arXiv subjects

Kamila Szewczyk

Publications and source records attributed to Kamila Szewczyk.

3 recordsLinked to original sources

arXiv2026

Linear KL-Optimal Frequency Normalisation

Fast implementations of range coding and asymmetric numeral systems (ANS) owe their excellent performance to replacing slow division instructions by bit-shifts in their encoding and decoding algorithms. This is possible when the frequency distribution of symbols is normalised such that it sums to a power of two. However, such normalisation typically introduces a marginal increase in the Kullback-Leibler divergence between the original and the normalised distribution, leading to a worse compression ratio. We show that the currently used methods for frequency normalisation are suboptimal in both their running time and the achieved Kullback-Leibler divergence. We propose a new method for frequency normalisation that is asymptotically linear in the number of symbols and achieves the smallest possible Kullback-Leibler divergence between the original and the normalised distribution. The method is based on a solution to a separable concave optimisation problem, which may be of independent interest.

cs.IT↗

arXiv2026

A Gallager-Type Redundancy Bound for Binary Shannon-Fano Coding

Krajči, Liu, Mikeš, and Moser proved in 2015 that the redundancy of binary Shannon-Fano coding is always below one bit. We sharpen this to a bound depending on the largest source probability $p_1$: an explicit seven-piece envelope $R<f(p_1)$. The envelope equals the exact supremum of $R$ given $p_1$ for every $p_1\ge\tfrac12$ and on a subinterval below $\tfrac13$, and gives the cap $R<\tfrac52-\tfrac56\log_2 5=0.5651$ for $p_1<\tfrac12$. It is the first $p_1$-dependent redundancy bound for Fano codes. The method is more sophisticated than the approach typical for Huffman codes: Fano trees are built top-down by contiguous balanced splits and lack the sibling property. From the $R<1$ theorem the rest follows from the Fano recursion, through a min-corrected affine potential and a no-burial lemma. Every scalar inequality in the proof reduces to a comparison of integer powers.

cs.IT↗

arXiv2026

Hecate: A Modular Genomic Compressor

We present Hecate, a modular lossless genomic compression framework. It is designed around uncommon but practical source-coding choices. Unlike many single-method compressors, Hecate treats compression as a conditional coding problem over coupled FASTA/FASTQ streams (control, headers, nucleotides, case, quality, extras). It uses per-stream codecs under a shared indexed block container. Codecs include alphabet-aware packing with an explicit side channel for out-of-alphabet residues, an auxiliary-index Burrows-Wheeler pipeline with custom arithmetic coding, and a blockwise Markov mixture coder with explicit model-competition signaling. This architecture yields high throughput, exact random-access slicing, and referential mode through streamwise binary differencing. In a comprehensive benchmark suite, Hecate provides the best compression vs. speed trade-offs against state-of-the-art established tools (MFCompress, NAF, bzip3, AGC), with notably stronger behaviour on large genomes and high-similarity referential settings. For the same compression ratio, Hecate is 2 to 10 times faster. When given the same time budget as other algorithms, Hecate achieves up to 5% to 10% better compression.

cs.DS↗