Finite word length effects on transmission rate in zero forcing linear precoding for multichannel DSL

Eitan Sayag*, Amir Leshem, Nicholas D. Sidiropoulos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Crosstalk interference is the limiting factor in transmission over copper lines. Crosstalk cancellation techniques show great potential for enabling the next leap in DSL transmission rates. An important issue when implementing crosstalk cancelation techniques in hardware is the effect of finite word length on performance. In this paper, we provide an analysis of the performance of linear zero-forcing precoders, used for crosstalk compensation, in the presence of finite word length errors. We quantify analytically the tradeoff between precoder word length and transmission rate degradation. More specifically, we prove a simple formula for the transmission-rate loss as a function of the number of bits used for precoding, the signal-to-noise ratio, and the standard line parameters. We demonstrate, through simulations on real lines, the accuracy of our estimates. Moreover, our results are stable in the presence of channel estimation errors. Lastly, we show how to use these estimates as a design tool for DSL linear crosstalk precoders. For example, we show that for standard VDSL2 precoded systems, 14 bit representation of the precoder entries results in capacity loss below 1% for lines over 300 m.

Original languageAmerican English
Pages (from-to)1469-1482
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number4
StatePublished - 2009
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received November 27, 2007; accepted September 15, 2008. First published January 13, 2009; current version published March 11, 2009. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Mounir Ghogho. This work was supported in part by EU-FP6 IST under Contract 506790, by The Netherlands Science and Technology Foundation under Grant STW 10459, and by the Israeli Ministry of Trade and Commerce under the Nehusha/iSMART project. This work appeared in part in the Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Las Vegas, NV, March 31–April 4, 2008, pp. 3077–3080.


  • Capacity estimates
  • Linear precoding
  • Multichannel DSL
  • Quantization
  • Vectoring


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