It is known from experiments that in the polymer electrolyte system, which contains poly(ethylene oxide) chains (PEO), lithium-cations (Li+), and bis (trifluoromethanesulfonyl)imide-anions (TFSI-), the cation and the anion diffusion and the ionic conductivity exhibit a similar chain-length dependence with increasing chain length, they start dropping Steadily, and later, they saturate to constant values. These results are surprising because Li-cations are Strongly correlated with the polymer chains, whereas TFSI-anions do not have such bonding. To Understand this phenomenon, we perform molecular dynamics simulations of this System for four different polymer chain lengths. The diffusion results obtained from our simulations display excellent agreement With the experimental data. The cation transport model based on the Rouse dynamics can successfully quantify the Li-diffusion results, which correlates Li diffusion with the polymer center-of-mass motion and the polymer segmental motion. The ionic conductivity as a function of the chain length is then estimated based on the chain-length dependent ion diffusion, which shows a temperature-dependent deviation for short chain lengths. We argue that in the first regime, counterion correlations modify the conductivity, whereas for the long chains, the system behaves as a strong electrolyte.