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What you are suggesting is indeed rooted on concepts that are important in DSP: On the channel coding side, you have for instance error correction codes (or error correcting codes, both ECC) On the source coding side, since you mention Sudoku, techniques like matrix completion, sparse sampling or compressive sensing are possibilities to approximately ...


Say each of the 10 pixel values on a row consists of $N$ bits. An $N$-bit wrap-around-arithmetic sum of the values gives just enough additional information to reconstruct the 10th value from the 9 previous values: subtract the 9-sum from the 10-sum. So 10 values that are needed for reconstruction each row, which is the same as the size of the original data. ...

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