Contribution of Multidimensional Trellis Coding in VDSL Systems

SETIT 005 3 rd International Conference: Sciences of Electronic, Technologies of Information and Telecommunications March 7-31, 005 TUNISIA Contribution of Multidimensional Trellis Coding in VDSL Systems Mohamed Tlich, Meryem Ouzzif, and Ahmed Zeddam France Télécom Division R&D RESA, Avenue Pierre Marzin-307 Lannion Cedex mohamed.tlich@rd.francetelecom.com meryem.ouzzif@francetelecom.com ahmed.zeddam@francetelecom.com Abstract: In this paper, we take a new look at the single-carrier modulation technique for VDSL system. Using powerful coding techniques can further increase the performance of a Quadrature Amplitude Modulation (QAM) system. This paper investigates an implementation of the trellis coding in a single-carrier modulation (SCM) VDSL system intended for transmissions over short copper cables. The suggested code is a 4-dimensional 16-state trellis coder; it gains typically 4dB over uncoded transmissions in an AWGN environment. For suitable values of the truncation length of the Viterbi decoder, the results of the simulations carried out showed that the trellis coding implemented over the SCM-VDSL system, introduces an important gain in either the range of the twisted copper-pair, or in channel capacity. Key words: twisted copper pair cable, xdsl, Quadrature Amplitude Modulation (QAM), Trellis Coded Modulation (TCM), Crosstalk. 1 VDSL Overview Figure 1 shows a simplified VDSL system deployment (M.D. Nava & C. Del-Toso, 00). In this general architecture, fiber links connect the optical line termination unit (OLT) at the central office (CO) to the optical network unit (ONU) at the local exchanges and street cabinets. The network termination unit (NT) provides the necessary protocol adaptation at the customer site. CO AN OLT Local Exchange ONU VTU-O FTTEx Liaison VDSL Customer Premises NT VTU-R the customer premises are close to the local exchange and can be served directly from it. This is suitable for business service. In the second configuration, FTTCab or FTTC, the residential premises can be served from the street cabinet. The subscriber loop is a very hostile medium and suffers from many impairments, such as the attenuation of the twisted pair, the crosstalk, and the thermal noise. 1. Attenuation of the twisted pair: the line attenuation increases with both frequency and wire length (Figure ). This results in potentially lower bit rate capacity when considering long loops and broadband signals like VDSL. Other xdsl Optical Fiber Cabinet ISDN HDSL ADSL Customer Premises ONU VTU-O Liaison VDSL NT VTU-R Distribution Cable FTTCab Figure 1. Typical VDSL deployment scenarios As shown in this figure, there are two configurations that connect the ONU to the CO: Fiber to the exchange (FTTEx) and Fiber to the cabinet/curb (FTTCab/FTTC). In the first configuration, FTTEx,

0Log10( H(f) 0 10 0 30 40 50 60 70 1300m Channel Attenuation 500m 1000m 70-1 v.0.6 part1, 00), we will deal with the 3QAM constellation shown in Figure 4 we used in our simulations. This constellation is invariant to 90 rotations. Therefore, to make the system transparent to 90 phase offsets, when mapping bits into constellation points: 1. 3 bits (Q3n, Q4n and Q5n) are assigned to points within a quadrant so that a 90 rotation leaves them unchanged, as shown in the constellation of Figure 4.. The two first bits (Q1n and Qn) are differentially encoded to specify the quadrant, i.e., bits Q1n and Qn will determine the change in quadrant from symbol to symbol using the rules listed in table 1. 80 0 0.5 1 1.5.5 Freq (Hz) 3 3.5 4 4.5 x 10 6 xx111 xx011 xx110 xx010 Figure. Signal attenuation for a 500m, 1000m and 1300m wire length. Crosstalk: is noise caused by electromagnetic radiation of other telephone lines physically located in close proximity in the same cable binder. Such coupling increases with frequency, so it is very harmful for VDSL, which uses bandwidth up to 1 MHz. Practically, we can distinguish two types of crosstalk: Near-End crosstalk (NEXT) caused by signals traveling in opposite directions in the same cable binder, and Far-End crosstalk (FEXT) caused by signals traveling in the same direction as shown in Figure 3. Line 1 Line i NEXT Line 1 Line i Figure 3. NEXT and FEXT in cable binder FEXT 3. Thermal or background noise: a convention in standardization committees is to model background noise as additive white Gaussian noise (AWGN) with a fixed Power Spectral Density (PSD) level equal to - 140 dbm/hz as defined in (ETSI TS 101 70-1 v.0.6 part1, 