Abstract:
A method and apparatus for encoding data bits in a DMT modulation system is provided utilizing a 64-state Trellis encoder to achieve further improvement in the achievable coding gain by employing coset partitioning, bit conversion, and constellation encoding that fit the DMT modulation. The coding gain of the new coder is around 5.63 dB, which is about 0.96 dB higher than the current Trellis coder in the DMT standard.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to U.S. Provisional Patent Application No. 60/404,390 entitled “Method and Apparatus For Generating A 64-State 4-D Trellis Code In DMT” filed Aug. 20, 2002, the entirety of which is incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to the field of telecommunications and, more particularly, to data communications over telephone networks and more specifically to voice band modems operating at data signaling rates of up to 33600 bits/second for use on telephone switched networks and leased point-to-point two-wire telephone type circuits in which a method for improving noise immunity using a 64 state four-dimensional (4D) Trellis coder in the DMT (discrete multi-tone) physical layer. 
     The explosive growth of internet has created a demand for high data rates for home users that rely on standard analog plain old telephone systems (POTS) that use a copper wire twisted pair to carry the information. The need for high-speed access to the home is inevitable due to the availability of information, data, high-bandwidth video and the like from the world wide web and because of such demand, higher speed modems are required. Modems operating at higher rates of up to 33,600 bits/second are in use nowadays. A multitude of competing communication technologies provide high-speed access to the home such as cable modems, digital subscriber line (xDSL) that utilizes the existing analog plain old telephone systems (POTS) that use a copper wire twisted pair to carry the information. Because of bandwidth limitation (4 KHz), and power limitation of the telephone network, line coding schemes are used to encode digital signals into analog signals that convey the analog information over the analog telephone network, such line coding schemes should avoid undesirable bandwidth or power increase. The line coding schemes manipulate the analog carrier signal which has three attributes (amplitude, phase and frequency) of which one or more of such attributes are manipulated by known modulation techniques, one of which is quadrature amplitude modulation (QAM) whereby the carrier signal&#39;s phase and amplitude is modulated in order to encode more data within a frequency bandwidth. One example of a QAM modulation system sends two bits of information per QAM symbol, where the digital values can be encoded and the corresponding amplitude and phase can be represented using the constellation. By increasing the constellation size and in the meantime the bit density per symbol will be increased, hence achieving higher data rates. As the constellation size increases, the granularity of the phase and the amplitude difference between different constellation points diminishes, making it increasingly difficult to decode the constellation points, especially in the presence of noise. One way of circumventing such a problem is to increase the Euclidean distance between symbols employing Trellis coding which is a bandwidth efficient, since the symbol rate and, hence the bandwidth is not increased. As the constellation size gets bigger, the problem of detecting constellation due to density increases and shorter Euclidean distance between symbols, therefore it is desirable to introduce redundancy without doubling the constellation size. Therefore, a way of counter-acting the effects the short Euclidean distance between symbols is to partition the quadrature amplitude modulated signal into subsets, thereby creating an acceptable Euclidean distance between symbols. 
     Data from a personal computer or other equipment at the customer premise (CPE) is sent to a transmitter which arranges the data into frame packets; the packetized signal is then quadrature amplitude modulation encoded and error encoded using trellis encoding to improve the noise immunity using a convolutional coder to select a sequence of subsets in a partitioned signal constellation. A numerical symbol vector is trellis encoded. The trellis encoding starts with the most significant symbol and ends with the least significant symbol of the vector, a process which employs convolutional encoding that converts the input symbol to another symbol and then maps the encoded symbol to its corresponding 16 QAM signal constellation point. The current trellis encoder in the DMT (discrete multi tone) standard is a 4-D (four-dimensional), 16-state Wei encoder which is a ¾ encoder with a coding gain of 4.6 dB (it varies depending on the bits per bin). The 4-D symbol is formed by 2 bins, each of which contains 2-D (two-dimensional) constellations partitioned into four 2-D co-sets which are further partitioned into 8 4-D co-sets. The minimum squared distance (MSD) of the 4-D co-set is 4d 2   0  and the branch minimum squared distance trellis tree is also 4d 2   0 . This invention is an improvement on the existing 64 state 4-D trellis encoder recommended by the ITU-T (international telecommunication union). 
