Bijective mapping techniques with uniformly distributed constellation diagrams, like PSK and QAM, are standard in today's communications systems. Yet, it is well known that without additional effort in form of active signal shaping, bijective mapping techniques are not capacity achieving. In recent years, an alternative technique called superposition modulation (SM) has been investigated, which theoretically is capacity achieving on the Gaussian channel. However, non-bijective mapping (which can be interpreted as lossy source coding) is challenging with respect to the design of proper channel codes. In this paper, the suitability of irregular convolutional coding in conjunction with superposition modulation is investigated. With proper code design, this combination is capable of achieving 6 bits/symbol at just 0.7 dB away from the Shannon capacity limit given a memory-4 mother code.