Current air traffic communication systems are mainly based on voice communication, with a newer digital communication technology called L-Band Digital Aeronautical Communication System (LDACS) being investigated in the Single European Sky Air Traffic Management Research (SESAR) project. An essential feature of this communication infrastructure is the encoding of data that guarantees reliable transport. While the encoding in the transmission path is straightforward, the decoding is computationally expensive due to the peculiarities of the convolutional codes used. As the target platform for the communication equipment is an embedded system, a proper system design is essential for the receiving path to ensure real-time processing. This paper therefore focuses on the hardware/software co-design of the functional system parts needed for decoding in the LDACS radio receiver. We describe the fundamental design considerations, followed by the actual implementation in form of software and FPGA-based hardware modules. Subsequently, the decoding solution was verified to prove a standard-compliant system. In an experimental validation, the actual system was fed with test data from a reference system. This allows conclusions to be drawn about system characteristics like data throughput, latency, and error correction. The resulting system demonstrates high-performance decoding that can exceed the desired requirements for quality and speed for use in the LDACS communication system.