  Crosstalk interference is the limiting factor in transmission over copper
lines. Crosstalk cancelation 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 world
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 trade off
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. Finally, 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 bits representation of the
precoder entries results in capacity loss below 1% for lines over 300m.
