Insight into source/channel duality and more based on an intuitive covering/packing lemma

The issue of source/channel duality is as old as information theory itself. Whereas type covering has been identified as a basis for source coding and sphere packing as the basis for channel coding, very little effort has been directed at tying covering and packing together. In this paper, a covering result has been derived which gives asymptotically optimal packing as well. We propose our covering/packing lemma as a mathematical basis of duality. Our lemma also sheds light on outstanding issues of source coding such as explicit rate-distortion tradeoff and unifying basis for lossless and lossy coding.