00)(ETSI TS 101 70- v.0.3 part, 00). qi Serial to Parallel Converter xx010 xx110 xx011 xx101 xx100 xx001 xx111 xx101 xx100 Q5n Q4n Q3n Qn Q1n xx010 xx001 xx100 xx101 xx111 xx000 xx000 xx001 xx011 xx000 xx000 xx100 xx110 xx110 xx001 xx101 xx010 xx011 Table.1 xx111 Yn 1 D Y1n 1 D Differential Encoder Figure 4. Symbol Mapper Y5n Y4n Y3n Yn Y1n Complex Symbol Mapper Inputs Previous Outputs Current Outputs Q1n Qn Y1n-1 Yn-1 Y1n Yn 1 0 0 0 0 1 1 0 0 1 1 0 Cn Trellis Coding in AWGN Passband Channels Trellis Coded Modulation using four-dimensional constellations have a better performance in terms of complexity and coding gain over the usual twodimensional schemes (Lee-Fang Wei, 1987). Actual SCM-VDSL systems use the twodimensional Differential Quadrature Amplitude Modulation (DQAM) scheme (ETSI TS 101 70-1 v.0.6 part1, 00). In this section, we demonstrate that using the 4-dimensional Trellis Coded Modulation as a function of the truncation length of the Viterbi decoder can further increase the performance of this DQAM system, from a coding gain and cable range viewpoints..1 DQAM Principe To fully understand the DQAM (ETSI TS 101 1 0 1 0 1 1 1 0 1 1 0 0 Table 1. Differential QAM Coding table. Trellis Coded Modulation: A modified WEI 16- State 4D Code An inherent cost of the coded schemes is that the size of the D constellation is doubled over uncoded schemes. This is due to the fact that a redundant bit is added every signaling interval. Otherwise, the coding gain of those coded schemes would be 3 db greater. Using multidimensional (>) constellations with a trellis code of rate m/m+1 (Lee-Fang Wei, 1987) can reduce that cost because fewer redundant bits are added for each D signaling interval. Furthermore, multidimensional encoding provides more flexibility than D encoding in that it can use a fractional number of bits per symbol.

We will focus, now, on the case where the number Q of information bits transmitted per signaling interval is equal to 5. These five information bits arriving in the current signaling interval n are denoted as I1n, In and I5n. A /3 rate, 16-state code with a 4D rectangular constellation of 11 points and a Minimum Square Euclidean Distance (MSED) d 0 is shown in Figure 5. The 4D constellation is constructed from a 48-point D constellation partitioned into eight subsets with enlarged MSED equal to 4d 0, as explained in (Lee- Fang Wei, 1987). I5_n+1 I4_n+1 I3_n+1 I_n+1 I1_n+1 I5_n I4_n I3_n I_n I1_n DIFFERENTIAL ENCODING I3_n I_n Wn W3n Trellis ENCODER W1n W4n I3_n I_n I1_n Y0_n BIT CONVERTOR T T Z10_n Z9_n Z8_n Z7_n Z6_n Z5_n Z4_n Z1_n+1 Z0_n+1 Z1_n Z0_n Exlusive OR Signaling Interval Delay Element Figure 5. 16-State code with 4D Rectangular constellation If we denote the current and next states of the trellis encoder as W1pWpW3pW4p, p=n and n+, the corresponding 16-state trellis diagram is shown in Figure 6. CURRENT NEXT STATE STATE 10log 4d0 31.33d d0 0d0 0 10 = 4.0713 db Where 31.33 d 0 is the average power of the 4D constellation, and 0d 0 is the average power of the 3QAM..3 Simulation Results Bit Error Rates (BER) for the two different systems have been simulated, the uncoded system (3 DQAM), and the 4D 16-state code TCM system with a Viterbi decoder using a truncation length equal to K. In this stage of simulation, the system is simulated only with the AWGN disturbance. The results of the BER simulations, for 105 information bits sent, are shown in Figure 7. This figure shows the BER values for different Signal-to- Noise Ratios (SNR) and for different values of the truncation length K. Both systems have the same information rate (5 information bits/symbol period). Table shows that the BER decreases with K. However, the BER values become very similar for the values of K that exceed 15. BER 10 0 10 1 10 10 3 3QAM non codée MCT:Tronc 10 MCT:Tronc 40 MCT:Tronc 15 MCT:Tronc 500 MCT:Tronc 5000 MCT:No Tronc 4D SUBSET 0 1 3 4 6 5 7 0 3 1 W1n Wn W3n W4n W1n+ Wn+ W3n+ W4n+ 0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 0 1 0 0 1 0 0 0 1 0 10 4 6 4 7 5 1 3 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 10 5 0 5 10 15 0 5 SNR (db) 5 7 4 6 3 1 0 7 5 6 4 0 3 1 6 4 7 5 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 Figure 7. 4D TCM performance in AWGN channel As shown in Figure 7, asymptotically, the system employing 4D TCM code gains approximately 4 db of SNR over the uncoded system. 0 1 3 1 0 1 0 1 0 1 0 4 6 5 7 3 1 0 7 5 6 4 1 3 0 5 7 4 6 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 Figure 6. Trellis Diagram of 16-State code of Figure 5 The coding gain of the trellis coded modulation over the uncoded 3QAM therefore is: SNR = 18 K 10 0 40 15 BER 0.0171 0.0096 0.0065 0.004 K 500 5000 No Trunc BER 0.0051 0.0031 0.0039 SNR = 19 K 10 0 40 15 BER 0.0054 0.006 0.0018 5.6e-4 K 500 5000 No Trunc BER 3e-4 e-4.7e-4

