This paper studies whether emergent languages in a signaling game follow Zipf’s law of abbreviation (ZLA), especially when the communication ability of agents is limited because of interfering noises. ZLA is a well-known tendency in human languages where the more frequently a word is used, the shorter it will be. Surprisingly, previous work demonstrated that emergent languages do not obey ZLA at all when neural agents play a signaling game. It also reported that a ZLA-like tendency appeared by adding an explicit penalty on word lengths, which can be considered some external factors in reality such as articulatory effort. We hypothesize, on the other hand, that there might be not only such external factors but also some internal factors related to cognitive abilities. We assume that it could be simulated by modeling the effect of noises on the agents’ environment. In our experimental setup, the hidden states of the LSTM-based speaker and listener were added with Gaussian noise, while the channel was subject to discrete random replacement. Our results suggest that noise on a speaker is one of the factors for ZLA or at least causes emergent languages to approach ZLA, while noise on a listener and a channel is not.