Uniquely decodable and directly accessible non-prefix-free codes via wavelet trees

Unique decodability is the essential feature of any coding scheme, which is naturally provided by prefix-free codes satisfying the Kraft-McMillan inequality. Non-prefix-free codes have received much less attention due to the lack of an efficient method to support this property. In this study we introduce a novel technique that uses wavelet trees to bring unique decodability to non-prefix-free codes. Proposed method also provides direct access to the ith codeword, which can be extended to any variable-length coding scheme. The space overhead required for unique decoding is upper bounded by n·log q bits, where n is the number of symbols, and q is the number of distinct codeword lengths, which is normally expected to be a small number in non-prefix-free codes. Direct access is supported by using an additional o(n · log q) bits. We show that the overhead space requirement is much less than sampling methods using state-of-the-art compact integer representations.