receiving a vector by the receiver from a transmitter of a different device, wherein the vector comprises an encoded codeword which has been modulated over a communication channel;

determining a decoding result by sequentially applying the received vector to one or more decoding algorithms; and

decoding the codeword based on an analysis on the decoding result of a detector corresponding to each of the one or more decoding algorithms,

wherein the detector determines whether the decoding of the codeword succeeds based on a calculated threshold value determined by analyzing a statistical distribution of an inner product of the received vector and the decoding result of the decoding algorithm,

wherein the calculated threshold value for a possibility of failure in detection of mis-decoding to be a certain value is determined by: a function that integrates the probability density function of a standard normal deviate, a code length N, a minimum distance of codes and a variance.