Shannon's source and channel separation principle indicates that there is no benefit ( in terms of efficiency or performance) to permitting cooperation between the source coding (compression) and channel coding (error control) functions in a digital communication system. However, this separation principle holds only asymptotically for long and infinitely complex codes. This observation has led to increasing research on joint source/channel coding design as an alternative for achieving reliable communication over noisy channels. Joint source/channel coding schemes have been well studied for fixed-length coded sources. But widely used entropy codes, such as Huffman codes and arithmetic codes, are variable length in nature. The compressed bit stream produced by variable length codes is susceptible to error propagation. Thus joint source/channel coding design is of interest for variable length codes. With the wide popularity of arithmetic codes in a variety of standards including MPEG4, JPEG2000 and H.26L, joint design for systems involving arithmetic codes has generated interest. This dissertation focuses on the design of schemes for recovering arithmetically encoded data transmitted through a noisy AWGN channel. The joint arithmetic/channel coding system presented in this dissertation is based on an arithmetic sequential decoder that can accept soft input. Operating on a source symbol-constrained tree structure, it improves performance compared with the conventional arithmetic decoder which can only accept binary bits. Several joint source/channel coding schemes are proposed in which channel coding is used to protect the arithmetically encoded data. First, a joint sequential decoder that sweeps sequentially through a composite tree including the states of both the arithmetic and channel codes is developed. Second, a soft tandem system in which an arithmetic decoder uses the soft output from a channel decoder is studied. The turbo principle is then applied to a serially concatenated arithmetic/channel coding system in which the arithmetic decoder and the channel decoder share extrinsic information as in turbo codes. The convergence behavior of this iterative system is analyzed via density evolution. All the joint systems outperform the conventional hard tandem system in which arithmetic decoding and channel decoding are done separately.