This dissertation studies methods to achieve reliable communication over unreliable channels. Iterative decoding algorithms for low-density parity-check (LDPC) codes and generalized LDPC (GLDPC) codes are analyzed. A new class of error-correcting codes to enhance the reliability of the communication for high-speed systems, such as optical communication systems, is proposed. The class of spatially-coupled GLDPC codes is studied, and a new iterative hard- decision decoding (HDD) algorithm for GLDPC codes is introduced. The main result is that the minimal redundancy allowed by Shannon’s Channel Coding Theorem can be achieved by using the new iterative HDD algorithm with spatially-coupled GLDPC codes. A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with iterative decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. To the best of our knowledge, this is the first system that can approach the channel capacity using iterative HDD. The optimality of a codeword returned by the weighted min-sum (WMS) algorithm, an iterative decoding algorithm which is widely used in practice, is studied as well. The attenuated max-product (AttMP) decoding and weighted min-sum (WMS) decoding for LDPC codes are analyzed. Applying the max-product (and belief- propagation) algorithms to loopy graphs are now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence and/or the optimality of converged solutions. This work presents an analysis of both AttMP decoding and WMS decoding for LDPC codes which guarantees convergence to a fixed point when a weight factor, β, is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-programming (LP) and maximum-likelihood (ML) decoding solution.

This thesis considers the uplink of cell-free single input multiple output systems, in which the access points employ matched-filter reception. In this setting, our objectiveis to develop a scalable uplink power control scheme that relies only on large-scale channel gain estimates and is robust to changes in the environment. Specifically, we formulate the problem as max-min and max-product signal-to-interference ratio optimization tasks, which can be solved by geometric programming. Next, we study the performance of supervised and unsupervised learning approaches employing a feed-forward neural network. We find that both approaches perform close to the optimum achieved by geometric programming, while the unsupervised scheme avoids the pre-computation of training data that supervised learning would necessitate for every system or environment modification. / Den här avhandlingen tar hänsyn till upplänken till cellfria multipla utgångssystem med en enda ingång, där åtkomstpunkterna använder matchad filtermottagning. I den här inställningen är vårt mål att utveckla ett skalbart styrsystem för upplänkskraft som endast förlitar sig på storskaliga uppskattningar av kanalökningar och är robusta för förändringar i miljön. Specifikt formulerar vi problemet som maxmin och max-produkt signal-till-störningsförhållande optimeringsuppgifter, som kan lösas genom geometrisk programmering. Därefter studerar vi resultatet av övervakade och okontrollerade inlärningsmetoder som använder ett framåtriktat neuralt nätverk. Vi finner att båda metoderna fungerar nära det optimala som uppnås genom geometrisk programmering, medan det övervakade schemat undviker förberäkningen av träningsdata som övervakat inlärning skulle kräva för varje system- eller miljöändring.