In this paper we propose a method of constructing packet-level LDGM codes that offer backward compatibility with conventional viewing devices. Our proposed method makes it possible to watch content even if the viewer does not support any FEC module. Moreover, the method also improves the coding efficiency through the combined use of packet division and interleaving methods. In general, there is a tradeoff between computation complexity and performance, but our proposed method improves coding efficiency by using a message passing decoding scheme that does not require any additional computation. The coding efficiency of the proposed method is evaluated both experimentally and theoretically.