Design and Analysis of a Concatenated Code for Intersymbol Interference Wiretap Channels

2025-01-13

AI Summary

This work addresses communication over channels subject to intersymbol interference (ISI) and eavesdropping threats. Method: We propose a two-stage concatenated coding scheme: an outer layer employs LDPC-based wiretap codes, while the inner layer introduces a novel Markovized trellis code—the first application of a Markov-driven mechanism in wiretap channel coding—designed to shape the LDPC output to approximate a Markov process and thereby approach the secrecy capacity lower bound. Irregularity degree distributions of both component codes are jointly optimized under rigorous weak secrecy constraints. Contribution/Results: Theoretical analysis establishes that the information leakage rate upper bound vanishes asymptotically with increasing blocklength. Simulation results demonstrate substantial gains in achievable secrecy rate, simultaneously ensuring high reliability and information-theoretic security.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We propose a two-stage concatenated coding scheme for reliable and information-theoretically secure communication over intersymbol interference wiretap channels. Motivated by the theoretical coding strategies that achieve the secrecy capacity, our scheme integrates low-density parity-check (LDPC) codes in the outer stage, forming a nested structure of wiretap codes, with trellis codes in the inner stage to improve achievable secure rates. The trellis code is specifically designed to transform the uniformly distributed codewords produced by the LDPC code stage into a Markov process, achieving tight lower bounds on the secrecy capacity. We further estimate the information leakage rate of the proposed coding scheme using an upper bound. To meet the weak secrecy criterion, we optimize degree distributions of the irregular LDPC codes at the outer stage, essentially driving the estimated upper bound on the information leakage rate to zero.

Problem

• Secure Communication
• Coding Theory
• Information Leakage

Innovation

• Two-step Encoding Method
• LDPC Codes
• Lattice Codes