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Codes based on SUDOKU puzzles are discussed, and belief propagation decodingintroduced for the erasure channel. Despite the non-linearity of the codeconstraints, it is argued that density evolution can be used to analyse codeperformance due to the invariance of the code under alphabet permutation. Thebelief propagation decoder for erasure channels operates by exchanging messagescontaining sets of possible values. Accordingly, density evolution tracks theprobability mass functions of the set cardinalities. The equations governingthe mapping of those probability mass functions are derived and calculated forvariable and constraint nodes, and decoding thresholds are computed for longSUDOKU codes with random interleavers.

Density Evolution for SUDOKU Codes on the Erasure Channel