A low-precision analog-to-digital converter (ADC) is required to implement a frontend device of wideband digital communication systems in order to reduce its power consumption. The goal of this paper is to present a novel joint quantizer optimization method for minimizing lower-precision quantizers matched to the sum-product algorithms. The principal idea is to introduce a quantizer that includes a feed-forward neural network and the soft staircase function. Since the soft staircase function is differentiable and has non-zero gradient values everywhere, we can exploit backpropagation and a stochastic gradient descent method to train the feed-forward neural network in the quantizer. The expected loss regarding the channel input and the decoder output is minimized in a supervised training phase. The experimental results indicate that the joint quantizer optimization method successfully provides an 8-level quantizer for a low-density parity-check (LDPC) code that achieves only a 0.1-dB performance loss compared to the unquantized system.