No abstract

In this paper, we consider the diagnosis of asynchronous discrete event systems. We follow a so-called true concurrency approach, in which no global state and no global time is available. Instead, we use only local states in combination with a partial order model of time. Our basic mathematical tool is that of net unfoldings originating from the Petri net research area. This study was motivated by the problem of event correlation in telecommunications network management.

We analyze the dependencies between the variables involved in the source and channel coding chain. This analysis is carried out in the framework of Bayesian networks, which provide both an intuitive representation for the global model of the coding chain and a way of deriving joint (soft) decoding algorithms. Three sources of dependencies are involved in the chain: 1) the source model, a Markov chain of symbols; 2) the source coder model, based on a variable length code (VLC), for example a Huffman code; and 3) the channel coder, based on a convolutional error correcting code. Joint decoding relying on the hidden Markov model (HMM) of the global coding chain is intractable, except in trivial cases. We advocate instead an iterative procedure inspired from serial turbo codes, in which the three models of the coding chain are used alternately. This idea of using separately each factor of a big product model inside an iterative procedure usually requires the presence of an interleaver between successive components. We show that only one interleaver is necessary here, placed between the source coder and the channel coder. The decoding scheme we propose can be viewed as a turbo algorithm using alternately the intersymbol correlation due to the Markov source and the redundancy introduced by the channel code. The intermediary element, the source coder model, is used as a translator of soft information from the bit clock to the symbol clock.Index Terms-Bayesian network, data compression, entropy coding, iterative decoding, joint source-channel decoding, probabilistic inference, soft decoding, turbo code, variable length code.