Comparison of Precoding Schemes for Digital Subscriber Lines

1. Comparison of Precoding Schemes for Digital Subscriber Lines Project presentation for ECE 492 Vishnu Prasan April 19, 2007 Comparison of Precoding Schemes for Digital Subscriber Lines

2. Agenda • Introduction • Precoding in uncoded Transmissions for THP and FLP • Precoding with coded modulation for THP and FLP • Precoding in combination with signal shaping for THP and FLP • Implementation Comparison of Precoding Schemes for Digital Subscriber Lines

3. Introduction • Precoding is a technique which uses the same idea as frequency equalization, except that the ISI is inverted at the transmitter instead of the receiver. • Precoding at the transmitter side is a practicable method of transmission over intersymbol interference channels (ISI). • Copper wire transmission can build a bridge between analog telephone service to high speed lightwave communications. • This technique is called high rate digital subscriber lines (HDSL) or asymmetric digital subscriber lines (ADSL). • This paper compares the Tomlinson-Harashima Precoding (THP) and Flexible precoding (FLP) Comparison of Precoding Schemes for Digital Subscriber Lines

4. Introduction (cont.) Why Precoding ? • For ISI channels if coded modulation is applied MLSE has to work on combined ISI and code trellis. • If ideal ZF (zero forcing) decision feedback equlization (DFE) is used , MLSE does not have to be optimal. However DFE suffers from error propagation and coded modulation cannot be applied in a straight forward way. • Precoding has ideally no error propagation as equilization is done at the transmitter (coding techniques can be applied in the same way as for channels without ISI). Comparison of Precoding Schemes for Digital Subscriber Lines

5. Transmission Model Comparison of Precoding Schemes for Digital Subscriber Lines

6. Agenda • Introduction • Precoding in uncoded Transmissions for THP and FLP • Precoding with coded modulation for THP and FLP • Precoding in combination with signal shaping for THP and FLP • Implementation Comparison of Precoding Schemes for Digital Subscriber Lines

7. Precoding in uncoded Transmissions(THP) • A unique sequence d[k] called precoding sequence is added to the data sequence a[k] • Effective data sequence v[k] = a[k] + d[k], v[k] is filtered with the inverse of the inverse of H(z). • d[k] is chosen such that • The precoder is fitted with H(z) and subtracts the interference f[k] Figure 2 Comparison of Precoding Schemes for Digital Subscriber Lines

8. Precoding in uncoded Transmissions(cont.) • The receiver output is given by Figure 2 Comparison of Precoding Schemes for Digital Subscriber Lines

9. Precoding in uncoded Transmissions(cont.) • An ordinary slicer produces estimates of v[k] which is the effective data symbols, from which the estimated data symbol â[k] are produced. • d[k] is an element of the precoding lattice • The congruent signal points are obtained by extending the signal set A periodically to the set ѵ = {a + d|a ϵ A, d ϵ }. From ѵ that current effective symbol is selected which minimizes the magnitude of the corresponding channel symbol • Precoding loss Comparison of Precoding Schemes for Digital Subscriber Lines

10. Precoding in uncoded Transmissions(THP) Back Comparison of Precoding Schemes for Digital Subscriber Lines

11. Precoding in uncoded Transmissions(FLP) • In contrast to Tomlinson Harashima Precoding ,Flexible Precoding resembles linear equalization at the receiver. • Let x[k] = a[k] be transmitted over the channel without precoding. Channel output v[k] = a[k] +f[k]. • The slicer placed before the channel inverter can eliminate the noise and recover the a[k] without noise enhancement. • However f[k] ;Therefore using H(z) f[k] is generated at the transmitter. • The main difference with THP is that here f[k] is not completely subtracted at the transmitter but quantized to the nearest point d[k]. • Quantized error m[k] = f[k] – d[k] is subtracted. v[k] = x[k] + f[k] = a[k] – m[k] +d[k] + m[k] = a[k] + d[k] Figure 3 Comparison of Precoding Schemes for Digital Subscriber Lines

12. Precoding in uncoded Transmissions(cont.) • At the receiver an estimate of v[k] is generated by the threshold device. • The channel inverse is then used to get an estimate of x[k] (transmit symbol) • But we need a[k], so estimate of a[k] is obtained by adding estimate of m[k] to the estimate of x[k]. • Since we use the inverse of H(z) it has to be a strict minimum phase. • The precoding loss is given by : Comparison of Precoding Schemes for Digital Subscriber Lines

13. Precoding in uncoded Transmissions(cont.) Back Comparison of Precoding Schemes for Digital Subscriber Lines

14. Simulation Results Comparison of Precoding Schemes for Digital Subscriber Lines

15. Agenda • Introduction • Precoding in uncoded Transmissions for THP and FLP • Precoding with coded modulation for THP and FLP • Precoding in combination with signal shaping for THP and FLP • Implementation Comparison of Precoding Schemes for Digital Subscriber Lines

