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首页> 外文期刊>IEEE Transactions on Information Theory >Large deviations for coding Markov chains and Gibbs random fields
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Large deviations for coding Markov chains and Gibbs random fields

机译：马尔可夫链和吉布斯随机场编码的大偏差

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摘要

Fixed block coding schemes for Gibbs random fields are proposed in which the empirical expectations of the local interactions of the Gibbs measure is compared to its expectation with respect to all Gibbs measures having those interactions. The exponential decay of the error probabilities is proven and it is shown that the code rates equal the entropy of the random field. In addition, it is shown that any coding scheme based on regarding the field as a 1-D sequence of symbols has rate greater than the entropy of the field. The theory of fixed length coding is approached from the point of view of large deviations, both for the calculation of the error exponents or error probabilities and for the calculation of the encoding rates or the asymptotic combinatorics of the coding schemes. This approach is also applied to fixed length coding schemes of Markov sources for which estimates on the error exponents and on the rates are derived.
机译：提出了针对吉布斯随机场的固定块编码方案，其中将吉布斯测度的局部相互作用的经验期望与其对所有具有那些相互作用的吉布斯测度的期望进行比较。证明了误差概率的指数衰减，并且表明码率等于随机场的熵。另外，示出了基于将场视为符号的一维序列的任何编码方案具有大于场的熵的速率。从大偏差的观点出发，采用了固定长度编码的理论，既用于计算误差指数或误差概率，又用于计算编码方案的编码率或渐近组合。这种方法也适用于马尔可夫信源的固定长度编码方案，由此得出对误差指数和速率的估计。

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