Efficient evaluation of the error probability for pilot-assisted finite-blocklength transmission

Paper in proceeding, 2022

We propose a numerically efficient method for evaluating the random-coding union bound with parameter s on the error probability achievable in the finite-blocklength regime by a pilot-assisted transmission scheme employing Gaussian code-books and operating over a memoryless block-fading channel. Our method relies on the saddlepoint approximation, which, differently from previous results reported for similar scenarios, is performed with respect to the number of fading blocks (a.k.a. diversity branches) spanned by each codeword, instead of the number of channel uses per block. This different approach avoids a costly numerical averaging of the error probability over the realizations of the fading process and of its pilot-based estimate at the receiver and yields a significant reduction of the number of channel realizations required to estimate the error probability via Monte-Carlo simulation. For example, in a single-input single-output scenario, when four or more diversity branches are available, an error probability of 10-4can be estimated accurately using our method by using less than 3000 samples. In contrast, the conventional saddlepoint approach requires around 106samples.