%
The determinations of parton distributions at the LHeC are of unique
range and quality because of a number of salient features which
characterise this experiment, especially with respect to HERA:
i) The LHeC greatly extends the kinematic range compared to HERA. The
increase in negative momentum transfer squared $Q^2$ is from
a maximum of about $0.03$ at HERA to $1$\,TeV$^2$ at the LHeC, and 
in $x$, e.g. for $Q^2 = 3$\,GeV$^2$,
from about $4 \cdot 10^{-5}$ to $2 \cdot 10^{-6}$.
ii) The projected increase of integrated luminosity
by a factor of $100$ allows to also extend the 
kinematic range at large $x$, from practically
about $0.4$ to $0.8$ in charged currents (CC).
This enables a precision mapping of the
high $x$ region, corresponding to large masses, of a few TeV,
in Drell-Yan scattering at the LHC.
iii) The increase in $Q^2$ implies that all parts of the neutral current
cross section, due to pure photon and pure $Z$ exchange, and their 
interference become of equal strength. This, combined with high
precision and CC data in a large kinematic range, enables a complete
separation of sea and valence quarks. It is crucial to understand that
such a basis of PDF determinations will render all previous
PDF determinations of inferior importance and practically reduce
any parameterisation uncertainty in QCD PDF fits to a negligible
level of importance. 

The superior nature of 
the DIS process for testing partons, with respect to Drell-Yan scattering,
the higher precision in $ep$ wrt $pp$ and the availability of
an enormous range in $Q^2$ for fixing parton evolution, as opposed
to the $Q^2 \simeq M_{W,Z}^2$ scale of the most accurate DY process at the LHC,
these and further features make the LHeC the appropriate
machine for transforming the LHC into a precision QCD, search
and Higgs factory in the twenties. 


The analysis of PDF measurements of the LHeC has been based
on a full simulation of the NC and CC inclusive cross section measurements.
The assumptions on sources of systematic uncertainty
 are listed in Table\,\ref{tab:sys}~\cite{AbelleiraFernandez:2012cc}.
Broadly speaking, it is assumed
that with a new detector and high luminosity the H1 level of systematic
uncertainty is reached and improved by up to a factor of two.
%
\begin{table}[h]
  \centering
  \begin{tabular}{|l|c|}
    \hline
source of uncertainty & error on the source or cross section \\ \hline
scattered electron energy scale $\Delta E_e' /E_e'$ & 0.1 \% \\
scattered electron polar angle  & 0.1\,mrad \\
hadronic energy scale $\Delta E_h /E_h$ & 0.5\,\% \\
calorimeter noise (only $y < 0.01$) & 1-3\,\% \\ 
radiative corrections & 0.5\% \\
photoproduction background (only $y > 0.5$) & 1\,\% \\
global efficiency error & 0.7\,\%  \\
 \hline
  \end{tabular}
\caption{
Assumptions used in the simulation of the NC cross sections
on the size of uncertainties from various sources. 
These assumptions correspond to typical best values
achieved in the H1 experiment. The total cross section error
due to these uncertainties, e.g. for $Q^2 = 100$\,GeV$^2$,
is about $1.2$, $0.7$ and $2.0$\,\% for $y=0.84,~0.1,~0.004$.
}
\label{tab:sys}
\end{table}
%
The measurements of PDFs at the LHeC are complemented by high 
precision measurements of the heavy flavour quark densities
owing to a small beam spot, high luminosity and modern 
Silicon tracking techniques of high precision and wide acceptance.
An important part of the PDF programme at the LHeC is due
to the projected run with deuterons, which extends the knowledge
of neutron structure from DIS by $4$ orders of magnitude in
kinematic range. It needs deuterons to measure a singlet combination
of parton densities and to unfold the light sea flavour composition 
at low $x$. The LHeC is also an ideal and necessary configuration
to determine the nuclear PDFs for the first time in most of the 
kinematic range as is emphasised below. 
