Abstract:
LDPC (Low Density Parity Check) coded 128 DSQ (Double Square QAM) constellation modulation and its associated labeling. A novel means is introduced by which a constellation may be arranged and mapping in its symbols may be determined to provide for improved performance. One application area in which this may be employed is transmission over twisted pair (typically copper) cabling existent within data centers of various networks. The operation of the IEEE 802.3 Ethernet local area networks currently being used (as well as those currently under development) would benefit greatly by employing the various principles presented herein. When this novel approach of an LDPC coded 128 DSQ constellation modulation combined with TH (Tomlinson-Harashima) preceding is employed within a communication device at a transmitter end of a communication channel (i.e., in a transmitter and/or a transceiver), the overall operation of a communication system may improve significantly when compared to prior techniques.

Description:
CROSS REFERENCE TO RELATED PATENTS/PATENT APPLICATIONS 
   Provisional Priority Claim 
   The present U.S. Utility patent application claims priority pursuant to 35 U.S.C. § 119(e) to the following U.S. Provisional patent application which is hereby incorporated herein by reference in its entirety and made part of the present U.S. Utility patent application for all purposes: 
   1. U.S. Provisional Application Ser. No. 60/604,426, entitled “Low-Density Parity Check (LDPC) coded 128 double square QAM constellation modulation and its set-partition and Gray code labeling,” filed Wednesday, Aug. 25, 2004, pending. 
   Incorporation by Reference 
   The following U.S. Utility patent application is hereby incorporated herein by reference in its entirety and made part of the present U.S. Utility patent application for all purposes: 
   1. U.S. Utility patent application Ser. No. 11/190,657, entitled “A short length LDPC (Low Density Parity Check) code and modulation adapted for high speed Ethernet applications,” filed Wednesday, Jul. 27, 2005, pending. 

