As the powerful performance of deep learning has been proven, many computer vision researchers have applied deep learning methods to their works as a breakthrough that could not be achieved with conventional computer vision algorithms. Particularly in pathological image analysis, deep learning plays an important role because some diagnosis requires a considerable cost or much time. In a recent, convolutional neural network (CNN)-based deep learning models have shown meaningful results in pathological image analysis, reducing time and cost. However, existing CNN-based segmentation models perform the same convolution operation for all channels of a feature map. It could be an inefficient operation according to information theory. We propose (Shannon) entropy-based convolutional module (ECM) for efficient convolutional operation in terms of a communication system. The fundamental coding manner of a communication system based on information theory is to allocate fewer bits for data showing the high probability of occurrence, and vice versa. Following up this coding manner, a feature is divided into dominant and recessive features according to the channel importance calculated from the channel attention module, and a heavy operation is conducted on the recessive feature and a light operation is conducted on the dominant feature. This operating manner can make a network perform efficient calculations and improve its performance. Furthermore, our proposed module is a portable unit, thus it can be a replacement of any convolution without modification of the whole architecture. To the best of our knowledge, our proposed module is the first trial to mimic the coding manner of information theory. The models equipped with our proposed module outperform the original models achieving 0.855 of F1 score and 0.832 of Jaccard score on colorectal cancer (CRC) image data-set.INDEX TERMS Segmentation, deep learning, information theory, Shannon entropy, colorectal cancer image.