16. Precoding with coded modulation (THP) • The precoding lattice should be a subset of coset lattice • At moderate to high SNR only the nearest signal points in the Euclidean space contribute significantly for ML decoding. • After reducing the received signal r[k] to the region R the best representation of each subset is determined (the uncoded levels are extracted) • The only difference to TCM over the ISI free channels are the modulo reduction of the receiver input signal and the decoder metrics • Precoding loss is given by Comparison of Precoding Schemes for Digital Subscriber Lines

17. Precoding with coded modulation (FLP) • FLP can be combined with the TCM in a straight forward manner. • When a coded sequence is used the modulo operation has to be performed based on lattice rather than • Therefore d[k] and a[k] and v[k] are the same subset sequence • In contrast to THP the algorithm has to work dynamic range v[k] – no modulo reduction is possible. • At the receiver the trellis decoder which provides an estimate of v[k] is followed by the inverse of the channel, a[k] can be derived from the estimated channel symbol x[k]. Precoding loss is now given by Comparison of Precoding Schemes for Digital Subscriber Lines

18. Simulation Results Comparison of Precoding Schemes for Digital Subscriber Lines

19. Agenda • Introduction • Precoding in uncoded Transmissions for THP and FLP • Precoding with coded modulation for THP and FLP • Precoding in combination with signal shaping for THP and FLP • Implementation Comparison of Precoding Schemes for Digital Subscriber Lines

20. Precoding in combination with signal shaping (THP) • A straightforward combination of THP and shaping techniques designed for the AWGN channel is not possible. • The solution is to combine the shaping and precoding to one unity • The shaping bits have to be scrambled with the data symbols. The optimal algorithm searches for the best combination of the shaping bits and precoding sequence. • To avoid a descrambler at the receiver, shaping and precoding have a combined to be tight. • Viterbi algorithm is used to select the best sequence at the transmitter. • A simple modulo operation is needed to recover the data sequence. Comparison of Precoding Schemes for Digital Subscriber Lines

21. Precoding in combination with signal shaping (FLP) • Shaping for FLP is restricted to “power shaping”  reduction of average transmit power which implies the generation of a Gaussian distribution • FLP converts the ISI channel H(z) into a burst error channel with discrete additive disturbance • The great advantage with regard to implementation of separating the shaping and precoding is paid with the price of increased error propagation and restriction of power shaping Comparison of Precoding Schemes for Digital Subscriber Lines

22. Simulation Comparison of Precoding Schemes for Digital Subscriber Lines

23. Agenda • Introduction • Precoding in uncoded Transmissions for THP and FLP • Precoding with coded modulation for THP and FLP • Precoding in combination with signal shaping for THP and FLP • Implementation Comparison of Precoding Schemes for Digital Subscriber Lines

24. Implementation • THP can be easily be realized using fixed point arithmetic. If two’s compliment is applied modulo reduction can be done automatically • For implementation receiver structure is more critical. With dynamic shaping THP realization is simple while that of FLP is only possible if the basic requirement of separating shaping and precoding is dropped. • For strict band limited channels, transmission at fractional rates is essential for optimum performance. FLP in combination with shell mapping can provide this. In contrast THP does not support fractional rates. • For both precoding procedures signal shaping is essential for transmission at non integer rates, but FLP does this in a much flexible way. Comparison of Precoding Schemes for Digital Subscriber Lines

25. Conclusion • In THP, precoding and shaping have to be done in a single step while FLP combines precoding and channel coding. • FLP is more flexible it allows cross and circular constellation to be used and shaping is preserved. THP puts constraints on the signal set. • The flexibility of FLP and the possibility to support fractional rates is paid with the price of error propagation. • Applications such as voice band modems where channel is strictly band limited or has non linear distortion FLP is the way to adopt the transmission scheme • For use in digital subscriber lines the loss due to integer rates is negligible as compared to error propagation in FLP. • Both schemes are attractive for digital transmission. The system designer has to decide which one is best suited Comparison of Precoding Schemes for Digital Subscriber Lines

26. References [1] Robert F. H Fisher and Johannes B Huber “Comparison of precoding Schemes for Digital Subscriber Lines”, IEEE 1997 [2] Robert F. H. Fisher Precoding and Signal Shaping for Digital transmission, New York IEEE 2004 Wiley - Interscience [3] R. Laroia “Coding for intersymbol interface channels – combined coding and precoding” [4] Andrea Goldsmith ,Wireless communication Cambridge University Publication 2005 [5] J. G. Proakis, Digital communications , New York McGraw Hill 2004 Comparison of Precoding Schemes for Digital Subscriber Lines

27. Lattice A lattice in R is a discrete subgroup of R which spans the real vector space R. Every lattice in R can be generated from a basis for the vector space by forming all linear combinations with integral coefficients. A lattice may be viewed as a regular tiling of a space by a primitive cell. Lattices in two dimensions This is a rectangular lattice which is a special case of a square lattice * * * * * * * * * * * * * * * * * * * * * * * * Back Comparison of Precoding Schemes for Digital Subscriber Lines