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In this paper will be presented methodology of encoding information invaluations of discrete lattice with some translational invariant constrains inasymptotically optimal way. The method is based on finding statisticaldescription of such valuations and changing it into statistical algorithm,which allows to construct deterministically valuation with given statistics.Optimal statistics allow to generate valuations with uniform distribution - weget maximum information capacity this way. It will be shown that we can reachthe optimum for one-dimensional models using maximal entropy random walk andthat for the general case we can practically get as close to the capacity ofthe model as we want (found numerically: lost 10^{-10} bit/node for HardSquare). There will be also presented simpler alternative to arithmetic codingmethod which can be used as cryptosystem and data correction method too.

Optimal encoding on discrete lattice with translational invariant constrains using statistical algorithms