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Long-range context modeling is crucial to both dialogue understanding and generation. The most popular method for dialogue context representation is to concatenate the last-$k$ utterances in chronological order. However, this method may not be ideal for conversations containing long-range dependencies, i.e., when there is a need to look beyond last-$k$ utterances to generate a meaningful response. In this work, we propose DialoGen, a novel encoder-decoder based framework for dialogue generation with a generalized context representation that can look beyond the last-$k$ utterances. The main idea of our approach is to identify and utilize the most relevant historical utterances instead of last-$k$, which also enables the compact representation of dialogue history with fewer tokens. We study the effectiveness of our proposed method on both dialogue generation (open-domain) and understanding (DST). Even with a compact context representation, DialoGen performs comparably to the state-of-the-art models on the open-domain DailyDialog dataset. We observe a similar behavior on the DST task of the MultiWOZ dataset when the proposed context representation is applied to existing DST models. We also discuss the generalizability and interpretability of DialoGen and show that the relevance score of previous utterances agrees well with human cognition.