To improve reliability in latency-critical applications, a point-to-point communication system with heterogeneous decoding deadlines is considered. Unlike existing work, this system allows for a message to arrive before the decoding deadline of a prior message. A new coding scheme with finite blocklength codewords is introduced exploiting the dirty paper coding principle. Rigorous bounds are derived for achievable error probabilities. Moreover, numerical results illustrate that the proposed scheme outperforms time sharing for a wide range of blocklengths
