Source Coding for Quasiarithmetic Penalties

Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not mean codeword length but rather a generalized mean known as a quasiarithmetic or quasilinear mean. Such generalized means have a number of diverse applications, including applications in queueing. Several quasiarithmetic-mean problems have novel simple redundancy bounds in terms of a generalized entropy. A related property involves the existence of optimal codes: For ``well-behaved'' cost functions, optimal codes always exist for (possibly infinite-alphabet) sources having finite generalized entropy. Solving finite instances of such problems is done by generalizing an algorithm for finding length-limited binary codes to a new algorithm for finding optimal binary codes for any quasiarithmetic mean with a convex cost function. This algorithm can be performed using quadratic time and linear space, and can be extended to other penalty functions, some of which are solvable with similar space and time complexity, and others of which are solvable with slightly greater complexity. This reduces the computational complexity of a problem involving minimum delay in a queue, allows combinations of previously considered problems to be optimized, and greatly expands the space of problems solvable in quadratic time and linear space. The algorithm can be extended for purposes such as breaking ties among possibly different optimal codes, as with bottom-merge Huffman coding.Comment: 22 pages, 3 figures, submitted to IEEE Trans. Inform. Theory, revised per suggestions of reader

Optimal Prefix Codes for Infinite Alphabets with Nonlinear Costs

Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a source code that is optimal in the sense of minimizing expected codeword length. For some applications, however, a source code should instead minimize one of a family of nonlinear objective functions, $\beta$-exponential means, those of the form $\log_a \sum_i p(i) a^{n(i)}$, where $n(i)$ is the length of the $i$th codeword and $a$ is a positive constant. Applications of such minimizations include a novel problem of maximizing the chance of message receipt in single-shot communications ($a<1$) and a previously known problem of minimizing the chance of buffer overflow in a queueing system ($a>1$). This paper introduces methods for finding codes optimal for such exponential means. One method applies to geometric distributions, while another applies to distributions with lighter tails. The latter algorithm is applied to Poisson distributions and both are extended to alphabetic codes, as well as to minimizing maximum pointwise redundancy. The aforementioned application of minimizing the chance of buffer overflow is also considered.Comment: 14 pages, 6 figures, accepted to IEEE Trans. Inform. Theor

Prefix Codes for Power Laws with Countable Support

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many random variables encountered in practice. For such random variables, compression performance is judged via estimates of expected bits per input symbol. This correspondence introduces a family of prefix codes with an eye towards near-optimal coding of known distributions. Compression performance is precisely estimated for well-known probability distributions using these codes and using previously known prefix codes. One application of these near-optimal codes is an improved representation of rational numbers.Comment: 5 pages, 2 tables, submitted to Transactions on Information Theor

Non-critical String Cosmologies

Non-critical String Cosmologies are offered as an alternative to Standard Big Bang Cosmology. The new features encompassed within the dilaton dependent non-critical terms affect the dynamics of the Universe\'s evolution in an unconventional manner being in agreement with the cosmological data. Non-criticality is responsible for a late transition to acceleration at redshifts z=0.2. The role of the uncoupled rolling dilaton to relic abundance calculations is discussed. The uncoupled rolling dilaton dilutes the neutralino relic densities in supersymmetric theories by factors of ten, relaxing considerably the severe WMAP Dark Matter constraints, while at the same time leaves almost unaffected the baryon density in agreement with primordial Nucleosynthesis.Comment: 16 pages, 7 figures, conference tal

Trileptons from Chargino-Neutralino Production at the CERN Large Hadron Collider

We study direct production of charginos and neutralinos at the CERN Large Hadron Collider. We simulate all channels of chargino and neutralino production using ISAJET 7.07. The best mode for observing such processes appears to be pp\to\tw_1\tz_2\to 3\ell +\eslt. We evaluate signal expectations and background levels, and suggest cuts to optimize the signal. The trilepton mode should be viable provided m_{\tg}\alt 500-600~GeV; above this mass, the decay modes \tz_2\to\tz_1 Z and \tz_2\to H_{\ell}\tz_1 become dominant, spoiling the signal. In the first case, the leptonic branching fraction for $Z$ decay is small and additional background from $WZ$ is present, while in the second case, the trilepton signal is essentially absent. For smaller values of $m_{\tg}$, the trilepton signal should be visible above background, especially if $|\mu|\simeq m_{\tg}$ and m_{\tell}\ll m_{\tq}, in which case the leptonic decays of \tz_2 are enhanced. Distributions in dilepton mass $m(\ell\bar{\ell})$ can yield direct information on neutralino masses due to the distribution cutoff at m_{\tz_2}-m_{\tz_1}. Other distributions that may lead to an additional constraint amongst the chargino and neutralino masses are also examined.Comment: preprint nos. FSU-HEP-940310 and UH-511-786-94, 13 pages (REVTEX) plus 7 uuencoded figures attache