Wireless communication at near-capacity transmission throughputs is facilitated by employing sophisticated Error Correction Codes (ECCs), such as turbo codes. However, real-time communication at high transmission throughputs is only possible if the challenge of implementing turbo decoders having equally high processing throughputs can be overcome. Furthermore, in many applications, turbo decoders are required to have the flexibility of supporting a wide variety of turbo code parametrizations. This motivates the implementation of turbo decoders using networks-on-chip (NoCs), which facilitate flexible and high-throughput parallel processing. However, turbo decoders conventionally operate on the basis of the Logarithmic Bahl-Cocke-Jelinek-Raviv (Log-BCJR) algorithm, which has an inherently serial nature, owing to its data dependencies. This limits the exploitation of the NoC's computing resources, particularly as the size of the NoC is scaled up. Motivated by this, we propose a novel turbo decoder algorithm, which eliminates the data dependencies of the Log-BCJR algorithm and, therefore, has an inherently parallel nature. We show that by jointly optimizing the proposed algorithm with the NoC architecture, a significantly improved utility of the available computing resources is achieved. Owing to this, our proposed turbo decoder achieves a factor of up to 2.13 higher processing throughput than a Log-BCJR bench marker.