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Simulation Coding Schemes

Sequence Mode

All coding schemes in this project rely on a coset decoder, combined with different channel models: BIAWGN and several CVQKD virtual channels \(-\) real, complex, quaternion, octonion, and Householder with complexities \(O(d^3)\) and \(O(d^2)\).

In addition, we include an extra coding scheme based on syndrome concatenation, used purely for performance comparison.

The objective is to compare:

  • a standard coset coding approach (decoding toward a given syndrome), and
  • a coset coding with syndrome concatenation.

A direct comparison with a classical decoder (i.e., decoding toward the zero syndrome) is not performed. This would require the original AFF3CT decoder, which is not suited for low-SNR CV-QKD regimes and does not provide satisfactory performance in terms of efficiency (\(\beta\)) and frame error rate (FER).

Instead, we use a general-purpose coset decoder that can target any syndrome (including the zero syndrome), and compare coset coding with coset coding + syndrome concatenation.

Note

This additional scheme is NOT intended for practical use, but rather to isolate and evaluate the impact of syndrome concatenation in a controlled setting.

Since the focus is on the decoder behavior (not the channel model), this comparison is implemented only for the BIAWGN channel, as extending it to CVQKD virtual channels would not bring additional insight.

Pipeline Mode

The current pipeline includes:

  • A BIAWGN channel with a coset decoder
  • A BIAWGN channel with a coset decoder + syndrome concatenation overlay
  • A \(O(d^2)\)-Householder-based CVQKD virtual channel with a coset decoder