Recent researches on information theory shed new light on the continuous attempts to open the black box of neural signal encoding. Inspired by the problem of lossy signal compression for wireless communication, this paper presents a Bitwise Bottleneck approach for quantizing and encoding neural network activations. Based on the rate-distortion theory, the Bitwise Bottleneck attempts to determine the most significant bits in activation representation by assigning and approximating the sparse coefficients associated with different bits. Given the constraint of a limited average code rate, the bottleneck minimizes the distortion for optimal activation quantization in a flexible layer-by-layer manner. Experiments over ImageNet and other datasets show that, by minimizing the quantization distortion of each layer, the neural network with bottlenecks achieves the state-of-the-art accuracy with low-precision activation. Meanwhile, by reducing the code rate, the proposed method can improve the memory and computational efficiency by over six times compared with the deep neural network with standard single-precision representation. The source code is available on GitHub: https://github.com/CQUlearningsystemgroup/BitwiseBottleneck.