We give an overview of several the mathematical works Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets his personality.

The digital rights management (DRM) techniques are very important in the fields of multimedia security. The major areas of multimedia data security includes secrecy, ownership protection and traitor tracing. Even though, a number of encryption techniques were developed for multimedia encryption, most of them are vulnerable to several types of attacks. Hence, an encryption system having better s...

We present the Z Coder a new adaptive data compression coder for coding binary data The Z Coder is derived from the Golomb run length coder and retains most of the speed and simplicity of the earlier coder The Z Coder can also be thought of as a multiplication free approximate arithmetic coder showing the close relationship between run length coding and arithmetic cod ing The Z Coder improves u...

Arithmetic coding is a very efficient and most popular entropy coding technique. Arithmetic coding method is based on the fact that the cumulative probability of a symbol sequence corresponds to a unique subinterval of the initial interval [0, 1). In this method, when encoding a symbol, it first computes new interval [low, high) based on cumulative probability segment of the symbol. Thereafter ...

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 ...

In this paper, we propose a novel adaptive arithmetic coding method that uses dual symbol sets: a primary symbol set that contains all the symbols that are likely to occur in the near future and a secondary symbol set that contains all other symbols. The simplest implementation of our method assumes that symbols that have appeared in the previously are highly likely to appear in the near future...

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

We present a new arithmetic coding algorithm based on a small cache memory. The complexity of multilevel arithmetic coding has been reduced by restricting the operations to those symbols stored in the cache. We analyze the best organisation of the cache, trying out different configurations, associativity and replacement algorithms. Finally, a new architecture for encoding and decoding has been ...

Here we describe a baseline-based binary shape coding method in which arbitrarily shaped object is represented b y the traced 1-D data from baseline and turning point (TP). The shape coding is performed based on contour-based method in each separated shape. There are two coding modes in shape coding, i.e. intra and inter mode as in texture coding. In inter coding mode, object identification, gl...