Abstract:
A transmitter and method include a LDPC encoder configured to encode source data, and a mapper configured to generate three coordinates in accordance with a 3D signal constellation where the coordinates include an amplitude coordinate and two phase coordinates. A laser source is modulated in accordance with each of the three coordinates to provide a transmission signal. A receiver, includes a demapper receives an input signal from three branches to demap the input signal using a three-dimensional signal constellation having three coordinates. The three branches include a direct detection branch, and two coherent detection branches such that the direct detection branch detects an amplitude coordinate of the input signal and the two coherent detection branches detect in-phase and quadrature coordinates of the input signal. A bit prediction module and at least one LDPC decoder are configured to iteratively decode bits by feeding back extrinsic LLRs to the demapper.

Description:
RELATED APPLICATION INFORMATION 
     This application claims priority to provisional application Ser. No. 60/956,797 filed on Aug. 20, 2007, incorporated herein by reference. 
    
    
     BACKGROUND 
     1. Technical Field 
     The present invention relates to optical communication, and more particularly to a modulation system and method for using three-dimensional (3D) Low Density Parity Check (LDPC) coded modulation. 
     2. Description of the Related Art 
     Optical communication systems are rapidly developing to meet the ever increasing transmission capacity demands. Electrically time-division multiplexed (ETDM) transmitters and receivers operating at 100 Gb/s are becoming commercially available. Despite the cost, the major concerns at such high speed are the polarization mode dispersion (PMD), and the intrachannel nonlinearities. Consequently, approaches of achieving beyond 100-Gb/s transmission using commercially available components operating at lower speed are becoming increasingly important. 
     SUMMARY 
     A transmitter and method include an LDPC encoder configured to encode source data, and a mapper configured to generate three coordinates in accordance with a 3D signal constellation where the coordinates include an amplitude coordinate and two phase coordinates. A power source is modulated in accordance with each of the three coordinates to provide a transmission signal. 
     A receiver, includes a demapper which receives an input signal from three branches to demap the input signal using a three-dimensional signal constellation having three coordinates. The three branches include a direct detection branch, and two coherent detection branches such that the direct detection branch detects an amplitude coordinate of the input signal and the two coherent detection branches detect in-phase and quadrature coordinates of the input signal. A bit prediction module and at least one LDPC decoder are configured to iteratively decode bits by feeding back extrinsic LLRs to the demapper. 
     These and other features and advantages will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The disclosure will provide details in the following description of preferred embodiments with reference to the following figures wherein: 
         FIG. 1  is a block diagram showing a transmitter and transmission method using the three-dimensional bit-interleaved low-density parity-check coded modulation (3D BI-LDPC-CM) scheme in accordance with the present principles; 
         FIG. 2  is a block diagram showing a hybrid coherent/direct detection receiver and receiver method using the 3D BI-LDPC-CM scheme in accordance with the present principles; 
         FIG. 3  is a constellation diagram for a 64-ary 2-dimensional constellation in accordance with the present principles; 
         FIG. 4  is a constellation diagram for a 64-ary 3-dimensional constellation in accordance with the present principles; and 
         FIGS. 5 and 6  are plots showing bit error rate (BER) versus optical signal to noise ratio (OSNR) performance of 2D and 3D LDPC-CM schemes for: 40-Giga symbols/s ( FIG. 5 ), and 100-Giga symbols/s ( FIG. 6 ). 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     In accordance with the present principles, three-dimensional low-density parity-check (LDPC) coded modulation (3D-LDPC-CM) systems and methods enable transmission beyond 100-Gb/s, and more preferably beyond 320-Gb/s rates using, e.g., commercially available components operating at say, 40-Giga symbols/s. To achieve such aggregate rates, the present principles provide: (i) an additional (third) basis function for a signal constellation; (ii) to facilitate a decoder implementation, a structured LDPC code is employed; and (iii) to improve performance, an iterative exchange of the extrinsic soft bit-reliabilities between an a posteriori probability (APP) demapper and an LDPC decoder is conducted. 
     The added basis function increases the Euclidean distance between the signal constellation points for the same average power per constellation point compared to an equivalent M-ary 2D constellation, leading to the improved bit-error ratio (BER) performance. The 3D LDPC-CM offers an improvement of up to 4.1 dB over a corresponding two-dimensional (2D) modulation scheme, and provides, e.g., up to 14 dB overall net effective gain at BER 10 −9 . The LDPC(8547,6922) code of rate 0.8098, illustratively employed herein, belongs to the class of balanced-incomplete block-design (BIBD) based LDPC codes of girth-8. Decoding may be based on an efficient implementation of sum product algorithm. 
     The present principles may be employed in many technical areas and in particular find utility in ultra-high-speed optical transmission systems to achieve Nx40-Gb/s aggregate rate (N=4, 16, . . . ) or in a next generation of Ethernet. Since Ethernet has grown in 10-fold increments 100-Gb/s transmission is envisioned as the transmission technology for next generation of Ethernet. 
     The present coded-modulation scheme employing a 1024-3D-constellation can also achieve a 1-Tb/s aggregate rate using transmission equipment operating at 100-Giga symbols/s. 
     Embodiments described herein may be entirely hardware, entirely software or including both hardware and software elements. In a preferred embodiment, the present invention is implemented in hardware with software elements. The software may include but is not limited to firmware, resident software, microcode, etc. 
     Embodiments may include a computer program product accessible from a computer-usable or computer-readable medium providing program code for use by or in connection with a computer or any instruction execution system. A computer-usable or computer readable medium may include any apparatus that stores, communicates, propagates, or transports the program for use by or in connection with the instruction execution system, apparatus, or device. The medium can be magnetic, optical, electronic, electromagnetic, infrared, or semiconductor system (or apparatus or device) or a propagation medium. The medium may include a computer-readable medium such as a semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disk and an optical disk, etc. 
     Referring now to the drawings in which like numerals represent the same or similar elements and initially to  FIG. 1 , architecture of a transmitter  100  employing a LDPC-coded modulation scheme is illustratively shown. Bit streams  104  coming from m different information sources  102  are encoded using different (n,k p ) LDPC codes in the set of encoders  106 . (For an (n,k p ) LDPC code, n is the codeword length which is the same for all LDPC codes and k p  is the number of information bits of the pth component LDPC code, where pε{1, 2, . . . , m}, (code rate r p =k p /n)). Using different LDPC codes allows optimal code rate allocation. Employing identical LDPC codes for all components is a special case of the multilevel coding (MLC) scheme that is called the bit-interleaved coded modulation (BITC) scheme. The encoded bit streams  107  are written row-wise to an m×n block-interleaver  108 . At time instance i, a mapper  110  reads m bits column-wise to determine the corresponding M-ary signal constellation point s i =(φ 1,i ,φ 2,i ,φ 3,i ). 
     In Equation (1), we denote orthonormal basis functions as Φ 1 , Φ 2 , and Φ 3 , where T is a symbol duration and 0&lt;t&lt;T. 
     
