The universal operation of LDPC codes over scalar fading channels

Abstract — Root and Varaiya proved the existence of a code that can communicate reliably over any linear Gaus-sian channel for which the channel mutual information level exceeds the transmitted rate. This paper provides sev-eral examples of scalar (single-input single-output) fading channels and shows that on these channels the performance of Low-Density Parity-Check (LDPC) codes lies in close proximity to the performance limits identified by Root and Varaiya. Specifically, we consider periodic fading channels and partial-band jamming channels. A special case of periodic fading is the variation of signal-to-noise ratio across orthogonal frequency division modulation subchannels. The robustness of LDPC codes to periodic fading and partial-band jamming across parameterizations of these different channels is demonstrated through the consistency of the required mutual information to provide a specified bit error rate. For the periodic fading case, the Gaussian approximation to density evolution has been adapted such that asymptotic threshold measures can be compared to simulated code performance in various periodic fading scenarios. Index Terms – low-density parity-check code design, orthogonal frequency division modulation, partial-band jamming, robust channel coding, uni-versal codes. I