   BACKGROUND OF THE INVENTION 
   1. Technical Field of the Invention 
   The invention relates generally to communication systems; and, more particularly, it relates to coding and modulation of signals within such communication systems. 
   2. Description of Related Art 
   Data communication systems have been under continual development for many years. In recent years, communication systems employing concatenated coding schemes of various types, like turbo coding, or LDPC (Low Density Parity Check) coding have attained significant interest. In combination with iterative decoding, these types of communication systems can achieve relatively low BERs (Bit Error Rates) near the Shannon limit of a given communication channel. 
   The Shannon limit may be viewed either as the lowest SNR (Signal-to-Noise Ratio) at which for a given data rate theoretically error-free data transmission may be accomplished, or the maximum data rate for error-free transmission over a channel with given SNR. The ideal goal has been to closely approach the Shannon limit with affordable complexity and limited latency for decoding and decoding while maintaining a given target BER performance. 
   LDPC coding has been shown to provide for excellent error performance near the Shannon limit in some cases. In one example, by using a so-called irregular LDPC code with a block length of one million bits performance within 0.1 dB of the Shannon limit for a BER of 10 −6  has been shown. However, most applications require shorter block lengths leading to lower complexity and smaller latency for encoding and decoding. LDPC coding is considered as a premier candidate technology for such applications as well. 
   The use of LDPC coded signals continues to be explored within many newer application areas. For example, the use of LDPC coded modulation has been of significant concern within the IEEE (Institute of Electrical &amp; Electronics Engineers) P802.3an (10GBASE-T) Task Force. This group has been chartered by IEEE with the development and standardization of a new Ethernet standard for 10 Gbit/s transmission over copper cabling with four twisted pairs and a cable length of up to 100 m. Public information concerning the IEEE P802.3an (10GBASE-T) Task Force is available at the Internet address http://www.ieee802.org/3/an/. Near-capacity achieving coded modulation is required to enable 10 Gbit/s operation over the envisaged copper cabling at a target BER of 10 −12 . An upper limit on latency of 2048 modulation intervals, or 25&#39;600 bits on four wire pairs, precludes the use of most traditional concatenated coding schemes. 
   Clearly, there is a need in the art for a coding scheme which permits achieving the objectives of a project like IEEE P802.3an. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention is directed to apparatus and methods of operation that are further described in the following Brief Description of the Several Views of the Drawings, the Detailed Description of the Invention, and the claims. Other features and advantages of the present invention will become apparent from the following detailed description of the invention made with reference to the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       FIG. 1  and  FIG. 2  depict various embodiments of communication systems that may be built in accordance with certain aspects of the invention. 
       FIG. 3  shows the bipartite graph of an LDPC (Low Density Parity Check) code. 
       FIG. 4  illustrates a 128 DSQ (Double Square Quadrature amplitude modulation) constellation. 
       FIG. 5  shows a “doughnut” 128 QAM (Quadrature Amplitude Modulation) constellation. 
       FIG. 6A  gives a diagram illustrating a system that employs mapping of 3 uncoded bits and 4 coded bits according to certain aspects of the invention. 
       FIG. 6B  gives a diagram illustrating a system that employs mapping of 4 uncoded bits and 3 coded bits according to certain aspects of the invention. 
       FIG. 7  shows a labeling of points within a 128-DSQ (Double Square QAM) constellation with 3 uncoded bits according to certain aspects of the invention. 
       FIG. 8  shows another labeling of points within a 128-DSQ constellation with 3 uncoded bits according to certain aspects of the invention. 
       FIG. 9  illustrates two-dimensional Gray labeling of the 16 constellation points within the individual 8 regions with 4 uncoded bits and labeling these regions with 3 uncoded bits as in  FIG. 7  or  FIG. 8 . 
       FIG. 10  provides a more detailed view of the two-dimensional Gray labeling of 128-DSQ constellation points with 4 coded bits. 
       FIG. 11  shows the arrangement of uncoded bits and coded bits in a block of 512 7-bit labels according to certain aspects of the invention. 
       FIG. 12A ,  FIG. 12B , and  FIG. 12C  depict diagrams illustrating various steps by which the 128-DSQ constellation mapping may be achieved according to certain aspects of the invention. 
       FIG. 13  illustrates an embodiment by which the bit mapping may be implemented for a 128-DSQ constellation. 
       FIG. 14  presents another view of the association of 3 uncoded bits and 4 coded bits with points within the basic 128-DSQ constellation region and its cyclic modulo  32  extensions according to certain aspects of the invention. 
       FIG. 15  shows a flowchart illustrating the transmitter processing in a system employing a 128-DSQ constellation and TH precoding performed according to certain aspects of the invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The goal of digital communications systems is to transmit digital data from one location, or subsystem, to another either error free or with an acceptably low error rate. As shown in  FIG. 1 , data may be transmitted over a variety of communication media: metallic cable, wireless radio, optical fiber, magnetic or optical storage media, and other types of media as well. 
     FIG. 1  and  FIG. 2  illustrate various embodiments of communication systems,  100  and  200 , respectively, which may be built in accordance with certain aspects of the invention. 
   Referring to  FIG. 1 , a communication system  100  comprises a communication channel  199  that communicatively couples two communication devices  110  and  120  (including a transmitter  112 / 212  having an encoder  114 / 214  and/or including a receiver  116 / 216  having a decoder  118 / 218 ) situated at the ends of the communication channel  199 . The communication channel  199  may be, e.g., a satellite communication channel  130  using satellite dishes  132  and  134 , a wireless communication channel  140  using towers  142  and  144  and/or local antennae  152  and  154 , a wired communication channel  150 , and/or a fiber-optic communication channel  160  using electrical to optical (E/O) interface  162  and optical to electrical (O/E) interface  164 . 
