We derive a new method to quantify the impact of correlated firing on the information transmitted by neuronal populations. This new method considers, in an exact way, the effects of high order spike train statistics, with no approximation involved, and it generalizes our previous work that was valid for short time windows and small populations. The new technique permits one to quantify the information transmitted if each cell were to convey fully independent information separately from the information available in the presence of synergy-redundancy effects. Synergy-redundancy effects are shown to arise from three possible contributions: a redundant contribution due to similarities in the mean response profiles of different cells; a synergistic stimulus-dependent correlational contribution quantifying the information content of changes of correlations with stimulus, and a stimulus-independent correlational contribution term that reflects interactions between the distribution of rates of individual cells and the average level of cross-correlation. We apply the new method to simultaneously recorded data from somatosensory and visual cortices. We demonstrate that it constitutes a reliable tool to determine the role of cross-correlated activity in stimulus coding even when high firing rate data (such as multi-unit recordings) are considered.