The objectives of this article are two-fold: First, to present the problem of joint source and channel (JSC) coding from a graphical model perspective and second, to propose a structure that uses a new graphical model for jointly encoding and decoding a redundant source. In the first part of the article, relevant contributions to JSC coding, ranging from the Slepian-Wolf problem to joint decoding of variable length codes with state-of-the-art source codes, are reviewed and summarized. In the second part, a double low-density parity-check (LDPC) code for JSC coding is proposed. The double LDPC code can be decoded as a single bipartite graph using standard belief propagation (BP) and its limiting performance is analyzed by using extrinsic information transfer (EXIT) chart approximations.