High Performance Embedded and Distributed Systems (HiPEDS), ranging from implantable smart sensors to secure cloud service providers, offer exciting benefits to society and great opportunities for wealth creation. Although currently UK is the world leader for many technologies underpinning such systems, there is a major threat which comes from the need not only to develop good solutions for sharply focused problems, but also to embed such solutions into complex systems with many diverse aspects, such as power minimisation, performance optimisation, digital and analogue circuitry, security, dependability, analysis and verification. The narrow focus of conventional UK PhD programmes cannot bridge the skills gap that would address this threat to the UK's leadership of HiPEDS. The proposed Centre for Doctoral Training (CDT) aims to train a new generation of leaders with a systems perspective who can transform research and industry involving HiPEDS. The CDT provides a structured and vibrant training programme to train PhD students to gain expertise in a broad range of system issues, to integrate and innovate across multiple layers of the system development stack, to maximise the impact of their work, and to acquire creativity, communication, and entrepreneurial skills. The taught programme comprises a series of modules that combine technical training with group projects addressing team skills and system integration issues. Additional courses and events are designed to cover students' personal development and career needs. Such a comprehensive programme is based on aligning the research-oriented elements of the training programme, an industrial internship, and rigorous doctoral research. Our focus in this CDT is on applying two cross-layer research themes: design and optimisation, and analysis and verification, to three key application areas: healthcare systems, smart cities, and the information society. Healthcare systems cover implantable and wearable sensors and their operation as an on-body system, interactions with hospital and primary care systems and medical personnel, and medical imaging and robotic surgery systems. Smart cities cover infrastructure monitoring and actuation components, including smart utilities and smart grid at unprecedented scales. Information society covers technologies for extracting, processing and distributing information for societal benefits; they include many-core and reconfigurable systems targeting a wide range of applications, from vision-based domestic appliances to public and private cloud systems for finance, social networking, and various web services. Graduates from this CDT will be aware of the challenges faced by industry and their impact. Through their broad and deep training, they will be able to address the disconnect between research prototypes and production environments, evaluate research results in realistic situations, assess design tradeoffs based on both practical constraints and theoretical models, and provide rapid translation of promising ideas into production environments. They will have the appropriate systems perspective as well as the vision and skills to become leaders in their field, capable of world-class research and its exploitation to become a global commercial success.