1. A receiver system for generating a soft decision signal from a hard decision signal, the receiver system comprising: a hard output receiver for determining a received bit to generate the hard decision signal; and a hard input soft output receiver for determining an estimated probability of symbol data corresponding to the received bit based on the hard decision signal and for generating the soft decision signal represented by a log-likelihood ratio from the estimated probability, wherein the hard input soft output receiver includes: an adder, connected to the hard output receiver, for receiving the hard decision signal; a bit counter connected to the adder, wherein the bit counter and the adder oversample the received bit using a predetermined sampling number to calculate a Hamming distance for the sampling sequence of the received bit; and a probability-log likelihood ratio converter, connected to the bit counter, for determining the estimated probability of the symbol data based on the Hamming distance and the sampling number and generating the soft decision signal from the estimated probability.