SNR = 0 K 10 0 40 15 BER 0.0013 3.3e-4 1.5e-4 0 K 500 5000 No Trunc BER 0 0 0 Table. Effect of truncation length on the performance of the 4D TCM Code 3 Trellis Coding in Twisted Copper-Pair Passband Channels As specified in ANSI and ETSI (ETSI TS 101 70-1 v.0.6 part1, 00)(ETSI TS 101 70- v.0.3 part, 00) functional documents, SCM-VDSL systems don t use convolutional coding. In what follows, we will study the contribution of the TCM in the SCM-VDSL systems. The achievable gains for systems using the scheme consisting of 4D Trellis Coded Modulation have been analyzed in the previous section, and are typically equal to 4 db for an AWGN channel. 3.1 SCM-VDSL system Figure 8 presents the SCM-VDSL system (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 003) we used in our simulations. For the sake of simplification, the Reed-Solomon coding and interleaving functions, whose main purpose is to protect the data from Impulse Noise, have not been introduced in that system because the purpose of our study is not to investigate the impact of Impulse Noise on VDSL transmission, but to demonstrate the advantage of using the TCM rather than the DQAM modulation. fractionally spaced equalizer (MMSE) at a new sampling rate equal to symbolrate because the input is now a baseband signal. The received symbols are decoded and compared to the originally transmitted data in order to compute the errors caused by the noise burst, and consequently, to compare the DQAM and TCM modulations. 3. Impairment Generator The impairment generator produces the noise that is injected into the simulation set. It includes both crosstalk noise and background noise. The crosstalk noise power level varies with the frequency, the length of the cable loop, and the transmit direction (Upstream or Downstream). The crosstalk model (ETSI TS 101 70- v.0.3 part, 00) applied according to the test scenarios we choose is described below. Figure 9 defines a functional diagram of the composite impairment noise. This diagram has the following elements: 1. The three impairment "generators" G1, G, and G3 generate noise as defined in (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 003).. The transfer function H 1 (f, d) models the length and frequency dependency of the NEXT impairment as specified in (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 003). 3. The transfer function H (f, d) models the length and frequency dependency of the FEXT impairment as specified in (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 003). NEXT noise Independent noise Generators G1 Crosstalk transfer functions H1(f,d) S1 FEXT noise G H(f,d) S FSAN SUM Background noise Cable independent G3 S3 Figure 9. Functional diagram of the impairment noise composition Figure 8. VDSL Transmission Chain To satisfy the sampling theorem, the QAM symbols x k are over-sampled at the sampling rate 4 symbolrate, and are shaped using a raised cosine filter ϕ p (t) before being sent through the channel. Inter-Symbol Interference (ISI), Additive White Gaussian Noise (AWGN), and crosstalk impair singlecarrier transmission over the copper pairs. After being modulated and sent through the channel, an Additive White Gaussian and crosstalk Noises are superimposed to the channel output in the time domain. After crossing the whitening filter g(t), the data, brought back to the baseband, are sent through a low-pass filter in order to eliminate the whitened noise situated out of the frequency band. After that, they are sent through a finite minimum-mean-square-error Several deployment scenarios have been identified to achieve VDSL simulations. Each scenario (noise model) results in a length dependant PSD description of noise. Some of the three individual impairment generators G1, G, and G3, are used more once in the same noise model. We denote six models, Type "A", Type "B", and Type "C" for cabinet modeling and Type "D", Type "E", and Type "F" for exchange modeling (ETSI TS 101 70- v.0.3 part, 00). In our simulations, we chose Type "A" as the impairment modeling. Type "A" models (Cabinet) are intended to represent a mixed scenario including full ADSL where the VDSL system is placed in a distribution cable (up to ten of wire pairs) that is filled with many other transmission systems: 10 ADSL, 4 HDSL, and 0 ISDN interferers.

