Abstract: Communication systems and methods are disclosed that utilize Probability Amplitude Shaping (PAS) and Trellis Coded Modulation (TCM) to transmit short block-length messages. While capacity-approaching codes, such as Low Density Parity Check (LDPC) codes, Turbo codes, and Polar codes, can achieve data rates approaching the Shannon limit at large block-lengths, the performance of these codes can deteriorate dramatically at short block-lengths. Communication systems configured in accordance with various embodiments of the invention can utilize classical codes to encode short block-length messages to achieve communication rates exceeding Polyanskiy's Random Coding Union bound. In several embodiments, message bits are transmitted using a TCM system in which message bits that have been previously encoded by an error detection code are encoded using a convolutional code (CC). In a number of embodiments, the error detection code and the CC are obtained via a joint optimization with respect to a Frame Error Rate bound.