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This correspondence is concerned with new connections between source coding and two kinds of families of hash functions known as the families of universal hash functions and N-strongly universal hash functions, where N ges 2 is an integer. First, it is pointed out that such families contain classes of well-known source codes such as bin codes and linear codes. Next, performance of a source coding scheme using either of the two kinds of families is evaluated. An upper bound on the expectation of the decoding error probability is obtained for each family. The expectation of the decoding error probability is analyzed in detail for the cases of discrete memoryless sources and sources without the memoryless assumption under a certain class of decoders.