Recently, so-called Fuchsian codes have been proposed in [I. BlancoChacón et al., “Nonuniform Fuchsian codes for noisy channels”, J. of the Franklin Institute 2014] for communication over channels subject to additive white Gaussian noise (AWGN). The two main advantages of Fuchsian codes are their ability to compress information, i.e., high code rate, and their logarithmic decoding complexity. I...

This paper discusses the obstacles that stand in the way of doing a good job of machine-code analysis. Compared with analysis of source code, the challenge is to drop all assumptions about having certain kinds of information available (variables, control-flow graph, callgraph, etc.) and also to address new kinds of behaviors (arithmetic on addresses, jumps to “hidden” instructions starting at p...

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

A typical adaptive arithmetic coder consists of three steps: range calculation, renormalization, and probability model updating. A method, called greedy re-normalization, is given in this paper that significantly reduces the computational complexity of the renormalization step of arithmetic coding. This is achieved by reducing both the number of re-normalizations required to encode a sequence a...

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

First unequal error protection (UEP) proposals date back to the 1960’s (Masnick and Wolf; 1967), but now with the introduction of scalable video, UEP develops to a key concept for the transport of multimedia data. The paper presents an overview of some new approaches realizing UEP properties in physical transport, especially multicarrier modulation, or with LDPC and Turbo codes. For multicarrie...

The family of Reed-Solomon (RS) codes plays a prominent role in the construction of quasilinear probabilistically checkable proofs (PCPs) and interactive oracle proofs (IOPs) with perfect zero knowledge and polylogarithmic verifiers. The large concrete computational complexity required to prove membership in RS codes is one of the biggest obstacles to deploying such PCP/IOP systems in practice....

The issue of robust and joint source-channel decoding of quasi-arithmetic codes is addressed. Quasi-arithmetic coding is a reduced precision and complexity implementation of arithmetic coding. This amounts to approximating the distribution of the source. The approximation of the source distribution leads to the introduction of redundancy that can be exploited for robust decoding in presence of ...