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We present a sequential investment algorithm, the-weighted universal portfolio with side-information, which a c hieves, to rst order in the exponent, the same wealth as the best side-information dependent i n v estment strategy the best state-constant re-balanced portfolio determined in hindsight from observed market and side-information outcomes. This is(More)
A discrete denoising algorithm estimates the input sequence to a discrete memoryless channel (DMC) based on the observation of the entire output sequence. For the case in which the DMC is known and the quality of the reconstruction is evaluated with a given single-letter fidelity criterion, we propose a discrete denoising algorithm that does not assume(More)
The problem of optimal sequential decision for individual sequences, relative to a class of competing oo-line reference strategies, is studied for general loss functions with memory. This problem is motivated by applications in which actions may h a ve \long term" eects, or there is a cost for switching from one action to another. As a rst step, we consider(More)
The degrees-of-freedom of a K-user Gaussian interference channel (GIFC) has been defined to be the multiple of (1/2) log<inf>2</inf> P at which the maximum sum of achievable rates grows with increasing P. In this paper, we establish that the degrees-of-freedom of three or more user, real, scalar GIFCs, viewed as a function of the channel coefficients, is(More)
Sanov's theorem, Pinsker's inequality, large deviations, L 1 distance, divergence, variational distance, Chernoff bound We derive bounds on the probability that the L 1 distance between the empirical distribution of a sequence of independent identically distributed random variables and the true distribution is more than a specified value. We a lso derive a(More)
This paper describes the embedded block coding algorithm at the heart of the JPEG2000 image compression standard. The algorithm achieves excellent compression performance, usually somewhat higher than that of SPIHT with arithmetic coding, but in some cases substantially higher. The algorithm utilizes the same low complexity binary arithmetic coding engine(More)
We find an on-line portfolio selection strategy which minimizes the worst case regret with respect to the growth rate of wealth achieved by the best off-line optimized constant rebalanced portfolio. The resulting regret is compared to that of the infinite horizon Dirichlet-weighted universal portfolio. Both strategies track the performance of the best(More)
We consider the problem of optimally recovering a finite-alphabet discrete-time stochastic process {X/sub t/} from its noise-corrupted observation process {Z/sub t/}. In general, the optimal estimate of X/sub t/ will depend on all the components of {Z/sub t/} on which it can be based. We characterize nontrivial situations (i.e., beyond the case where (X/sub(More)
Let {X/sub t/} be a stationary finite-alphabet Markov chain and {Z/sub t/} denote its noisy version when corrupted by a discrete memoryless channel. Let P(X/sub t//spl isin//spl middot/|Z/sub -/spl infin///sup t/) denote the conditional distribution of X/sub t/ given all past and present noisy observations, a simplex-valued random variable. We present a new(More)