   To achieve low error rates in the presence of signal disturbances and signal distortion, modern communication systems employ channel coding and error correction techniques, which are realized by an encoder at the transmitter and a decoder at the receiver. 
   Referring to the communication system  200  of  FIG. 2 , at a transmitting end of a communication channel  299 , information bits  201  are provided to a transmitter  297  that is operable to perform encoding of these information bits  201  using an encoder and symbol mapper  220  (which may be viewed as being distinct functional blocks  222  and  224 , respectively) thereby generating a sequence of discrete-valued modulation symbols  203 . The modulation symbols are then provided to a transmit driver  230  that uses a DAC (Digital to Analog Converter)  232  and a transmit filter  234  to generate a continuous-time filtered transmit signal  204  suitable for transmission over the communication channel  299 . At a receiving end of the communication channel  299 , a continuous-time receive signal  206  is provided to an AFE (Analog Front End)  260  that includes a receive filter  262  (that generates a filtered, continuous-time receive signal  207 ) and an ADC (Analog to Digital Converter)  264  (that generates discrete-time receive signals  208 ). The output of the ADC is processed by an equalizer  270 , which often is an adaptive filter to compensate for a priori unknown signal distortion by the communication channel. A metric generator  275  then calculates symbol metrics  209  that are employed by a decoder  280  to make best estimates of the discrete-valued modulation symbols and information bits  210  encoded therein. 
   Moreover, a TH (Tomlinson-Harashima) precoder  229  may be interposed between the encoder and symbol mapper  220  and the transmit driver  230 . The TH precoder  229  transforms the output of the symbol mapper  220  according to a predetermined symbol response of the overall channel, which extends from the precoder output in the transmitter to the input of the metric generator  275  in the receiver. The transformation consists in filtering the sequence of modulation symbols  203  by the inverse of the predetermined symbol response and performing a nonlinear modulo operation that constrains the output signal of the precoder, as described in the literature on TH preceding. 
   Several of the following Figures describe other and particular embodiments (some in more detail) that may be used to support the devices, systems, functionality and/or methods that may be implemented in accordance with certain aspects of the invention. One particular type of signal that may be processed according to certain aspects of the invention is an LDPC coded signal. Before more details are provided below, a general description of LDPC codes is provided. 
   LDPC codes were introduced by R. Gallager [1] and rediscovered by M. G. Luby et al. [2] in the publications given below. 
   [1] R. Gallager,  Low-Density Parity-Check Codes , Cambridge, Mass.: MIT Press, 1963. 
   [2] M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, D. A. Spielman, and V. Stemann, “Practical Loss-Resilient Codes”,  Proc.  29 th    Symp. on Theory of Computing,  1997, pp. 150-159. 
   A binary LDPC code of block length N is defined by a sparse binary parity check matrix H=(h i,j ) M×N , i.e., a matrix with, a low density of 1&#39;s.  FIG. 3  illustrates the bipartite graph  300  of an LDPC (Low Density Parity Check) code. In the art, this graph is also referred to as a Tanner graph. On the left side of the graph  300  are the variable nodes (or bit nodes)  310 , which correspond to the N bits of the LDPC code, and on the right side of the graph  300  are the check nodes  320 , which correspond to the M parity check equations defining the LDPC code. The d v (i) branches  314  extending from the i-th variable node, for 1≦i≦N, correspond to the 1&#39;s in the i-th column of H M×N . Likewise, the d c (j) branches  324  extending from the j-th check node, for 1≦j≦M, correspond to the 1&#39;s in the j-th row of H M×N . If d v (i)=d v  for all i, and d c (j)=d c  for all j, then the LDPC code is called a (d v , d c ) regular LDPC code, otherwise the LDPC code is called an irregular LDPC code. It is evident that the sum of branches extending from the variable nodes must be equal to the sum of branches extending from the check nodes, since both sums represent the total number of 1&#39;s in the parity check equation. To provide a complete code description, the left hand branches and the right hand branches in the bipartite graph are pairwise connected through a permuter  330  (also referred to as an interleaver). The connections are randomly chosen or constructed in some pseudo random fashion based on a number of rules. Each connection defines an edge  340  e=(i, j) between an i-th variable node  312  and a j-th check node  322 . 
   Several decoding algorithms for LDPC codes are known in the art. Generally, these algorithms accomplish decoding in an iterative fashion by passing messages along the edges of the bipartite graph, first from the variable nodes to the check nodes, then from the check nodes back to the variable nodes, then again from the variable nodes to the check nodes, and so on. The messages represent probabilistic information about the variables (bits) of the code. 
     FIG. 4  depicts an embodiment of a two-dimensional 128-point Double Square QAM constellation (128-DSQ), which consists of two interleaved 64-point square QAM constellations (64-QAM). In the following references, a similar constellation but with 32 constellation points, in [3] called 32 AMPM, is presented: 
   [3] G. Ungerboeck, “Channel Coding with Multilevel/Phase signals,”  IEEE Trans. on Information Theory , Vol. IT-28, No. 1, January 1982, pp. 55-67. 
   [4] L-F. Wei, “Generalized square and Hexagonal constellations for intersymbol-interference channels with generalized Tomlinson-Harashima precode,”  IEEE Trans. on Communications , Vol. 42, No. 9, September 1994, pp. 2713-2721. 
