In this paper, we propose to adapt both the modulation scheme and the transmit power in the frequency domain using a heuristic evaluation of the bit error rate (BER) for each subcarrier. The proposed method consists in ordering in terms of fading impact, grouping a certain number of subcarriers and performing local power adaptation in each subcarrier group. The subcarrier grouping is performed in order to equalize the average channel condition of each subcarrier group. Grouping and local power adaptation allow us to take advantage of the channel variations and to reduce the computational complexity of the proposed power distribution scheme, while avoiding the performance degradation due to the suboptimum power adaptation as much as possible. Compared to the conventional power distribution methods, the proposed scheme does not require any iterative process and the power adaptation is directly performed using an analytical formula. Simulations show a gain in terms of BER performance compared to equal power distribution and existing algorithms for power distribution. In addition, due to the subcarrier group specificity, the trade-off between the computational complexity and the performance can be controlled by adjusting the size of the subcarrier groups. Simulation results show significant improvement of BER performance compared to equal power allocation.

We have proposed a neural network called the Lagrange programming neural network with polarized high-order connections (LPPH) for solving the satisfiability problem (SAT) of propositional calculus. The LPPH has gradient descent dynamics for variables and gradient ascent dynamics for Lagrange multipliers, which represent the weights of the clauses of the SAT. Each weight wr increases according to the degree of unsatisfaction of clause Cr. This causes changes in the energy landscape of the Lagrangian function, on which the values of the variables change in the gradient descent direction. It was proved that the LPPH is not trapped by any point that is not a solution of the SAT. Experimental results showed that the LPPH can find solutions faster than existing methods. In the LPPH dynamics, a function hr(x) calculates the degree of unsatisfaction of clause Cr via multiplication. However, this definition of hr(x) has a disadvantage when the number of literals in a clause is large. In the present paper, we propose a new definition of hr(x) in order to overcome this disadvantage using the "min" operator. In addition, we extend the LPPH to solve the constraint satisfaction problem (CSP). Our neural network can update all neurons simultaneously to solve the CSP. In contrast, conventional discrete methods for solving the CSP must update variables sequentially. This is advantageous for VLSI implementation.