Wireless communication technologies have evolved from the original analog networks to IP-based network. Today's wireless communications have been affected by increasing customer expectations on wireless wideband internet services and continuously evolving improvements on technologies. Wireless communication systems must increase their ability to respond to the challenges. The new generation wireless systems (3G/4G) are designed for this purpose. The notable characteristic of 3G/4G is that it provides high data rate transmission at data rate up to 348kbps/2Mbps for 3G and 100Mbps/1Gbps for 4G. Designing the system for such high data rate transmission has become very challenging for wireless systems where the multipath fading is an important factor. In recent years, researches are ongoing in the industry and academic to increase capacity performance of wireless systems through antenna diversity. Multiple Input Multiple Output (MIMO) is one of the major recent developments in the study of high data rate transmission. There has been considerable attention paid to remarkable performance improvements in MIMO in terms of capacity. Another technology that has been traditionally adopted for wireless communications is the channel coding. Combining MIMO with channel coding has received increasing interest to support a variety of high data rate applications. These schemes have been termed as "space-time codes". Space-time codes are currently an area of exciting activity and have been studied as promising candidates for future 3G/4G systems. The most important characteristic of space-time codes is that it can provide full diversity gain as well as coding gain. In this dissertation, both performance analysis of upper bound of Pair-Wise Error Probability (PEP) and exact PEP are performed. In the derivation of exact PEP, a new method is presented. The method is straightforward and comprehensible. The upper bound provides the insight to understand the performance behavior for high Signal-to-Noise Ratio (SNR), while the exact PEP provides a better understanding of the performance behavior to other range of SNR. Design criteria for space-time codes had been first developed by Tarokh, which utilize the analysis of the upper bound on PEP to maximize diversity gain and coding gain from the property of the codeword distance matrix. These criteria are the most widely accepted, which form the basis for space-time codes. The criteria assume that the performance of space-time codes is dominated by the dominant error events. However, there are no dominant error events in fading channel for space-time codes. Therefore, Tarokh's criteria do not provide design guideline for the coding gain. Union bound analysis offers a alternative solution to this problem. The union bound technique is a more attractive method that allows us to analyze the contribution of all error events to the performance. In this thesis, the performance of space-time codes are analyzed using union bound analysis. Based on the union bound on Frame Error Rate (FER), new design criteria are proposed. This is achieved by applying more accurate upper bound of PEP in the union bound analysis. With the proposed criteria, new coding gain performance metrics had been defined. New codes based on the new performance metrics are designed and their coding gain performance superiority are demonstrated. Space-time block codes have been initially designed to provide full diversity order with low decoding complexity, but without coding gain. By integrating space-time trellis codes with space-time block codes, super-orthogonal space-time trellis codes can significantly enhance the coding gain performance. However, the super-orthogonal space-time trellis codes improve performance only in slow fading channel, but do not perform well in fast fading channel. In fast fading channel, the orthogonal design of space-time block codes has little effect on the coding gain and does not lead to noticeable improvement. Furthermore, super-orthogonal space-time trellis codes introduce the diversity gain loss in fast fading channel. It is well known that the performances of space-time codes are dominated by diversity gain and any diversity gain loss may cause substantial loss in performance. We therefore develop orthogonal space-time trellis codes, which improve performance in diversity gain in fast fading channel. The improvement is achieved by transferring the vector output of space-time trellis codes into an orthogonal matrix of space-time block codes, and meanwhile maintaining the symbol Hamming distance of space-time trellis codes. Theoretical analysis and simulation results had demonstrated that the proposed codes can improve diversity gain linearly with an increase in the number of transmit antennas. Performance saturation and decoding complexity increase with the increased number of trellis states are the major problems that trellis-based codes have to face in practice. Turbo codes that allow for reaching near Shannon limit performance are a significant advance in digital communications. Space-time turbo codes have been developed to achieve high performance. In a perfect world, system designers would like to achieve high performance while maintaining a full code rate. Therefore, puncture operation is always used in space-time turbo codes. The problem with the puncture operation in space-time turbo codes is that codeword distance matrix is rank deficient for small diversity gain in slow fading channel, which constitutes a major problem with space-time turbo codes. Space-time turbo codes that concern the rank deficiency have been developed. The codes improve performance by reducing the effect of rank deficiency on performance, but exist high complexity in both code structure and design criteria. This limitation makes the codes not suitable for the design of complex codes with large trellis state and/or large numbers of transmit antennas. A new space-time turbo codes have been proposed in this research. In previous works, it has been demonstrated the systematic structure with the rotation of the output of the low constitute encoder can effectively reduce the rank deficient effect on performance. Our new codes utilize the systematic characteristic to construct a simple code structure. Further, a simple but very effective trace criterion has been proposed. With the simple codes structure and design criteria, the design of complex codes can be achieved with significant improvement in coding gain performance for the systems with small diversity gain in slow fading channel. Overall, this dissertation presents new design criteria and new codes that contribute to improving performances of space-time codes.