arXiv subjects

Logan Lewis

Publications and source records attributed to Logan Lewis.

4 recordsLinked to original sources

arXiv2026

Set Shaping Theory Applied to Universal Coding

Universal coders process individual sequences without assuming that the source distribution is known. In this setting, uniformly generated sequences represent the most difficult test case: the source simulates pure randomness, contains no exploitable bias, and forces a frequency-estimating universal coder to infer the empirical composition entirely from the sequence itself. This paper reports that a Set Shaping Theory (SST) transformation systematically reduces the average universal coding length of uniformly generated sequences below the Krichevsky-Trofimov baseline N H_0(s) + R_KT(s). The transformation maps each input sequence s in A^N into an expanded sequence f(s) in A^(N+1), while storing the transformation index in the additional symbol in order to preserve reversibility. The comparison evaluates the exact Krichevsky-Trofimov baseline N H_0(s) + R_KT(s) against the shaped score (N+1)H_0(f(s)) + R_KT(f(s)), where H_0 is computed from the empirical frequencies of the individual sequence. A single unified transformation also yields reductions across distinct compression architectures, including adaptive arithmetic coding, enumerative coding, LZ78, adaptive Huffman coding, and adaptive ANS. These results support the interpretation of SST as a representation-level preprocessing layer that can structurally improve existing universal coders without requiring internal modifications to their coding mechanisms. All results reported in the article can be reproduced with the simulator available at https://sst-simulator.github.io/Set-Shaping-Theory-Simulator/.

cs.IT↗

arXiv2026

Using Set Shaping Theory to Trade RAM Accesses for CPU Computation

This paper studies Set Shaping Theory (SST) in a database-index setting under a revised interpretation: SST is not treated as a competing hashing method, but as a structural pre processing layer that can be applied before an existing indexing algorithm. The experimental question is therefore whether a method improves when it is used with SST rather than with out it. The study compares linear probing, double hashing, quadratic probing, and Robin Hood hashing against their corresponding SST-augmented variants for shaping orders K = 2,4,8. Beyond mean time, the benchmark reports mean successful probes, 95th and 99th percentile probes, collisions per stored record, and maxi mum cluster length. Experiments cover load factors from 0.75 to 0.95, database sizes from M =5000 to M =500000, query multipliers up to 200 lookups per stored record, and both uniform and hotspot query distributions. The results highlight two fundamental advantages. First, SST reduces the number of RAM accesses required during retrieval. By prevent ing clusters and long probe chains from forming at insertion time, the lookup phase requires fewer memory jumps, lower probe counts, and reduced tail latency. Second, the method introduces a new way of thinking about data storage: the data are not treated as fixed objects that must be placed passively into a table, but as reversible representations that can be struc turally adapted before being written. A small metadata tag records which transformation was selected, allowing the original key to remain recoverable and the lookup process to remain deterministic.This article is connected to the Set Shaping Theory simulator project, available online at https://sst-simulator.github.io/Set-Shaping-Theory-Simulator/ where it is possible to simulate part of the results presented in the article.

cs.IT↗

arXiv2026

Set Shaping Theory as a Complementary Payload-Shaping Layer for Steganography

This paper studies the use of Set Shaping Theory (SST) as a reversible payload-shaping layer for least significant bit (LSB) image steganography. The proposal is not intended to replace existing steganographic methods or to compete with them as a new embedding scheme. Instead, SST is positioned as a complementary preprocessing stage that makes an existing embedding method easier to apply with lower statistical disturbance. The SST transformation increases the message length by K symbols and is implemented with the approximate and fast transformation algorithm developed by Glen Tankersley. Although the embedded payload is lengthened from N to N+K bits, the selected representation can reduce D_KL(P||Q) and therefore make the subsequent steganographic insertion less detectable under histogram-based criteria. Across 1,800 controlled simulations on four synthetic cover-image models, SST reduced D_KL(P||Q) by an average of 25.16 percent relative to a fair N+K LSB baseline, with a 95 percent confidence interval of +/- 1.22 percent. For K=8, the average reduction reached 42.81 percent. Additional robustness simulations with keyed random embedding paths confirmed the effect across several distances: at K=8, SST reduced KL divergence by 42.44 percent, Jensen-Shannon divergence by 29.62 percent, total variation by 12.41 percent, and symmetric chi-square distance by 28.30 percent. An additional image-based matrix-embedding/STC-like simulation showed that SST also reduces the minimum weighted insertion cost: relative to the unshaped K=0 reference, K=8 reduced the cost by 6.93 percent.

eess.IV↗

arXiv2023

Overcoming the compression limit of the individualsequence (zero order empirical entropy) using the Set Shaping Theory

Given the importance of the claim, we want to start by exposing the following consideration: this claim comes out more than a year after the article "Practical applications of Set Shaping Theory in Huffman coding" which reports the program that carried out an experiment of data compression in which the coding limit NH0(S) of a single sequence was questioned. We waited so long because, before making a claim of this type, we wanted to be sure of the consistency of the result. All this time the program has always been public; anyone could download it, modify it and independently obtain the reported results. In this period there have been many information theory experts who have tested the program and agreed to help us, we thank these people for the time dedicated to us and their precious advice. Given a sequence S of random variables i.i.d. with symbols belonging to an alphabet A; the parameter NH0(S) (the zero-order empirical entropy multiplied by the length of the sequence) is considered the average coding limit of the symbols of the sequence S through a uniquely decipherable and instantaneous code. Our experiment that calls into question this limit is the following: a sequence S is generated in a random and uniform way, the value NH0(S) is calculated, the sequence S is transformed into a new sequence f(S), longer but with the symbols belonging to the same alphabet, finally we code f(S) using Huffman coding. By generating a statistically significant number of sequences we obtain that the average value of the length of the encoded sequence f(S) is less than the average value of NH0(S). In this way, a result is obtained which is incompatible with the meaning given to NH0(S).

cs.IT↗