       
         
           
             
               
                 
                   
                     
                       
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     This forms a three-dimensional (3D) M-ary constellation. The 3D M-ary constellation is formed using identical 2D signal-constellation points constructed on parallel layers equally spaced at distance a. (see  FIGS. 3 and 4 ). The symbol c=(c 1 , c 2 , . . . , c m ) is divided into two groups of bits. The left-most group of l bits, defines the amplitude coordinate φ 3  and so defines a layer index, while the right-most group of m−l bits, defines the coordinates φ 1  and φ 2  and determines a location of the constellation point within the layer. The amplitude coordinate φ 3  cannot be set to zero as the phase coordinates φ 1  and φ 2  will be cancelled. As an illustration of the bit arrangements, observe a 64-ary 3D-constellation, in which each symbol carries 6 bits. Possible arrangements of the bits include: (i) 64-constellation points are split into two 32 2D layers (l=1), (ii) 64-constellation points are split into four 16-point layers l=2, etc. 
     The coordinates φ 1  and φ 2  are used for modulation in modulators  116  (e.g., Mach-Zehnder Modulators (MZM)). In this case, the power source is a distributed feedback (DFB) optical source (laser)  112 . A phase shifter  118  is employed at the output of one of the modulators  116  so that the signals can be combined by a coupler and modulated by φ 3  in a third modulator  116  and transmitted to/on a fiber  120 . 
     Referring to  FIG. 2 , an architecture of a hybrid coherent/direct detection receiver  200  is illustratively shown. The receiver  200  employs the LDPC-coded modulation scheme in accordance with the present principles. The hybrid receiver  200  uses direct detection for the amplitude coordinate φ 3 , and coherent detection for phase (in-phase and quadrature) coordinates φ 1  and φ 2 . A received electrical field  202  at the ith transmission interval is denoted by S i =|S i |e jφ     Si   , φ S,i =φ i φ S,PN , where a data phasor φ 1 ε{0, 2π/2 m−l , . . . , 2π(2 m−l −1)/2 m−l } and φβS,PN denote a laser phase noise process of a transmitting laser. A local laser electrical field  204  is denoted by L=|L|e jφ     L   , where φ L  is the laser phase noise process of the local laser. An amplitude detection branch  206  has an output that is proportional to |S i | 2 . Energy from the fiber and from the local laser are coupled by couplers  224  and  226  in accordance with Equation (2). A phase shifter  222  and splitters  228  are employed. The outputs of the upper- and lower-balanced branches  212  and  214  are proportional to Re{S i L*} and Im{S i L*}, as given below:
 
 Re{S   i   L*}=|S   i   ∥L |cos(φ i +φ S,PN −φ L )
 
