A random noise generation module for generating noisy LLRs for testing an error correction circuit of a nonvolatile memory storage module. The random noise generation module includes a coefficient generator for generating one or a plurality of coefficients, each of the plurality of coefficients associated with one region of a plurality of regions defining a linear space proportionately divided according to an area under a probability distribution curve for a nonvolatile memory storage module. The random noise generation module further includes a linear random number generator for generating a linear random number and a comparator for comparing the linear random number to one or more of the plurality of coefficients to identify the region of the plurality of regions of the probability distribution curve in which the linear random number belongs to generate a noisy LLR for testing an error correction circuit of a nonvolatile memory storage module.