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We would wish to answer to the following basic question. Assuming that $s$ and $t$ differ in at most $k$ positions, how many bits does player $A$ need to send to player $C$ so that he can recover $s$ with certainty? 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Assume that $s$ and $t$ are both over an integer alphabet $[\\sigma]$, where the first string contains $n$ non-zero entries. We would wish to answer to the following basic question. Assuming that $s$ and $t$ differ in at most $k$ positions, how many bits does player $A$ need to send to player $C$ so that he can recover $s$ with certainty? 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