     FIG. 5  shows an embodiment of another two-dimensional 128-point “doughnut” constellation, which is obtained from a 144-point square QAM constellation (144-QAM=12-PAM×12-PAM) by omitting 16 points around the origin. This constellation was proposed in a presentation [5] referred to below. 
   [5] D. Dabiri and J. Tellado of Teranetics, “Modifications to LDPC Proposal offering Lower Symbol Rate and Lower Latency,” contribution to standards project IEEE 802.3an (10GBASE-T), March 2004; publicly available at Internet address “http://www.ieee802.org/3/an/public/mar04/dabiri — 1 — 0304.pdf”. 
   The 128-DSQ constellation and the 128 “doughnut” constellation are both suited for TH (Tomlinson-Harashima) preceding, as explained in reference [4]. If both constellations are normalized to the same minimum distance between adjacent points, then without TH preceding the average energy of the 128-DSQ constellation points is smaller than the average energy of the 128 “doughnut” constellation points by the factor 0.8019 (−0.959 dB). With TH preceding, the average energy for the 128-DSQ constellation at the precoder output is still smaller than the corresponding energy for the 128 “doughnut” constellation by the factor 0.8889 (−0.5115 dB). Hence, the 128-DSQ constellation is preferable over the 128 “doughnut” constellation in terms of average power required for a given minimum distance between constellation points. In addition, the construction of the 128-DSQ constellation provides more regularity. 
     FIG. 6A  illustrates an embodiment of a system in which according to certain aspects of the invention 3 uncoded bits, shown as reference numeral  610 , and 4 coded bits (e.g., generated by an LDPC encoder), shown as reference numeral  620 , are combined to form a 7 bit symbol label. This label is then mapped to a point of the 128 DSQ constellation, shown as reference numeral  650 . 
   The diagram in  FIG. 6B  shows an embodiment of a system in which according to certain aspects of the invention 4 uncoded bits, shown as reference numeral  615 , and 3 coded bits (e.g., generated by an LDPC encoder), shown as reference numeral  625 , are combined to form a 7 bit symbol label. This label is then mapped to a point of the 128 DSQ constellation, shown as reference numeral  655 . 
   Clearly, without departing from the scope and spirit of the invention other embodiments may also be envisioned with (n&lt;6) uncoded bits and 7-n LDPC coded bits. Further, the coded bits may be provided by other types of encoders. 
     FIG. 7  depicts a mapping scheme  700  for associating 3 uncoded bits of a 7 bit label with 8 regions of a 128-DSQ constellation. The 16 points of each subset are all labeled with the same 3 uncoded bits, i.e., 000, 001, 010, 011, 100, 101, 110, or 111. The regions associated with uncoded bits 000, 010, 110, 011, and 001 are contiguous quadratic regions within the boundary region with corner points (±15,±15) enclosing the entire 128-DSQ constellation. The regions associated with uncoded bits 100, 101, and 111 are fragmented. They become contiguous when their wrapping in a modulo- 32  fashion around the boundary lines is considered. 
     FIG. 8  shows another embodiment  800  similar to that of  FIG. 7 , but with a different mapping of the uncoded bits. 
     FIG. 9  provides a combined view of the two mappings of 3 uncoded bits to the 8 regions of the 128-DSQ constellation given in  FIG. 7  and  FIG. 8  and a mapping of 4 coded bits to the 16 constellation points within these region. The same two-dimensional Gray mapping is repeated for each region. The Gray mapping has the property that 4-bit labels of coded bits associated with any two adjacent points throughout the entire 128-DSQ constellation differ only in one bit position. Some details of the mapping are further illustrated in  FIG. 10 . 
   In the case of TH (Tomlinson-Harashima) repetitions of the 128-DSQ constellation in the X and/or the Y direction occur. It should be noted that the labeling of the points of the 128-DSQ constellation is such that the labeling properties within the constellation are seamlessly maintained beyond the constellation boundary, where points in the extended 128-DSQ constellation simply alias to points inside the boundary region through a modulo- 32  operation. 
     FIG. 11  shows an arrangement  1100  of uncoded bits and coded bits within a block according to certain aspects of the invention. In this arrangement a block of 3×512=1536 uncoded bits  1110  and a block of 4×512=2048 coded bits  1120  are arranged as a block of 512 7-bit labels. The 2048 coded bits are obtained from a systematic (2048, 1723) LDPC encoder which adds to 1723 coded information bits, shown as reference numeral  1121 , and 325 check bits, shown as reference numeral  1122 . The 512 7-bit labels are then mapped to a block of 512 128 DSQ symbols conveying 1536+1723=3259 information bits. This corresponds to a code rate of 3259/512 information bits per two-dimensional 128-DSQ symbol or 3.1826 bit per symbol dimension. 
   The emerging 10GBASE-T Ethernet standard calls for a payload data rate of 10 Gbit/s. With baseband transmission over 4 wire pairs at a modulation rate of 800, a code rate of 3.125 bit per symbol dimension is required: 4×800 Mbaud×3.125 bit/dimension=10 Gbit/s. With the arrangement of  FIG. 11 , there is room for the inclusion of 9 overhead bits among the 3259 information bits of one block. 
     FIG. 12A ,  FIG. 12B , and  FIG. 12C  illustrate a further mapping of 3 uncoded bits and 4 coded bits into points of the 128 DSQ constellation. The construction of this mapping, which exhibits the same principle characteristics as the mappings of  FIG. 7 ,  FIG. 8 ,  FIG. 9 , and  FIG. 10 , was motivated by a desire for a simple algorithmic description of the mapping process. 
   The mapping of 3 uncoded bits (u 1  u 2  u 3 ) and 4 coded bits (c 1  c 2  c 3  c 4 ) into a point (a 1  a 2 ) of the 128-DSQ constellation may be broken down into 3 steps as follows: 
   Step 1: The seven bits are first mapped into a point (x 1  x 2 ) with integer coordinates in the interval (0,15) as shown in  FIG. 12A . The uncoded bits (u 1  u 2  u 3 ) define a lower left corner point of one of 8 regions. These regions are labeled with uncoded bits 000, 001, 010, 011, 100, 101, 110, and 111 such that the labels of adjacent regions differ at most in two bit positions when considered in a modulo  16  fashion. The coded bits (c 1  c 2  c 3  c 4 ) determine one of the 16 points within the chosen region. The employed two-dimensional Gray mapping is shown on the right side of the diagram  1201 . The following equations define this first mapping step.
 
