Comparison of Precoding Schemes for Digital Subscriber Lines 1 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 latticelattice The congruent signal points are obtained by extending the signal set A periodically to the set ѵ = {a + d|a A, d }. 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