     Since the Euclidean distance between symbols is a paramount feature of the QAM signal, and since the discrete multi-tone modulation scheme employed by some of the high data rate systems such as DSL requires transmitting of at least three DMT symbols per bin, there is a need to use Trellis codes in DMT. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides a method and apparatus for encoding data bits in DMT modulation system utilizing a 64-state Trellis encoder in order to achieve further improvement in the achievable coding gain by employing coset partitioning, bit conversion, and constellation encoder that fit the DMT modulation. 
     In one embodiment of the present invention, a method and system of Trellis encoding is initiated with receiving at least five input data bits and encoding at least four data bits of the received bits using a convolutional encoder, such an encoder employs 4/5 encoding process with at least six stages to encode the bits, the encoded bits are used to generate a redundant bit using a Trellis state machine. The encoded bits, the generated redundant bit as well as any raw uncoded data are passed onto a constellation mapper in order to create two 2-D coset groups, and the state machine is returned to zero once the all the 256 DMT bins are mapped into. 
     In another embodiment of the a present invention, At the end of each DMT symbol, the Trellis state machine has to be forced to return to 0 state and tied to the state of the state machine as required by the DMT standard. To achieve this, the following constraint has to applied, for both of the final two 4-D symbols, two separate steps are taken in order to create such state, and to improve rate, the termination may performed once several DMT symbols or completely eliminated. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention can be understood more completely by reading the following Detailed Description of the Preferred Embodiments, in conjunction with the accompanying drawings and tables. 
         FIG. 1  is flow chart illustrating the encoding method according to one of the embodiments of the present invention. 
         FIG. 2  is an 2-D co-sets of partitioning of the Right constellation. 
         FIG. 3  is a 2-D and 4-D co-set conversion table. 
         FIG. 4  is a state machine of a convolution encoder. 
         FIG. 5  is the conversion mechanism of 2-D co-sets. 
         FIG. 6  is an state transition table. 
         FIG. 7  is Co-set transition table. 
         FIG. 8  is a 3-bit constellation mapping. 
         FIG. 9  is a table to the top two bits of X and Y in the constellation mapping. 
         FIG. 10  is a 7-bit constellation mapping. 
         FIG. 11  is a simulation of co-set decoding error comparison. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The following description is intended to convey a thorough understanding of the invention by providing a number of specific embodiments and details involving the Trellis code in the DMT physical layer for further performance enhancement techniques. Various improvements and modifications to the preferred embodiments will become apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments. Therefore, the present invention is not limited to the specific embodiments shown and described, but interpreted to a larger scope consistent with the novel features disclosed herein. 
     In one embodiment of the present invention and in reference to  FIG. 1 , a method and system of Trellis encoding begins with receiving at least five input data bits in step  110 , and encoding at least four data bits of the received bits using a convolutional encoder in step  115 , such an encoder employs 4/5 encoding process with at least six stages to encode the bits as shown in step  120 , the encoded bits are used to generate a redundant bit using a Trellis state machine in step  125 . In step  130 , the encoded bits, the generated redundant bit as well as any raw uncoded data is passed onto a constellation mapper in order to create two 2-D coset groups in step  135 . In step  140 , the state machine is returned to zero once the all the 256 DMT bins are mapped into, and finally in step  145 , the steps are repeated in order to map the following DMT bins. 
     In reference to  FIG. 2 , and in accordance to one embodiment of the present invention, a 64-state 4-D Trellis code is employed in the DMT physical layer for further performance enhancement. This Trellis encoder which is based on the 4-D 64-state Wei encoder defined in the ITU-T Recommendation V.34 may cope with the DMT constellation signaling. The theoretical coding gain of the new coder is around 5.63 dB, about 0.96 dB higher than the current Trellis coder in the DMT standard. 
     According to another embodiment of the present invention, and in reference to  FIG. 4 , a Trellis coder for use in DMT which is an 4/5 systematic coder, and which employs a 6-state finite machine  400 , six-stages  420 ,  450 ,  465 ,  470 ,  475 , and  485 . The six stage finite state machine  400  receives four bits  405  and generates one redundant bit  495  from the 4 input bits, u 3 u 2 u 1 u 0 . 
     The above state machine can be mathematically expressed as follows:
 
