In this paper, we consider the design of the day-ahead market for the smart electrical grid. Consumers with flexible demand and generator companies participate in the market to settle on their load and supply schedules, respectively. The market is operated by an Independent System Operator (ISO) whose purpose is to maximize social welfare while keeping load and supply balanced in the electricity network. We develop two distributed pricing algorithms that achieve optimum welfare. The first algorithm yields time-dependent market prices under convexity assumptions on utility and cost functions and the second algorithm yields bundle prices for arbitrary utility and cost functions. In both algorithms, flexible consumers and generator companies simply determine their own schedules based on the prices updated by the ISO at each iteration. We show that the participation of flexible demand in the day-ahead market reduces supply volatility, which would be present when flexible demand does not take part in price setting procedure.

We consider the digital fingerprinting (FP) problem and model it as a multiuser communications problem and develop a detection theoretic framework. In the general case, colluders apply uniform linear averaging followed by additive colored Gaussian noise. For each user, the receiver computes the correlation between the attacked signal and a linear-transformed version of that user's fingerprint, and performs thresholding (focused detection). Assuming independent colluders with potentially unequal priors, we derive generic exact bit-error probability (BEP) expressions, together with tight bounds, for arbitrary FP codes. Then, we specialize our results to orthogonal, simplex and Gaussian codes in the presence of additive white Gaussian noise; under mean squared error distortion constraints on the embedder and the colluders, we analytically quantify the optimal detection rule, the resulting minimum BEP and its asymptotic behavior, the collusion resistance, and the error exponent for the aforementioned codes, and compare their performances. We show that the minimum BEP expressions for these codes obey the same functional form and that they can be ordered as simplex, orthogonal, and Gaussian in terms of increasing BEP.