The task of optimal sampling for the statistical simulation of a discrete random field is addressed from the perspective of minimizing the posterior uncertainty of non-sensed positions given the information of the sen...
详细信息
The task of optimal sampling for the statistical simulation of a discrete random field is addressed from the perspective of minimizing the posterior uncertainty of non-sensed positions given the information of the sensed positions. In particular, information theoretic measures are adopted to formalize the problem of optimal sampling design for field characterization, where concepts such as information of the measurements, average posterior uncertainty, and the resolvability of the field are introduced. The use of the entropy and related information measures are justified by connecting the task of simulation with a source coding problem, where it is well known that entropy offers a fundamental performance limit. On the application, a one-dimensional Markov chain model is explored where the statistics of the random object are known, and then the more relevant case of multiple-point simulations of channelized facies fields is studied, adopting in this case a training image to infer the statistics of a non-parametric model. In both contexts, the superiority of information-driven sampling strategies is proved in different settings and conditions, with respect to random or regular sampling.
Linear interactive encoding and decoding (IED) for near lossless source coding with decoder only side information is considered, where the interactive encoder uses linear codes (described by parity-check matrices over...
详细信息
Linear interactive encoding and decoding (IED) for near lossless source coding with decoder only side information is considered, where the interactive encoder uses linear codes (described by parity-check matrices over a finite field chi) for encoding. It is first demonstrated how to convert any classical universal lossless code C(n) (with block length n and with side information available to both the encoder and decoder) into a universal random linear IED scheme based on Gallager's parity check ensemble. It is then shown that there is no performance loss by restricting IED to linear IED, and that the universal random linear IED scheme based on Gallager's parity check ensemble achieves essentially the same rate performance as does C(n) for each and every individual sequence pair (x(n), y(n)) while the word decoding error probability goes to 0 as n --> infinity. Define the density of a linear IED scheme as the percentage of nonzero entries in its parity-check matrix. To reduce the encoding complexity of linear IED, low density linear IED is further investigated in terms of the trade-off among its rate, decoding error probability, and density.
暂无评论