Coding for Relay and Wiretap Channels

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December 2022

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Abstract

For the three-node relay channel, this dissertation investigates the performance of discrete (coded) modulation in the full-duplex compress-forward (CF) relay channel using multilevel coding (MLC). Low-density parity check (LDPC) codes are used as the component binary codes to provide error protection, and the rates assigned to them are numerically analyzed. For compression at the relay, two methods are utilized: scalar quantization that has the advantage of simplicity, and trellis coded quantization (TCQ) to capture shaping gain. Part of the contributions of this dissertation is the design of TCQ for end-to-end relay performance, rather than distortion minimization. A 1 dB gain over prior results for phase shift keying (PSK) modulation is obtained. For short-block length relayed communication, this dissertation designs multilevel polar- coded modulation for the amplify-forward, decode-forward, and compress-forward protocols, in half-duplex and full-duplex modes. At block length 128 and 256, the presented results are the first of their kind. At block length 512, improvements of around 2.5dB were obtained over the state of the art. The design of polar-adjusted convolutional coded modulation is also presented, in some regimes providing improvements over polar-coded modulation. Dispersion bounds and error exponent analysis explains and puts in perspective the simulated performance of the designed coded modulation. For the wiretap channel, practical design of secrecy codes needs empirical evaluation through simulations, which has been performed mainly through bit-error rate (BER) simulations. However, this approach has deficiencies: high BER does not always guarantee zero leakage, does not give visibility into local weaknesses in the code, and has sensitivity issues due to the low slope of BER at high error rates. This dissertation proposes a secrecy simulation metric based on log-likelihood ratios (LLR) and justifies its underlying foundations via its relationship with equivocation. To give visibility to any local weaknesses, a local version of this metric is developed, and a principled method is provided for combining local values of LLR into a single number. For reporting the secrecy performance, the need for specifying the residual leakage and the confidence level of the simulation is highlighted. A corresponding confidence interval analysis is provided that is assisted by a density evolution analysis of the LLR metric. This approach also provides guidance on the number of Monte Carlo samples needed in simulations, thus helps in the design of secrecy simulations. LDPC and polar codes for the wiretap channel are simulated and analyzed according to the proposed secrecy metric. To improve secrecy performance, a serially concatenated coding scheme is proposed.

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Engineering, Electronics and Electrical

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