A Simple Sign-Bit Probabilistic Shaping Scheme

Abstract

We consider the positioning problem in non line-ofsight (NLoS) situations, where several base stations (BS) try to locate a user equipment (UE) based on uplink angle of arrival (AoA) measurements and a digital twin of the environment. Ray launching in a Monte Carlo manner according to the AoA statistics enables to produce a map of points for each BS. These points represent the intersections of the rays with a xy plane at a given user equipment (UE) elevation. We propose to fit a parametric probability density function (pdf), such as a Gaussian mixture model (GMM), to each map of points. Multiplying the obtained pdfs for each BS enables to compute the position probability of the UE. This approach yields an algorithm robust to a reduced number of launched rays. Moreover, these parametric pdfs may be fitted and stored in an offline phase such that ray tracing can be avoided in the online phase. This significantly reduces the computational complexity of the positioning method.

A modified probabilistic amplitude shaping scheme to use sign-bit-like shaping with a BICM

“…The discrete Maxwell-Boltzmann (MB) distribution, which is a quasi-optimal input distribution for the symbols of X on the Gaussian channel [10], can be quantized at the cost of negligible performance loss [8][4]. As an example, the distribution of the 16-ASK constellation shown on Figure 3 (left) exhibits quasi-optimal performance in terms of mutual information: The loss is less than 0.1 dB for information rates smaller than 3 bits per channel use (bpcu), see Figure 4 in [4]. Consequently, this quantized MB-like distribution can be taken as the target shaping distribution.…”

“…Nevertheless, "sign-bit shaping" is a popular shaping technique where the conditional distribution of the sign bit is made non-equiprobable [7][13][2] [4]. Hence, it cannot be considered as a distribution matcher (DM) for the PAS scheme.…”

“…As a result, (to the best of our knowledge) sign-bit shaping has always been considered jointly with multilevel coding 1 . As an example, in our previous paper on sign-bit shaping [4], 1 Sign-bit shaping is conveniently implemented with multilevel coding as the last level (the sign-bit level with natural labelling) does not need to be coded. Indeed, the mutual information of the last bit level equals the entropy.…”

“…In this paper, we propose modifications to the conventional PAS scheme (Section III) and to the probabilistic sign-bit shaping scheme proposed in [4] (Section IV). These modifications enable to use the paradigm of sign-bit shaping with a BICM.…”

On the latency of multi-level polar coded modulations

“…3. If shaping is used, e.g., as in[9], the positions of the curves are slightly shifted but this does not change the result in terms of TC.4. Defined as Es/σ 2 , where σ 2 the variance of the noise.…”