We apply the level-3 reformulation-linearization technique (RLT3) to the quadratic assignment problem (QAP). We then present our experience in calculating lower bounds using an essentially new algorithm based on this RLT3 formulation. Our method is not guaranteed to calculate the RLT3 lower bound exactly, but it approximates this lower bound very closely and reaches it in some instances. For Nugent problem instances up to size 24, our RLT3-based lower bound calculation solves these problem instances exactly or serves to verify the optimal value. Calculating lower bounds for problem sizes larger than size 27 still presents a challenge because of the large amount of memory needed to implement the RLT3 formulation. Our presentation emphasizes the steps taken to significantly conserve memory by using the numerous problem symmetries in the RLT3 formulation of the QAP. We implemented this RLT3-based bound calculation in a branch-and-bound algorithm. Experimental results project significant runtime improvement over all other published QAP branch-and-bound solvers.

In this paper, we present a simple, but effective method of enhancing and exploiting diversity from multiple packet transmissions in systems that employ nonbinary linear modulations such as phase-shift keying (PSK) and quadrature amplitude modulation (QAM). This diversity improvement results from redesigning the symbol mapping for each packet transmission. By developing a general framework for evaluating the upper bound of the bit error rate (BER) with multiple transmissions, a criterion to obtain optimal symbol mappings is attained. The optimal adaptation scheme reduces to solutions of the well known quadratic assignment problem (QAP). Symbol mapping adaptation only requires a small increase in receiver complexity but provides very substantial BER gains when applied to additive white Gaussian noise (AWGN) and flat-fading channels.

We present a simple, but effective, method of enhancing and exploiting diversity from multiple packet transmissions in systems that employ nonbinary linear modulations such as PSK and QAM. This diversity improvement results from redesigning the symbol mapping for each packet transmission. Using a general framework for evaluating the upper bound of bit error rate (BER) with multiple transmissions, a criterion to obtain optimal symbol mappings is attained. The optimal adaptation scheme reduces to solving the well known quadratic assignment problem (QAP). Symbol mapping adaptation only requires a small increase in receiver complexity but provides very substantial BER gains when applied to flat-fading channels.

We present a simple, but effective, method of creating and exploiting diversity from packet retransmissions in systems that employ nonbinary modulations such as PSK and QAM. This diversity results from differing the symbol mapping for each packet retransmission. By developing a general framework for evaluating the bit error rate (BER) upper bound with multiple transmissions, a criterion to obtain optimal symbol (re)mappings is attained for memoryless AWGN channels. The optimal adaptation scheme reduces to solutions of the quadratic assignment problem (QAP). Symbol mapping adaptation only requires a small increase in receiver complexity but provides very substantial BER gains.

Importance sampling can significantly reduce simulation run time in estimating the bit error probability of digital systems if a suitable procedure is used. Various aspects of optimum and suboptimum biasing procedures are considered. It is shown that the strict optimum does not lead to a realistic procedure. An examination is made of the suboptimal variations that can be implemented reasonably; in one variation, it is found that for a linear system, the biasing scheme should have a time-varying mean proportional to the impulse response. Aspects of implementation are also discussed.>

Importance sampling is a technique that can significantly reduce computer run-time in the estimation of bit error rate (BER). However, in the conventional implementation (CIS), the improvement reduces markedly for systems with long memory. An approach to recover the full improvement for such systems has been previously suggested, and is called 'efficient' important sampling (EIS). A report is presented on an extensive series of simulation-based experiments with CIS and EIS, both to compare theoretical predictions to experimental observations, as well as to gain insight into the conditions of applicability, especially for EIS.>

The assessment of bit error rate (BER) performance of a digital communication system via computer simulation has traditionally been done using the Monte Carlo method. For very low BER, this method requires excessive computer time. This time can be substantially reduced by using extrapolation based on importance sampling (IS). In applying IS to a complex system, many considerations must be addressed, chief among which is the reliability (variance) of the estimator as a function of the system particulars. We discuss a number of these considerations and, specifically, derive a number of expressions for the variance. We find that the variance improvement may be severely limited by the dimensionality (or memory) of the system. We describe a means for circumventing this limitation through the definition of a statistically equivalent impulse response. For a linear system, this amounts to the ordinary impulse response. The simulation can be structured to estimate the equivalent impulse response using statistical regression. This new approach has been implemented and found to yield significant runtime improvement over conventional importance sampling for linear systems of large dimensionality. We believe this technique will work also for mildly nonlinear systems, as might be encountered in typical satellite Communications.