3.3 Simulation Results The VDSL system shall operate with a bit error ratio < 1 erroneous bit through 10 7 bits sent when operated over any loop with the noise models and simulation conditions specified in this section. Because of computer restrictions, we carried our simulations with a BER level equal to 10-5. Simulation defaults: We have simulated the 4D TCM method in the VDSL system described in Figure 8 with three configurations of the truncation length K of the Viterbi decoder: K = 10, K = 15, and without truncation. The set of default parameters used in the simulations is listed below: Number of Feed-Forward Equalizer (FFE) taps=3. Roll-off factor: α = 0.. Number of information bits per signaling interval=5. Symbol rate: f baud =.16 MHz. Carrier frequency: f c =.75 MHz. Sampling rate: f s = 4f baud = 8.64 MHz. The sampling rate at the input of the MMSE-FSE equalizer is L x f baud with L =. Transmitted constellations = 3QAM for noncoded transmission, and 48QAM for trellis coded transmission. The noise is additive, colored, and Gaussian ACGN. When whitened, its power spectral density (PSD) level is fixed to typically -140 dbm/hz, which usually corresponds to the reference noise floor in the VDSL system. As specified in the functional requirement documents (ETSI TS 101 70-1 v.0.6 part1, 00)(ETSI TS 101 70- v.0.3 part, 00), the PSD of the transmitted modulated signal is typically equal to -60 dbm/hz. Simulation results: In tables 3 and 4, we show the cable range reaches and the channel capacity gains for the 4D TCM VDSL system. On one hand, Table 3 shows the difference in cable range reaches if we vary the truncation length K. For the values of K that exceed 15, the 4D TCM VDSL cable range is typically constant. It is approximatively equal to 170 m. On the other hand, the reach in the case of the 3QAM non-coded VDSL system is typically equal to 1180 m. In fact, the channel capacity associated for this value of the cable range is equal to 4.983 bits. Beyond this value, the channel capacity becomes lower than the number of bits we want to send each signaling interval (b = 5). Thus, the 4D TCM VDSL system gives a cable range gain of 90m with the suitable value of K = 15. Table 4 shows the channel capacity gain in terms of number of bits we can send through the channel for different values of cable ranges and K. We note that the use of the trellis Coded Modulation rather than the DQAM allows sending 5 bits/signaling interval, even when the channel capacity (denoted bpsi in Table 4), calculated without taking into account the gain introduced by the TCM, is lower than 5. In our simulations, for K = 15 and BER = 10-5, the gain introduced by the TCM increases the channel capacity by 0.957 bits per signaling interval, which corresponds to 0.957.16 =.067 Mbps of rate gain. Cable Length Erroneous Symbols BER K = 10 110 0 0 10 0 0 130 0.6e-5 140 6 e-5 150 6 1.e-5 160 7 5.3e-5 K = 15 160 0 0 170 0 0 180 5 1.e-5 190 36 7e-5 1300 39 9.7e-5 Without Truncation 170 0 0 190 0 0 1300 0 4.3e-5 1400 47 5.e-4 Table 3. TCM SCM-VDSL: Cable range reaches for different values of the truncation length K K Cable Length Bpsi Gain 10 130 4.58 0.4178 15 170 4.043 0.957 No Trunc 190 3.817 1.188 Table 4. Channel capacity gain for different values of K Conclusion The VDSL system is expected to be the solution to provide broadband services to residential and business on the existing copper plant. In this paper, we demonstrated that the Trellis- Coded Modulation with 4-dimensional rectangular constellations is superior to using D constellations. Using multi-dimensional rectangular constellations not only reduces the size of the constituent D constellations, but also improves the performance in terms of both the coding gain and cable range reaches.

The simulation model was based on the singlecarrier modulation technique Quadrature Amplitude Modulation (QAM). 4-Dimensional 16-state trellis code with Viterbi decoding truncation length K was has been suggested as a suitable coding scheme with a value of K = 15. It has been evaluated in both AWGN and twisted copper-pair channels and has shown a coding gain of approximatively 4dB in the AWGN channel. It has, also, shown a cable range gain of approximatively 90m, and a channel capacity gain of typically 0.95 bits/signaling interval for K = 15 and a BER level of 10-5, which corresponds to a rate gain of.067 Mbps. References ETSI TS 101 70-1 v.0.6 (00-11). Transmission and Multiplexing (TM); Access transmission systems on metallic access cables; Very high speed Digital Subscriber Line (VDSL); Part 1 : Functional requirements. ETSI TS 101 70- v.0.3 (00-10). Transmission and Multiplexing (TM); Access transmission systems on metallic access cables; Very high speed Digital Subscriber Line (VDSL); Part : Transceiver Specification. Lee-Fang. Wei. Trellis-coded modulation with multidimensioanl constellations. IEEE Transactions on Communications Theory, IT-33(4), July 1987. Mario Diaz Nava and Christophe Del-Toso. A short overview of the vdsl system requirements. IEEE Communications Magazine, December 00. T. Starr, M. Sorbara, J.M. Cioffi, P.J. Silverman. DSL Advances, Prentice Hall Inc., New Jersey, 003.