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The Elias source coding scheme is modified to permit a source sequence of practically unlimited length to be coded as a single codeword using arithmetic of only limited precision. The result is shown to be a nonblock arithmetic code of the first in, first out (FIFO) type-- source symbols are decoded in the same order as they were encoded. Codeword lengths which are near optimum for the specified statistical properties of the source can be achieved. Explicit encoding and decoding algorithms are Provided which effectively implement the coding scheme. Applications to data compression and cryptography are suggested.