Kamila Szewczyk

Kamila Szewczyk, Sven Rahmann

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.

Kamila Szewczyk

Range coders and ANS replace empirical probabilities with integer frequencies summing to a fixed $M$; the resulting per-symbol code-length redundancy is exactly the KL divergence of the empirical distribution from the quantized one. Existing normalizers (Giesen, Bloom, Collet) are heuristic or only partially marginal-optimal. We give three provably KL-optimal algorithms: a bottom-up archetype, a bidirectional exchange repair of Bloom's heap correction, and a top-down window method that runs in $\mathcal{O}(r)$, asymptotically optimal in $r$, where $r$ is the number of positive-count symbols.