0≦( x   i =8 x   i   3 +4 x   i   2 +2 x   i   1   +x   i   0 )≦15:  x   i   k  ε(0,1);  i =1,2;  k= 0,1,2,3
 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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   Step 2: The point (x 1  x 2 ) is transformed by a rotation and expansion operation combined with a modulo  16  reduction into a point (y 1  y 2 ) with coordinates in (0,15). This is accomplished by the following operation. 
   
     
       
         
           
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   The constellation of points (y 1  y 2 ) is shown in  FIG. 12B . 
   Step 3: From (y 1  y 2 ) a point (a 1  a 2 ) in the 128-DSQ constellation illustrated in  FIG. 12C  is obtained by the further expansion and translation operation 
   
     
       
         
           
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     FIG. 13  illustrates an implementation of the entire mapping operation performed in the three steps discussed above. The embodiment designated by reference numeral  1300 , according to certain aspects of the invention, shows the transformation of the 3 uncoded bits (u 1  u 2  u 3 ) and 4 coded bits (c 1  c 2  c 3  c 4 ) to a point (a 1  a 2 ) in the 128-DSQ constellation. 
     FIG. 14  shows another aspect of the labeling of 128-DSQ constellation points with 3 uncoded bits and 4 coded bits. In the diagram  1401 , the labeling within the basic 128-DSQ constellation region  1403  enclosing the 128 points of the constellation is cyclically extended in a modulo  32  fashion outside of the basic constellation region as occurring in a system employing TH precoding. 
     FIG. 15  is a flowchart illustrating an embodiment of the transmitter processing  1500  performed in a system employing LDPC coded 128-DSQ modulation with TH preceding. The processing involves receiving a block of information bits  1510  and dividing the bits into bits remaining uncoded  1512  and input bits  1512  for encoding into a block of coded bits  1520 . Next, 7-bit labels comprising 3 uncoded bits  1511  and 4 coded bits  1520  are formed and mapped to a sequence of 128-DSQ modulation symbols  1530 . The sequence of modulation symbols then is processed by a TH precoder, thereby generating a sequence of discrete-time transmit signals  1540 . The sequence  1540  is then converted to a continuous-time signal  1540  and further to a filtered time-continuous signal  1550 , which is finally launched into a communication channel  1570 . 
   In view of the above detailed description of the invention and associated drawings, other modifications and variations may be effected without departing from the spirit and scope of the invention.