 X   4   =u   2   ⊕W   2   ⊕W   5 
 
 X   3   =u   1   ⊕W   4    ⊕W   5 
 
 X   2   =u   4   ⊕W   1   ⊕W   3   ⊕W   4 ⊕( u   2 &amp; W   5 )
 
 X   1   =u   3   ⊕W   3   ⊕W   4 ⊕( W   5 &amp;( W   4   ⊕u   1 ))
 
In another embodiment of the present invention, and in reference to  FIG. 5 , five input data bits are received  505 , and  510 , where input data bit  505  is passed onto a constellation mapper  525 , while the other four input data bits  510  are encoded in a convolutional encoder  515 , and along with a redundant bit  520 , passed onto the constellation mapper  525 . The encoded bits  510 , the generated redundant bit  520  along with the uncoded bit  505  are mapped into the constellation mapper  525 , and added together using modulo  2  addition generating a first 3-bit group  530  to be inputted into a one DMT bin and a second 3-bit group  535  to be inputted into a one DMT bin. Bit groups  530  and  535  are used to generate a first 2-D coset and a second 2-D coset as shown in the last two columns of  FIG. 3 , and the two 2-D cosets are mapped onto the DMT bins. The overall minimum squared distance (MSD) between the two 2-D cosets is calculated to be 5d 2   0 . And considering the constellation expansion due to adding the redundant bit  520 , the coding gain is estimated to be around 5.6 dB, slightly varying depending on the total bits/bin. The resulting state and coset transition diagrams are given in the  FIGS. 6 and 7 .
 
     In yet another embodiment of the present invention, to generate create a 3-bit constellation, each 2-D coset is mapped to one of the 8 points in  FIG. 8 . The number in the figure represents the 2D coset number (v′ 2 v′ 1 v′ 0  or w′ 2 w′ 1 w′ 0 ). And to have the mapping point to confine within the constellation set compliant with the DMT standard under the given coset specified by v′ 2 v′ 1 v 0  for bin  1  and w′ 2 w′ 1 w′ 0  for bin  2 , the following conversion is needed:
 
 v   0   =v′   0 
 
 v   1   =v′   1 
 
 v   2   =v′   3   +v′   2   +v′   1   +v′   0 
 
 v   3   =v′   3 
 
where v′ 3  is one of the uncoded bits. Together with other uncoded bits, the conversion bits are fed into the conventional encoder in the DMT standard to obtain X and Y in the final constellation mapping.  FIG. 2  is an example of 6 bit constellation resulted from the above constellation encoder. For bin  2 , the same conversion is done on w′ 3 w′ 2 w′ 1 w′ 0 . In the DMT standard, a table is needed to calculate the last two bits of X and Y to get the given shape of the constellation for odd-numbered bits constellation. To assign the points into right cosets with the 64-state Trellis encoder, the table is modified from the DMT standard, as shown in the  FIG. 7 . Additionally, since the proposed 64 state Trellis is a 4/5 coder, it is difficult to have both 2-D symbols each having a 2 bit constellation. Only the first 2-D symbol can be set to a 2 bit constellation but assuming u 5 =0 so that the resulting 2-D coset is restricted to 0-3. This can be verified in  FIG. 3 .
 
     In another embodiment of the a present invention, At the end of each DMT symbol, the Trellis state machine of  FIG. 3  has to be forced to return to 0 state and tied to the state of the state machine as required by the DMT standard. To achieve this, the following constraint has to applied, for both of the final two 4-D symbols of  FIG. 2 , two separate steps are taken in order to create such a state:
 
 u   2   =W   2   ⊕W   5 
 
 u   1   =W   4   ⊕W   5 
 
and for the last 4-D symbols.
 
 u   4   =W   1   ⊕W   2   W   5   ⊕W   3   ⊕W   4   ⊕W   5 
 
 u   3   =W   3   ⊕W   4   ⊕W   5 
 
To improve the encoding rate, such termination may be performed once every 256 DMT bins are mapped into.