On Optimal TCM Encoders

An asymptotically optimal trellis-coded modulation (TCM) encoder requires the joint design of the encoder and the binary labeling of the constellation. Since analytical approaches are unknown, the only available solution is to perform an exhaustive search over the encoder and the labeling. For large constellation sizes and/or many encoder states, however, an exhaustive search is unfeasible. Traditional TCM designs overcome this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. In this paper we study binary labelings for TCM and show how they can be grouped into classes, which considerably reduces the search space in a joint design. For 8-ary constellations, the number of different binary labelings that must be tested is reduced from 8!=40320 to 240. For the particular case of an 8-ary pulse amplitude modulation constellation, this number is further reduced to 120 and for 8-ary phase shift keying to only 30. An algorithm to generate one labeling in each class is also introduced. Asymptotically optimal TCM encoders are tabulated which are up to 0.3 dB better than the previously best known encoders

On palimpsests in neural memory: an information theory viewpoint

The finite capacity of neural memory and the reconsolidation phenomenon suggest it is important to be able to update stored information as in a palimpsest, where new information overwrites old information. Moreover, changing information in memory is metabolically costly. In this paper, we suggest that information-theoretic approaches may inform the fundamental limits in constructing such a memory system. In particular, we define malleable coding, that considers not only representation length but also ease of representation update, thereby encouraging some form of recycling to convert an old codeword into a new one. Malleability cost is the difficulty of synchronizing compressed versions, and malleable codes are of particular interest when representing information and modifying the representation are both expensive. We examine the tradeoff between compression efficiency and malleability cost, under a malleability metric defined with respect to a string edit distance. This introduces a metric topology to the compressed domain. We characterize the exact set of achievable rates and malleability as the solution of a subgraph isomorphism problem. This is all done within the optimization approach to biology framework.Accepted manuscrip

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR

A fractal set from the binary reflected Gray code

The permutation associated with the decimal expression of the binary reflected Gray code with N bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of an IFS. For large values of N the set is examined from the point of view of time series analysis

Harmonious Hilbert curves and other extradimensional space-filling curves

This paper introduces a new way of generalizing Hilbert's two-dimensional space-filling curve to arbitrary dimensions. The new curves, called harmonious Hilbert curves, have the unique property that for any d' < d, the d-dimensional curve is compatible with the d'-dimensional curve with respect to the order in which the curves visit the points of any d'-dimensional axis-parallel space that contains the origin. Similar generalizations to arbitrary dimensions are described for several variants of Peano's curve (the original Peano curve, the coil curve, the half-coil curve, and the Meurthe curve). The d-dimensional harmonious Hilbert curves and the Meurthe curves have neutral orientation: as compared to the curve as a whole, arbitrary pieces of the curve have each of d! possible rotations with equal probability. Thus one could say these curves are `statistically invariant' under rotation---unlike the Peano curves, the coil curves, the half-coil curves, and the familiar generalization of Hilbert curves by Butz and Moore. In addition, prompted by an application in the construction of R-trees, this paper shows how to construct a 2d-dimensional generalized Hilbert or Peano curve that traverses the points of a certain d-dimensional diagonally placed subspace in the order of a given d-dimensional generalized Hilbert or Peano curve. Pseudocode is provided for comparison operators based on the curves presented in this paper.Comment: 40 pages, 10 figures, pseudocode include