Difference threshold test for M-ary signaling with coherent detection

We present the difference threshold test (DTT) as a method for generating reliability information for M-ary signaling with coherent detection. The proposed DTT declares an erasure whenever the difference between the shortest Euclidean distance and the second shortest Euclidean distance from the received signal is less than a threshold. We show that the DTT is an approximation of the Bayesian test, and, for binary signaling, it is equivalent to the Bayesian test. We also extend the DTT for L-fold diversity systems. The performance of Reed-Solomon (RS) codes with errors-and-erasures decoding is analyzed when the DTT and the conventional SNR threshold test are applied.