Fundamental Limits of Sequence Reconstruction Problems in Immunogenomics

2026-09-25

AI Summary

This study addresses the sample complexity of D-gene segment reconstruction in personalized immunogenomics. Methodologically, it systematically analyzes three biological sequence reconstruction models, establishing exact trace complexity bounds for the TrimSuffixAndExtend and TrimAndExtend models via information-theoretic lower bound analysis. Furthermore, efficient algorithms are developed by integrating prefix filtering with bit-pattern decoding techniques. The primary contributions are twofold: first, this work reveals, for the first time, a fundamental complexity gap between Θ(n) and Θ(n²) across different models; second, it designs practical decoding algorithms that achieve these theoretical limits. Collectively, these advances provide optimal complexity solutions for genomic sequence reconstruction.

Abstract

The goal of personalized immunogenomics is to recover an individual's germline immunoglobulin gene segments from 'repertoire sequences' altered by trimming, extension, and mutation. In this work, we study the fundamental trace complexity (or the number of samples/traces required for accurate reconstruction) of D-gene reconstruction under three biologically motivated trace-generation models introduced by Bhardwaj et al. (2021) and develop practical algorithms for reconstruction problems left open in the original work. First, for the TrimSuffixAndExtend model, we establish the optimal trace complexity to be {Θ(n)}, and develop a low-complexity Prefix-Filtered Mode (PFM) decoder that achieves this scaling. Second, for the closely related two-sided TrimAndExtend model, we show that the optimal trace complexity is instead {Θ(n^2)}, and is achieved by the simple Bit-Wise Mode (BWM) decoder. Third, for the SuffixExtend-t(TrimSuffix) model, we establish polynomially separated lower and upper bounds on trace complexity. Our results follow from information-theoretic lower bounds coupled with tight analyses of the proposed reconstruction algorithms.

Innovation

• trace complexity
• sequence reconstruction
• immunogenomics
• decoder algorithms
• information-theoretic bounds