Achievable rates optimization for broadcast channels using finite size constellations under transmission constraints

Abstract

In this paper, maximal achievable rate regions are derived for power-constrained AWGN broadcast channel involving finite constellations and two users. The achievable rate region is studied for various transmission strategies including superposition coding and compared to standard schemes such as time sharing. The maximal achievable rates are obtained by optimizing over both the joint distribution of probability and over the constellation symbol positions. A numerical solution is proposed for solving this non-convex optimization problem. Then, we consider several variations of the same problem by introducing various constraints on the optimization variables. The aim is to evaluate efficiency vs. complexity tradeoffs of several transmission strategies, some of which (the simplest ones) can be found in actual standards. The improvement for each scheme is evaluated in terms of SNR savings for target achievable rates or/and percentage of gain in achievable rates for one user compared to a reference scheme. As an application, two scenarios of coverage areas and user alphabets are considered. This study allows to evaluate with practical criteria the performance improvement brought by more advanced schemes.

The impact of finite-alphabet input on the secrecy-achievable rates for broadcast channel with confidential message

“…The results obtained for the general case of superposition coding SC X ,PUX,PX lead to the same conclusions as for a broadcast channel model without security constraints [11]. In the model with security constraint, SC X ,PUX ,PX can achieve also better rates than superposition modulation which means that SM is not the optimal broadcast strategy as in the Gaussian alphabet case.…”

“…The simple schemes can be understood as adding constraints to the most general case. A detailed description of these strategies applied to the two-user broadcast channel (without security) can be found in [11].…”

“…Assume that SNR 2 < SNR 1 , otherwise there is no possibility to achieve a positive secrecy rate. To determine the secrecy-achievable rates region when using a certain broadcast strategy, we should solve the following weighted sum rate maximization problem: can be found in [11]. The AWGN channel for each user k is characterized by the classical conditional pdf of variance N k .…”

“…In this section, we present an alternative maximization algorithm to solve (3), similar to that in [11] without security constraint. First form the Lagrangian L of (3) :…”

Multilevel Coding for the Full-Duplex Decode-Compress-Forward Relay Channel

“…The optimizing distribution may require an exhaustive search. As shown in many point-to-point and multi-user scenarios [33,34], when the constellation becomes large enough, the achievable rate under a constrained constellation becomes very close to the Gaussian input rate.…”