x4D           8       182/154                       8   0.18                              -10.058.667    7.3333    1x3D   3       162 8   0.31                              -12.058.5    7.3125    5x2D + 6x1D           16      182/128                       8   0.17                              -10.058.5     2x2D + 3x4D           16      182/154                       8   0.17                              -11.058  7.25 1x2D + 2x1D           4       182/128                       8   0.14                              -10.558       1x4D   4       154 8   0.17                              -12.057.5    7.1875    3x2D + 10x1D           16      182/128                       8   0.10                              -10.957.5     3x4D + 4x1D           16      154/128                       8   0.13                              -12.057.333    7.1666    1x6D   6       144 8   0.10                              -12.257  7.125    1x2D + 6x1D           8       182/128                       8   0.07                              -11.557       1x4D + 4x1D           8       154/128                       8   0.09                              -12.156.7    7.0625    1x8D + 8x1D           16      140/128                       12  0.08                              -12.056  7.0  1x1D   1       128 16  0.36                              -12.155.5    6.9375    1x4D + 12x1D           16      128/108                       16  0.30                              -12.155  6.875    1x4D + 4x1D           8       128/108                       16  0.23                              -12.154.667    6.8333    1x6D   6       114 16  0.23                              -12.054.5    6.8125    3x4D + 4x1D           16      128/108                       16  0.17                              -12.054  6.75 1x4D   4       108 16  0.11                              -11.954       1x2D + 2x1D           4       128/92                       16  0.18                              -12.053.5    6.6875    11x1D + 5x1D           16      128/64                       16  0.25                              -12.153.5     3x4D + 2x2D           16      108/92                       16  0.08                              -11.953  6.625    1x4D + 2x2D           8       108/92                       16  0.06                              -12.053       1x8D   8       100 24  0.16                              -11.952.5    6.5625    1x8D + 4x2D           16      100/92                       24  0.08                              -12.052  6.5  1x2D   2        92 32  0.58                              -12.051.5    6.4375    1x4D + 6x2d           16      92/78                       32  0.50                              -12.051  6.375    1x4D + 2x2D           8       92/78                       32  0.42                              -12.050.667    6.3333    1x3D   3        82 32  0.34                              -12.050.5    6.3125    3x4D + 2x2D           16      92/78                       32  0.34                              -12.050  6.25 1x4D   4        78 32  0.26                              -12.049.5    6.1875    3x4D + 4x1D           16      78/64                       32  0.19                              -12.049.333    6.1666    1x6D   6        72 32  0.17                              -12.049  6.125    1x4D + 4x1D           8       78/64                       32  0.13                              -12.148.5    6.0625    1x4D + 12x1D           16      78/64                       32  0.06                              -12.148  6    1x1D   1        64 36  0.09                              -12.247.5    5.9375    1x4D + 12x1D           16      64/54                       36  0.07                              -12.147  5.875    1x4D + 4x1D           8       64/54                       36  0.05                              -12.046.5    5.8125    3x4D + 4x1D           16      64/54                       36  0.02                              -12.046  5.75 1x4D   4        54 60  0.07                              -11.945.5    5.6875    3x4D + 2x2D           16      54/46                       60  0.05                              -12.045  5.625    1x4D + 2x2D           8       54/46                       60  0.04                              -12.044.5    5.5625    1x4D + 6x2D           16      54/46                       60  0.02                              -12.044  5.5  1x2D   2        46 64  0.36                              -12.043.5    5.4375    1x4D + 6x2D           16      46/38                       64  0.27                              -12.043  5.375    1x4D + 2x2D           8       46/38                       64  0.18                              -12.042.5    5.3125    3x4D + 2x2D           16      46/38                       64  0.09                              -12.042  5.25 1x4D   4        38 72  0.11                              -12.041.5    5.1875    3x4D + 4x1D           16      38/32                       72  0.11                              -12.041  5.125    1x4D + 4x1D           8       38/32                       72  0.06                              -12.040.5    5.0625    1x4D + 12x1D           16      38/32                       72  0.03                              -12.140  5    1x1D   1        32 96  0.25                              -12.1__________________________________________________________________________