We make notable advances on the reliability and efficiency of several different information transmission systems by providing theoretical results supported by numerical evaluations. A known stability issue in peer-to-peer networks and our solution in the form of a new peer-to-peer protocol take the center stage in the first part of this dissertation. The second part of the dissertation focuses on finding the best possible efficiency for given reliability levels in a couple of multiple-encoder and one-decoder multiterminal source-coding information transmission systems. In the language of information theory, this reads as finding the rate region for a given set of distortions on the sources to be reconstructed at the central decoder. Recent studies have suggested that the stability of peer-to-peer networks may rely on persistent peers, who dwell on the network after they obtain the entire file. It has been proven that if peers depart the peer-to-peer network immediately after they complete the pieces of the file of interest, then one piece becomes extremely rare in the network, which leads to instability. Technological developments, however, are poised to reduce the incidence of persistent peers, giving rise to a need for a protocol that guarantees stability with non-persistent peers. We propose a novel peer-to-peer protocol, the group suppression protocol, to ensure the stability of peer-to-peer networks under the scenario that all the peers adopt non-persistent behavior. Using a suitable Lyapunov potential function, the group suppression protocol is proven to be stable when the file is broken into two pieces, and detailed experiments demonstrate the stability of the protocol for arbitrary number of pieces. We define and simulate a decentralized version of this protocol for practical applications. Straightforward incorporation of the group suppression protocol into BitTorrent while retaining most of BitTorrent's core mechanisms is also presented. Subsequent simulations show that under certain assumptions, BitTorrent with the official protocol cannot escape from the missing piece syndrome, but BitTorrent with group suppression does. We start the second part of the dissertation by revisiting the quadratic Gaussian two-encoder source-coding problem, for which a Gaussian quantize-and-bin scheme, also known as the Berger-Tung scheme, is known to achieve the entire rate region. We present a new proof of the impossibility half of the rate-region optimality result that is arguably more direct. Next, we consider the quadratic Gaussian one-help-two source-coding problem with Markovity, in which three encoders separately encode the components of a memoryless vector-Gaussian source that form a Markov chain and the central decoder aims to reproduce the first and the second components in the chain subject to individual distortion constraints. For this problem, we determine that the Gaussian quantize-and-bin scheme achieves the rate region if the distortion on the second source is small enough. The proof technique makes heavy use of the approach we first successfully applied to the quadratic Gaussian two-encoder source-coding problem. Finally, we present a method for outer bounding the rate-distortion region of Gaussian distributed compression problems in which the source variables can be embedded in a Gauss-Markov tree. The outer bound so obtained takes the form of a convex optimization problem. Numerical evaluations demonstrate that the outer bound is close to the Berger-Tung inner bound, coinciding with it in many cases.