This article proposes, given an independently-and-identically distributed binary source, an arithmetic code-like variable-to-variable length source code whose compression efficiency achieves nearly the rate function in a range of small distortion. Inheriting advantages of arithmetic codes, the proposed code requires neither large memory capacity nor large computation time for management of messages and codewords. The Elias code, which can be regarded as an antecedent of arithmetic codes, is defined originally in terms of the first-in-first-out (FIFO) coding form. The proposed code corresponds to an extension from the Elias code refined in terms of the last-in-first-out (LIFO) coding form into one considered a fidelity criterion.