On application of the modulus metric to solving the minimum Euclidean distance decoding problem

We prove equivalence of using the modulus metric and Euclidean metric in solving the soft decoding problem for a memoryless discrete channel with binary input and $Q$-ary output. For such a channel, we give an example of a construction of binary codes correcting $t$ binary errors in the Hamming metric. The constructed codes correct errors at the output of a demodulator with $Q$ quantization errors as $(t+1)(Q-1)-1$ errors in the modulus metric. The obtained codes are shown to have polynomial decoding complexity.