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Achieving Optimal Short-Blocklength Secrecy Rate Using Multi-Kernel PAC Codes for the Binary Erasure Wiretap Channel

Hsuan-Yin Lin, Yi-Sheng Su, Mao-Ching Chiu

TL;DR

It is shown that under the average total variation distance secrecy metric, multi-kernel polarization-adjusted convolutional codes can achieve the best possible theoretical secrecy rate at blocklengths of 16, 32, 64, and 128 if the secrecy leakage is less than or equal to certain values.

Abstract

We investigate practical short-blocklength coding for the semi-deterministic binary erasure wiretap channel (BE-WTC), where the main channel to the legitimate receiver is noiseless, and the eavesdropper's channel is a binary erasure channel (BEC). It is shown that under the average total variation distance secrecy metric, multi-kernel polarization-adjusted convolutional (MK-PAC) codes can achieve the best possible theoretical secrecy rate at blocklengths of 16, 32, 64, and 128 if the secrecy leakage is less than or equal to certain values.

Achieving Optimal Short-Blocklength Secrecy Rate Using Multi-Kernel PAC Codes for the Binary Erasure Wiretap Channel

TL;DR

It is shown that under the average total variation distance secrecy metric, multi-kernel polarization-adjusted convolutional codes can achieve the best possible theoretical secrecy rate at blocklengths of 16, 32, 64, and 128 if the secrecy leakage is less than or equal to certain values.

Abstract

We investigate practical short-blocklength coding for the semi-deterministic binary erasure wiretap channel (BE-WTC), where the main channel to the legitimate receiver is noiseless, and the eavesdropper's channel is a binary erasure channel (BEC). It is shown that under the average total variation distance secrecy metric, multi-kernel polarization-adjusted convolutional (MK-PAC) codes can achieve the best possible theoretical secrecy rate at blocklengths of 16, 32, 64, and 128 if the secrecy leakage is less than or equal to certain values.
Paper Structure (13 sections, 2 theorems, 17 equations, 4 figures)

This paper contains 13 sections, 2 theorems, 17 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Channel Model
  3. Notation
  4. Wiretap Coding, Polar, Reed--Muller, and PAC Codes
  5. The Semi-Deterministic Binary Erasure WTC (BE-WTC)
  6. Main Results
  7. Non-Asymptotic Fundamental Limits on Secrecy Rate
  8. Wiretap Coding Scheme
  9. Average TVD Secrecy Metric for the BE-WTC
  10. Numerical Results
  11. Average TVD of Bit-Channels for Multi-Kernel PAC Codes
  12. Lower Bounds on the Maximal Secrecy Rate
  13. Conclusion

Key Result

Theorem 1

Consider a semi-deterministic BE-WTC with erasure probability $0\leq p< 1$. There exists a binary $(n,2^k,\delta)$ wiretap code such that where $k\in\mathbb{N}$, and Here, $B(n,p)$ is the binomial RV with parameters $n$ and $p$. Conversely, every binary $(n,\textnormal{ M},\delta)$ wiretap code must satisfy

Figures (4)

  • Figure 1: A semi-deterministic binary erasure WTC (BE-WTC).
  • Figure 2: The average TVD of each bit-channel for BE-WTC with $p=0.4$ and $n=128$.
  • Figure 3: Code performance on semi-deterministic BE-WTC with $p=0.4$ and $\delta=0.001$.
  • Figure 4: Code performance on semi-deterministic BE-WTC with $p=0.4$ and $\delta=0.01$.

Theorems & Definitions (4)

  • Definition 1: Wiretap Codes BlochBarros11_1YangSchaeferPoor19_1
  • Definition 2: Maximal Secrecy Rate
  • Theorem 1
  • Theorem 2