In this chapter, an exact solution for the throughput of a general duplex communications system with forward error correction (FEC) and automatic repeat request (ARQ) is constructed. A graphical representation of this solution relating the channel throughputs in both the upstream and downstream directions is developed. The chapter is organized as follows. First, a nomenclature to fully describe a duplex communications system using FEC and ARQ is established. Then some fundamental properties of such a system are derived and used to formulate the equations for the joint optimization of throughput in both directions.