Unified Position-Invariant Random Access Through Two Compression Layers via Absolute-Offset Coordinates: A Bit-Perfect Device-Resident Proof

Abstract: Random access into compressed data is normally confined to a single layer. Entropy-layer methods (Recoil) seek within rANS by storing intermediate decoder states; dictionary/match-layer methods seek within LZ-style references. We are not aware of a format that supports a single position-invariant seek through both an entropy layer and a match layer addressed by one coordinate. We show that ACEAPEX's absolute-offset design provides exactly this: because the match layer resolves every back-reference to an absolute position at encode time, and the entropy layer is applied per block, an arbitrary block can be decoded through both layers using one coordinate, bit-perfect, in isolation. We prove this with a three-phase verification that closes the empty-buffer trap. The seek of one 16KB block through ANS-entropy and match completes in 0.334ms. We verify the full entropy+match pipeline end-to-end on four data profiles and characterize the hardware ceiling the format reaches: the absolute-offset structure unrolls to as many as 25,344 independent parsers on one H100, which sequential LZ77 cannot do. We state explicitly what is not claimed: this is a round-trip correctness proof, not a disk-archive format; throughput figures are match-phase; and the unified-seek result is demonstrated for two layers, with three-layer generalization left as a hypothesis. Code and the verification harness are in the project repository.

• The paper introduces a novel absolute-offset coordinate approach that enables unified, device-resident, high-parallelism random access across entropy and match layers.
• It demonstrates bit-perfect isolation and correctness using a three-phase verification protocol, achieving up to 183.3GB/s throughput on NVIDIA H100.
• The approach decouples traditional relative-offset dependencies, opening new avenues for scalable and adaptive decompression in genomic and archival data.

Position-Invariant Random Access to Compressed Data via Absolute-Offset Coordinates

Overview

This paper (2606.24531) rigorously demonstrates a unified, position-invariant random access method for compressed data streams, enabling a single absolute-offset coordinate to address both entropy and match layers. Leveraging ACEAPEX’s absolute-offset LZ77 match layer combined with GPU-resident ANS entropy coding, the work establishes bit-perfect isolation and correctness by a three-phase verification protocol. The approach decisively enables device-resident, high-parallelism random access, a capability unattainable with conventional relative-offset match layers.

Absolute-Offset Match Layer: Structure and Necessity

ACEAPEX employs global match search at encode time, storing each LZ77 back-reference as an absolute position in the decompressed output. This structural decision decouples block dependencies, allowing any block to be decoded independently once its source block is present. The pivotal observation is that only absolute-offset resolution circumvents the stateful dependency chain inherent to classic LZ77, thus enabling a position-invariant entry for both entropy and match layers. Relative offsets, by contrast, require the decoder to reconstruct the path and current position—disallowing isolated entry.

Unified Two-Layer Seek: Correctness and Isolation

The central experiment executes a one-coordinate seek for an arbitrary 16KB block through both layered compression schemes (ANS entropy + absolute-offset match), verifying:

1. Buffer Isolation: Pre-decode region differs from the original—proving genuine emptiness.
2. Bit-Perfect Recovery: Post-decode region matches original, validated via FNV hashing.
3. Isolation Guarantee: Neighboring blocks remain untouched, corroborating decode locality.

A unified seek completes in 0.334ms inclusive of kernel launch overhead, on NVIDIA H100 hardware, with no optimization. This protocol rigorously eliminates false positives from residual buffer artifacts or wide-range decode artifacts.

Performance, Parallelism, and Profiles

End-to-end verification on four distinct data profiles (real FASTQ, repetitive genome, English text, mixed) establishes sustained bit-perfect correctness. Match-phase throughput on device-resident streams achieves up to 183.3GB/s for repetitive genome, constrained only by block size and parser occupancy. For textual data (enwik9, 1MB blocks), throughput is lower (6.1GB/s) due to sub-optimal GPU block occupancy.

The absolute-offset design further unrolls up to 25,344 independent parsers per H100, saturating hardware parallelism. Sequential LZ77 cannot expose this level of parallelism due to byte-wise dependencies.

Data-Dependent Entropy Coding and Codec Design Implications

Analysis highlights the necessity for adaptive entropy coding. Applying ANS to all match streams universally often yields compression inflation (ratio < 1) for structural streams (offs/len/cmd) in genomic profiles, as opposed to beneficial compression for literal streams. Codec design should, therefore, measure and apply entropy selectively at encode time according to data profile, rather than with a fixed policy.

Limitations and Scope

The paper explicitly states boundaries:

• Claims are proven only for round-trip correctness, not for archival storage formats.
• Throughput figures pertain to match-phase only; full-pipeline ANS+match numbers are not reported.
• Experiments operate on block ranges rather than whole files.
• No claim is made for three-layer generalization, only two.
• The claim of novelty is stated as "to our knowledge," with targeted prior-art scan.

Related Work and Differentiation

The work differentiates sharply from prior approaches. Recoil (Lin et al., 2023) enables entropy-layer random access via stored decoder state; Kreft and Navarro (DCC 2010) achieve random access at the match-layer; DietGPU implements ANS entropy coding on GPU but without match-layer addressability. Hecate (Szewczyk et al., 16 Mar 2026) performs CPU-based, single-layer random access and slicing. The unique contribution here is the unified, position-invariant seek across both entropy and match layers, validated via absolute-offsets rather than stored states or metadata.

The hardware parallelism achieved is unmatched by sequential LZ77 codecs and complements, rather than competes with, frameworks like NVIDIA Parabricks, which prioritize decompression-then-discard workflows.

Implications and Future Directions

The demonstrated unified seek through two layers unlocks scalable, high-parallelism, device-resident random access for compressed data—a critical capability for genomics, archives, and wide-scale GPU pipelines. The absolute-offset principle may generalize to $N$ layers in a stack, providing each resolves dependencies at encode time to absolute positions. The three-layer generalization remains an explicit hypothesis for subsequent work.

Practical impact includes enabling direct random access to compressed archives in GPU memory, facilitating terabyte-scale data analytics, and supporting scalable, on-demand region decoding without penalty of decompression overhead. Theory implications suggest a new class of compression formats prioritizing absolute-position dependency resolution for multi-layer access patterns.

Conclusion

The paper conclusively proves the correctness and isolation of unified random access through entropy and match compression layers via absolute-offset coordinates, with bit-perfect verification and explicit practical boundaries. Empirical results demonstrate unprecedented parallelism and throughput in device-resident operation. This structural capability is unavailable without absolute-offset match layers, setting a new technical direction for multi-layer, random-accessible compression formats. The work leaves open the generalization to deeper stacks and the translation to archival formats, framing the next steps in scalable data access for compressed environments.