The three branches  206 ,  212  and  214  include photodetectors  208  which convert optical signals to electrical signals. Amplifiers  210  may be employed. The outputs of the three branches  206 ,  212  and  214  are sampled at a symbol rate and corresponding samples are forwarded to an a posteriori probability (APP) demapper  216 , which processes the samples. The demapper  216  provides bit log-likelihood ratios (LLRs) computed by a bit predictor (LLR calculation module)  218  needed for iterative LDPC decoding. These LLRs are calculated as follows:
 
                       λ   ⁡     (     s   i     )       =     log   ⁢       P   ⁡     (       s   i     =       s   0     |     r   i         )         P   ⁡     (         s   i     ≠     s   0       |     r   i       )             ,           (   3   )               
where P(s i |r i ) is determined by Bayes&#39; rule as:
 
     
       
         
           
             
               
                 
                   
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     In (3) and (4) r i =(r 1,i ,r 2,i ,r 3,i ) denotes the received constellation point (the samples at APP demapper input), and P(r i |s i ) denotes conditional probability estimated from histograms. The LDPC decoders  220  used in the receiver  200  correspond to the LDPC encoders  106  in the transmitter  100  in terms of LDPC codes used. Extrinsic LLRs of LDPC decoders  220 , that are defined as the difference between the decoder input and the output LLRs, are then forwarded to the APP demapper  216 , (this step is denoted as an outer iteration) and the extrinsic information is iterated in both directions until convergence or until a predefined number of iterations has been reached. Suitable LDPC codes for use in the present coded-modulation scheme have been selected based upon EXIT chart analysis. 
     Referring to  FIGS. 3 and 4 , example constellation diagrams for a 64-ary: 2-dimensional constellation ( FIG. 3 ), and a 3-dimensional constellation ( FIG. 4 ) are illustratively shown.  FIG. 3  shows a 2D Quadrature Amplitude Modulation (QAM) signal constellation, and  FIG. 4  shows a corresponding 3D signal constellations for 64-ary transmission. In this case, by using a 40-Giga symbols/s symbol rate, we can achieve a 240-Gb/s aggregate rate. Using a 256-3D-constellation and 1024-3D-constellation with the same symbol rate, we can achieve 320-Gb/s and 400-Gb/s aggregate rate, respectively. 
     In one embodiment, identical LDPC(8547,6922) code employed in all encoders of the simulations and is of girth-8 LDPC code designed using the concept of BIBDs. The LDPC decoder may be based on min-sum-with-correction-term algorithm. 
     Results and conclusions: Simulations were completed for an additive white Gaussian noise (AWGN) channel model for 30 iterations in sum-product LDPC decoding algorithm, and 5 outer iterations (between the LDPC decoder and the natural demapper). The following signal constellations formats were observed: 64-QAM, 64-3D-constellation, 256-QAM, 256-3D-constellation, and 1024-3D-constellation. The 3D-constellation dimensions H are selected to be a power of 2, and we choose the number of h layers to be a multiple of 2, and w points per layer to be a perfect square. For example, in case of 64-ary, the constellation has 4 layers of 16 points each, providing the maximum separation distance among the points. For the other 2 cases, h×w were 4×64 and 16×64 for the 256-ary, and the 1024-ary signal constellations, respectively. 
     Referring to  FIGS. 5 and 6 , bit error rate (BER) performance versus optical-signal-to-noise ratio (OSNR) for the five cases described were shown in addition to uncoded cases for 40 Gb/s ( FIG. 5 ) and 100 Gb/s ( FIG. 6 ), respectively. Note that, as the constellation size grows the 3D-constellation BER performance improvement over corresponding 2D-constellation increases, reaching about 4.1 dB gain in the case of the 256-3D-constellation at BER of 10 −9 . These results motivated testing the 1024-3D-constellation, which is not practical in 2D, and interestingly, the results indicate that if compared to the 64-3D-constellation, a 16-fold increase in data rate causes only a penalty of 8 dB at BER of 10 −9 . 
     The net effective coding gains (at BER of 10 −9 ) for 64-QAM and 256-QAM 2D-constellations are 9.5 dB and 10 dB, respectively. The corresponding coding gains for 3D-constellations are 10.5 dB and 14 dB, respectively. 
     An ultra-high spectrally efficient 3D-coded-modulation scheme, based on multilevel square QAM constellations, improves the BER performance of M-ary 2D-constellations. It is suitable for ultra-high-speed optical transmission beyond 320-Gb/s aggregate rate or even 1-Tb/s aggregate rate once 100-Gb/s technology reaches the maturity of today&#39;s 40-Gb/s systems. 
     Having described preferred embodiments of wavelength transmission system and method using 3-dimensional LDPC-coded modulation (which are intended to be illustrative and not limiting), it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. It is therefore to be understood that changes may be made in the particular embodiments disclosed which are within the scope and spirit of the invention as outlined by the appended claims. Having thus described aspects of the invention, with the details and particularity required by the patent laws, what is claimed and desired protected by Letters Patent is set forth in the appended claims.