A Comparative Study on Error Correction Algorithms for LEO-Based CubeSats

LDPC vs. Cascade information reconciliation for continuous-variable QKD under CubeSat-style constraints

Author: Maciek Zaweracz · Supervisor: Dr Adrian Bors · BSc Computer Science

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Abstract

This repository supports a simulation and systems study comparing one-way quasi-cyclic LDPC reconciliation (via the SPOQC-oriented cvqkd-reconciliation library) with the interactive Cascade protocol (via cascade-cpp, after Bruno Rijsman’s reference implementation). Work is framed around LEO CubeSat limits on compute, memory, classical bandwidth, and pass time, in the context of continuous-variable quantum key distribution (CV-QKD) and the Satellite Platform for Optical Quantum Communications (SPOQC).

Part I sweeps channel difficulty and records reconciliation efficiency, residual errors, classical overhead, timings, and interaction counts under matched pre-correction bit error rate between pipelines. Part II maps those measurements onto a first-order mission model (quantum window, RF vs. optical classical links, compute pace scenarios). Full methodology, results, and ethics statement are in the LaTeX dissertation (Overleaf-Dissertation-Files/).

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Table of contents

• Repository layout
• Prerequisites & running
• Sample figures
• Analysis
• LDPC statistics tracking
• Upstream and mission context

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Repository layout

Path	Role
cvqkd-reconciliation/	C library: CV-QKD-style channel, 8D reconciliation, Min–Sum LDPC; ldpc_experiment benchmark binary
cascade-cpp/	C++17 Cascade reference; bin/run_experiments drives JSON-defined sweeps
experiments/scripts/run_sweep.py	YAML-driven orchestration for LDPC SNR × matrix sweeps
experiments/config/	Example sweep configuration
experiments/scripts/part_1_results.ipynb	Part I plots and tables
Overleaf-Dissertation-Files/	UoYCS LaTeX project and bibliography

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Prerequisites & running

Piece	Need
LDPC	CMake ≥ 3.10, C11 (clang/gcc)
Cascade	C++17 clang++, Boost (program_options, filesystem), pthread; GTest for make test. Apple Silicon: Homebrew paths in cascade-cpp/Makefile.
Python	uv, Python ≥ 3.12 (pyproject.toml / uv.lock)

LDPC (from repository root)

cmake -S cvqkd-reconciliation -B cvqkd-reconciliation/build && cmake --build cvqkd-reconciliation/build
# optional single point: cvqkd-reconciliation/build/ldpc_experiment 0.07 123 10000 cvqkd-reconciliation/data/B_matrices/1024x1023_z1.coo 8

uv sync && uv run python experiments/scripts/run_sweep.py experiments/config/sweep_snr_ldpc.yaml

ldpc_experiment writes one NDJSON line per (matrix, SNR) into the run’s output dir; YAML keys: ldpc.binary, b_matrices, snr / snr_points, frames_per_point, output.raw_dir.

Cascade (from repository root)

cd cascade-cpp && make bin/run_experiments && mkdir -p study/data/dissertation && \
  ./bin/run_experiments study/experiments_papers_ec_compare.json --output-dir study/data/dissertation

JSON schema: cascade-cpp/README.md. Upstream full suite: make data-papers.

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Sample figures

Part I outputs under experiments/graphs/results/ (regenerate via part_1_results.ipynb).

Reconciliation efficiency η (matched pre-correction BER)	Classical bits per reconciled key bit

Residual BER after correction	Cascade sequential parity messages per frame

More plots in the same folder (e.g. FER, timings, SNR–BER mapping, zooms).

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Analysis

experiments/scripts/part_1_results.ipynb — Part I plots and tables. Use the .venv from uv sync (or uv run …).

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LDPC statistics tracking

cvqkd-reconciliation gained NDJSON stats from each ldpc_experiment run, with fields aligned to cascade-cpp experiment JSON so one analysis path covers both codes. Per-frame values are aggregated with Welford’s method in qkd_stats.c (stable mean/σ without storing every trial). Efficiency uses the same Shannon/BSC definition as Cascade, from measured pre-correction BER.

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Upstream and mission context

Component	Origin / notes
Cascade-cpp	brunorijsman/cascade-cpp (vendored/forked here with local Makefile tweaks).
cvqkd-reconciliation	Quantum Communications Hub / SPOQC-oriented CV-QKD reconciliation library; Hub-supervised use. Statistics NDJSON extension is intended to ship with the mission codebase.
SPOQC / HOGS	12U CubeSat and ground segment context for CV-QKD from space. See website.

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Acknowledgements

Supervision: Dr Adrian Bors (University of York). Quantum communications context: Dr Rupesh Kumar. Systems and implementation guidance: Killian Murphy. SPOQC / LDPC matrix design: SPOQC team (acknowledged in the dissertation). Cascade-cpp: Bruno Rijsman and contributors.

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_{Repository layout and commands reflect the state of this workspace; adjust paths if you relocate build directories.}