Burich, Mariano Eduardo2023-02-222023-02-222022https://udspace.udel.edu/handle/19716/32341Since Claude Shannon's seminal work in 1948, it is possible to quantify the optimal performance of communication systems in terms of information rate ("speed") vs channel quality (signal-to-noise ratio). The mathematical framework developed by Shannon established that it is asymptotically possible to achieve error rates arbitrarily close to zero provided that the information rate is below the channel capacity. Indeed, as the block length goes to infinity, certain families of linear codes are able to approach the channel capacity. However, since practical systems use codes with finite block length, in practice the joint design of channel and source coding (joint source-channel coding) and the use of non-linear codes can outperform linear schemes that separately perform compression and correction. ☐ In this work, we propose the use of non-linear codes that perform correction, compression, and modulation in one step. The proposed codes are random-like and defined by a graph and a non-linear mapping. The randomly built encoding graph allows us to design systems that are flexible in terms of rate and that are also able to transfer the source statistics to the output symbols, making the proposed schemes specially suitable for joint source-channel coding. We define design guidelines that lead to good performance for the use of graph-based non-linear codes in the transmission of binary, non-binary, and analog sources. The proposed non-linear mappings allow us to obtain good performance for the transmission of binary and non-binary sources at high rates, outperforming existing joint source-channel coding schemes for non-uniform sources, and achieving low error rates for the region under the Shannon limit, where the error cannot be arbitrarily close to zero. For the first time in the literature, we show that it is possible to approach the theoretical limits in the transmission of Gaussian sources over Gaussian channels by using graph-based analog codes of flexible rate that are decoded using message passing.Analog codingError correcting codesIterative decodingJoint source-channel codingNon-linear codesSparse codesThesis1370949198https://doi.org/10.58088/hd2y-77502022-09-21en