Near lossless source coding with side information only at the decoder, was first considered by Slepian and Wolf in 1970s, and rediscovered recently due to applications such as sensor network and distributed video coding. Suppose X is a source and Y is the side information. The coding scheme proposed by Slepian and Wolf, called SW coding, in which information only flows from the encoder to the decoder, was shown to achieve the rate H(X|Y) asymptotically for stationary ergodic source pairs, but not for non-ergodic case, shown by Yang and He. Recently, a new source coding paradigm called interactive encoding and decoding(IED) was proposed for near lossless coding with side information only at the decoder, where information flows in both ways, from the encoder to the decoder and vice verse. The results by Yang and He show that IED schemes are much more appealing than SW coding schemes to applications where the interaction between the encoder and the decoder is possible. However, the IED schemes proposed by Yang and He do not have an intrinsic structure that is amenable to design and implement in practice. Towards practical design, we restrict the encoding method to linear block codes, resulting in linear IED schemes. It is then shown that this restriction will not undermine the asymptotical performance of IED. Another step of practical design of IED schemes is to make the computational complexity incurred by encoding and decoding feasible. In the framework of linear IED, a scheme can be conveniently described by parity check matrices. Then we get an interesting trade-off between the density of the associated parity check matrices and the resulting symbol error probability. To implement the idea of linear IED and follow the instinct provided by the result above, Low Density Parity Check(LDPC) codes and Belief Propagation(BP) decoding are utilized. A successive LDPC code is proposed, and a new BP decoding algorithm is proposed, which applies to the case where the correlation between $Y$ and $X$ can be modeled as a finite state channel. Finally, simulation results show that linear IED schemes are indeed superior to SW coding schemes.

Near lossless source coding with side information only at the decoder, was first considered by Slepian and Wolf in 1970s, and rediscovered recently due to applications such as sensor network and distributed video coding. Suppose X is a source and Y is the side information. The coding scheme proposed by Slepian and Wolf, called SW coding, in which information only flows from the encoder to the decoder, was shown to achieve the rate H(X|Y) asymptotically for stationary ergodic source pairs, but not for non-ergodic case, shown by Yang and He. Recently, a new source coding paradigm called interactive encoding and decoding(IED) was proposed for near lossless coding with side information only at the decoder, where information flows in both ways, from the encoder to the decoder and vice verse. The results by Yang and He show that IED schemes are much more appealing than SW coding schemes to applications where the interaction between the encoder and the decoder is possible. However, the IED schemes proposed by Yang and He do not have an intrinsic structure that is amenable to design and implement in practice. Towards practical design, we restrict the encoding method to linear block codes, resulting in linear IED schemes. It is then shown that this restriction will not undermine the asymptotical performance of IED. Another step of practical design of IED schemes is to make the computational complexity incurred by encoding and decoding feasible. In the framework of linear IED, a scheme can be conveniently described by parity check matrices. Then we get an interesting trade-off between the density of the associated parity check matrices and the resulting symbol error probability. To implement the idea of linear IED and follow the instinct provided by the result above, Low Density Parity Check(LDPC) codes and Belief Propagation(BP) decoding are utilized. A successive LDPC code is proposed, and a new BP decoding algorithm is proposed, which applies to the case where the correlation between $Y$ and $X$ can be modeled as a finite state channel. Finally, simulation results show that linear IED schemes are indeed superior to SW coding schemes.

Luby Transform Codes were the first class of universal erasure codes introduced to fully realize the concept of scalable and fault‐tolerant distribution of data over computer networks, also called Digital Fountain. Later Raptor codes, a generalization of the LT codes were introduced to trade off complexity with performance. In this work, we show that an even broader class of codes exists that are near optimal for the erasure channel and that the Raptor codes form a special case. More precisely, Raptorlike codes can be designed based on an iterative (joint) decoding schedule wherein information is transferred between the LT decoder and an outer decoder in an iterative manner. The design of these codes can be formulated as a LP problem using EXIT Charts and density evolution. In our work, we show the existence of codes, other than the Raptor codes, that perform as good as the existing ones. We extend this framework of joint decoding of the component codes to the additive white Gaussian noise channels and introduce the design of Rateless codes for these channels. Under this setting, for asymptotic lengths, it is possible to design codes that work for a class of channels defined by the signal‐to‐noise ratio. In our work, we show that good profiles can be designed using density evolution and Gaussian approximation. EXIT charts prove to be an intuitive tool and aid in formulating the code design problem as a LP problem. EXIT charts are not exact because of the inherent approximations. Therefore, we use density evolution to analyze the performance of these codes. In the Gaussian case, we show that for asymptotic lengths, a range of designs of Rateless codes exists to choose from based on the required complexity and the overhead. Moreover, under this framework, we can design incrementally redundant schemes for already existing outer codes to make the communication system more robust to channel noise variations.