The continuous demands for higher throughput, higher spectral efficiency, lower latencies, lower power and large scalability in communication systems impose large challenges on the baseband signal processing. In the future, throughput requirements far beyond 100 Gbit/s are expected, which is much higher than the tens of Gbit/s targeted in the 5G standardization. At the same time, advances in silicon technology due to shrinking feature sizes and increased performance parameters alone will not provide the necessary gain, especially in energy efficiency for wireless transceivers, which have tightly constrained power and energy budgets. In this talk we will focus on channel coding, which is a major source of complexity in digital baseband processing. We will give an overview and first results of the EPIC project, funded by European Union's Horizon 2020 research and innovation program, that aims to develop a new generation of Forward-Error-Correction codes in a manner that will serve as a fundamental enabler of practicable beyond 5G wireless Tb/s solutions. We will highlight implementation challenges for the most advanced channel coding techniques, i.e. Turbo codes, Low Density Parity Check (LDPC) codes and Polar codes and present decoder architectures for all three code classes that are designed for highest throughput.