We study the problem of retrieving data from a channel that breaks the input sequence into a set of unordered fragments of random lengths, which we refer to as the chop-and-shuffle channel. The length of each fragment follows a geometric distribution. We propose nested Varshamov-Tenengolts (VT) codes to recover the data. We evaluate the error rate and the complexity of our scheme numerically. Our results show that the decoding error decreases as the input length increases, and our method has a significantly lower complexity than the baseline brute-force approach. We also propose a new construction for VT codes, quantify the maximum number of the required parity bits, and show that our approach requires fewer parity bits compared to known results.

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