Finite Word Length Effects on Transmission Rate in Zero Forcing Linear Precoding for Multichannel DSL

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.