The realization of high data rate wireless communication and large-scale connectivity with seamless coverage has been enabled by the introduction of various advanced transmission technologies, such as multiple access (MAC) technology and relay-assisted communications. However, beyond the accurate representation and successful transmission of information, in many applications it is the semantic aspect of that information that is really of interest. This thesis makes contributions to both the technology of conventional wireless communications and the theory of semantic communication. The main work is summarized as follows: We first consider an uplink system with K single-antenna users and one base station equipped with a single antenna, where each user utilizes a binary constellation to carry data. By maximizing the minimum Euclidean distance of the received sum constellation, the optimal user constellations and sum constellation are obtained for K=3 users. Using the principle of lattice coding, that design is extended to the K-user case. In both settings, the sum constellation belongs to additively uniquely decomposable constellation group (AUDCG). That property enables us to reduce the maximum likelihood multi-user detector to a single-user quantization based receiver. The symbol error probability (SEP) formula is derived, showing that our proposed non-orthogonal multiple access (NOMA) scheme outperforms the existing time division multiple access (TDMA) designs for the same system. Our design also sheds light on the general complex constellation designs for the MAC channel with arbitrary user constellation size. Specifically, K-user constellations with any 2^Mk size can be obtained using combinations of the proposed binary constellations. Next we concentrate on a multi-hop relay network with two time slots, consisting of single-antenna source and amplify-and-forward relay nodes and a destination node with M antennas. We develop a novel uniquely-factorable constellation set (UFCS) based on a PSK constellation for such system to allow the source and relay nodes to transmit their own information concurrently at the symbol level. By taking advantage of the uniquely-factorable property, the optimal maximum likelihood (ML) detection was equivalently reduced to a symbol-by-symbol detection based on phase quantization. In addition, the SEP formula was given, while enable us to show that the diversity gain of the system is one. For semantic communication, a new source model is considered, which consists of an intrinsic state part and an extrinsic observation part. The intrinsic state corresponds to the semantic feature of the source. It is not observable, and can only be inferred from the extrinsic observation. As an instance of the general model, the case of Gaussian distributed extrinsic observations is studied, where we assume a linear relationship between the intrinsic and extrinsic parts. We derive the rate-distortion function (in both centralized encoding and distributed encoding) of semantic-aware source coding under quadratic distortion structure by converting the semantic distortion constraint of the source to a surrogate distortion constraint on the observations. With proposed AUDCG and UFCS-based designs, high data rates as well as low detection latency can be achieved. Our modulation division method will be one of the promising technologies for the next generation communication and the analysis of the source coding with semantic information constraints also provides some insights that will guide the future development of semantic communication systems. / Thesis / Doctor of Philosophy (PhD) / The proliferation of smart phones and electronic devices has spurred explosive growth in high-speed multimedia services over the next generation of wireless cellular networks. Indeed, high data rates and large-scale connectivity with seamless coverage are the dominant themes of wireless communication system design. Moreover, beyond the accurate representation and successful transmission of information, the interpretation of its meaning is being paid more attention nowadays, which requires the development of approaches to semantic communication. The goal of this thesis is to contribute to the development of both conventional and semantic communication systems. Two advanced transmission technologies, namely, multiple access and relay-assisted communications are considered. By taking advantage of the special structures of digital communication signals, new approaches to multiple access and relay-assisted communications are developed. These designs enable high data rates, while simultaneously facilitating low-latency detection. Since there has been very limited analysis of the source coding of a vector source subject to semantic information constraints, we also study the rate distortion to trade-off for vector sources in both the case of centralized encoding and the case of distributed encoding, and we establish some insights that will guide the future development of semantic communication systems.