Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images

We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) associated to a 3D binary image I, to obtain a “well-composed” polyhedral complex P(I), homotopy equivalent to Q(I). There, we developed a new codification system for P(I), called ExtendedCubeMap (ECM) representation, that encodes: (1) the (geometric) information of the cells of P(I) (i.e., which cells are presented and where), under the form of a 3D grayscale image gP ; (2) the boundary face relations between the cells of P(I), under the form of a set BP of structuring elements. In this paper, we simplify ECM representations, proving that geometric and topological information of cells can be encoded using just a 3D binary image, without the need of using colors or sets of structuring elements. We also outline a possible application in which well-composed polyhedral complexes can be useful.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-32706Ministerio de Economía y Competitividad MTM2015-67072-

Encoding and Decoding of Balanced q-ary sequences using a gray code prefix

Abstract: Balancing sequences over a non-binary alphabet is considered, where the algebraic sum of the components (also known as the weight) is equal to some specific value. Various schemes based on Knuth’s simple binary balancing algorithm have been proposed. However, these have mostly assumed that the prefix describing the balancing point in the algorithm can easily be encoded. In this paper we show how non-binary Gray codes can be used to generate these prefixes. Together with a non-binary balancing algorithm, this forms a complete balancing system with straightforward and efficient encoding/decoding

Coding and Decoding Schemes for MSE and Image Transmission

In this work we explore possibilities for coding and decoding tailor-made for mean squared error evaluation of error in contexts such as image transmission. To do so, we introduce a loss function that expresses the overall performance of a coding and decoding scheme for discrete channels and that exchanges the usual goal of minimizing the error probability to that of minimizing the expected loss. In this environment we explore the possibilities of using ordered decoders to create a message-wise unequal error protection (UEP), where the most valuable information is protected by placing in its proximity information words that differ by a small valued error. We give explicit examples, using scale-of-gray images, including small-scale performance analysis and visual simulations for the BSMC.Comment: Submitted to IEEE Transactions on Information Theor

Constant-Weight Gray Codes for Local Rank Modulation

We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank- modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study constant-weight Gray codes for the local rank- modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. We provide necessary conditions for the existence of cyclic and cyclic optimal Gray codes. We then specifically study codes of weight 2 and upper bound their efficiency, thus proving that there are no such asymptotically-optimal cyclic codes. In contrast, we study codes of weight 3 and efficiently construct codes which are asymptotically-optimal. We conclude with a construction of codes with asymptotically-optimal rate and weight asymptotically half the length, thus having an asymptotically-optimal charge difference between adjacent cells