Efficient algorithms for decode efficient prefix codes
01 Mar 2021-pp 338
TL;DR: In this paper, the problem of finding a prefix tree having the best decode time under the constraint that the code length does not exceed a certain threshold for a natural class of memory access cost functions that use blocking (also referred to as lookup tables).
Abstract: The cost of decompressing (decoding) data can be prohibitive for certain real-time applications. In many scenarios, it is acceptable to sacrifice (to some extent) on compression in the interest of fast decoding. We study anovel problem of finding a prefix tree having the best decode time under the constraint that the code length does not exceed a certain threshold for a natural class of memory access cost functions that use blocking (also referred to as lookup tables). We present exact and approximation algorithms for this problem that are based on dynamic programming and capitalize on interesting structures of the optimal solutions. The full version of this paper is available at [1]
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TL;DR: In this paper, a symmetric P-code based on prefix codes is proposed, and a detailed analysis of the fundamental properties of P-codes shows that the keyspace of the cipher is too large to mount a brute-force attack.
Abstract: A prefix code, a P-code, is a code where no codeword is a prefix of another codeword. In this paper, a symmetric cipher based on prefix codes is proposed. The simplicity of the design makes this cipher usable for Internet of Things applications. Our goal is to investigate the security of this cipher. A detailed analysis of the fundamental properties of P-codes shows that the keyspace of the cipher is too large to mount a brute-force attack. Specifically, in this regard we will find bounds on the number of minimal P-codes containing a binary word given in advance. Furthermore, the statistical attack is difficult to mount on such cryptosystem due to the attacker’s lack of information about the actual words used in the substitution mapping. The results of a statistical analysis of possible keys are also presented. It turns out that the distribution of the number of minimal P-codes over all binary words of a fixed length is Gaussian.
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TL;DR: This work introduces and study a novel problem of finding a prefix tree having the best decode time under the constraint that the code length does not exceed a certain threshold for a natural class of memory access cost functions that use blocking (also referred to as lookup tables), i.e., these decoding schemes access multiple prefix tree entries in a single access, using associative memory table look-ups.
Abstract: Data compression is used in a wide variety of tasks, including compression of databases, large learning models, videos, images, etc. The cost of decompressing (decoding) data can be prohibitive for certain real-time applications. In many scenarios, it is acceptable to sacrifice (to some extent) on compression in the interest of fast decoding. In this work, we introduce and study a novel problem of finding a prefix tree having the best decode time under the constraint that the code length does not exceed a certain threshold for a natural class of memory access cost functions that use blocking (also referred to as lookup tables), i.e., these decoding schemes access multiple prefix tree entries in a single access, using associative memory table look-ups. We present (i) an exact algorithm for this problem that is polynomial in the number of characters and the codelength; (ii) a strongly polynomial pseudo approximation algorithm that achieves the best decode time by relaxing the codelength constraint by a small factor; and (iii) a more efficient version of the pseudo approximation algorithm that achieves near optimal decode time by relaxing the codelength constraint by a small factor. All our algorithms are based on dynamic programming and capitalize on an interesting structure of the optimal solution. To the best of our knowledge, there is no prior work that gives any provable theoretical guarantees for minimizing decode time along with the code length. We also demonstrate the performance benefits of our algorithm on different types of real-world data sets, namely (i) a deep learning model (Mobilenet-V2); (ii) image and (iii) text data. We also implement and evaluate the performance of our algorithms on the GPU.
3 citations