In the world of data compression, Huffman coding is a classic algorithm. However, it is notoriously fragile: a single bit error during transmission can lead to "synchronization loss," causing the decoder to misinterpret the entire remaining sequence.
In this problem, you are tasked with recovering a message from a corrupted Huffman-encoded bitstream.
The Setup:
1.Dictionary: You are given a cell array of binary strings (e.g., {'0', '10', '11'} ). The i-th element corresponds to the i-th letter of the alphabet (1->'A', 2-> 'B', etc.).
2.Bitstream: A string of '0's and '1's. This stream contains exactly one flipped bit (an error where a 0 became a 1 or vice versa).
3.ValidWords: A cell array of possible original strings (e.g.,{'ABC', 'BBA'}).
The Rules:
- The original (pre-corruption) bitstream, when decoded, results in one of the strings listed in ValidWords.
- A decoded string is only valid if the bitstream can be completely partitioned into codewords from the dictionary with no bits left over.
- You must identify the single erroneous bit, flip it back, and return the corrected decoded string.
Input:
- Dictionary: 1 x N cell array of bit strings.
- Bitstream: A string of '0's and '1's.
- ValidWords: A cell array of strings.
Output:
- decodedWords: The corrected string (must be an element of ValidWords).
Example:
- Dictionary = {'0', '10', '11'} (A = '0', B = '10', C = '11')
- ValidWords = {'ABC', 'BBA', 'ACC'}
- Bitstream = '00011'
Analysis:
- If we flip the 1st bit: '10011' -> 'B' + '0' + '11' = 'BAC' (Not in ValidWords)
- If we flip the 2nd bit: '01011' -> '0' + '10' + '11' = 'ABC' ( Matches ValidWords! )
- Result: 'ABC'
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