GRAND for Rayleigh Fading Channels

Guessing Random Additive Noise Decoding (GRAND) is a code-agnostic decoding technique for short-length and high-rate channel codes. GRAND attempts to guess the channel-induced noise by generating Test Error Patterns (TEPs), and the sequence of TEP generation is the primary distinction between GRAND variants. In this work, we extend the application of GRAND to multipath frequency non-selective Rayleigh fading communication channels, and we refer to this GRAND variant as Fading-GRAND. The proposed Fading-GRAND adapts its TEP generation to the fading conditions of the underlying communication channel, outperforming traditional channel code decoders in scenarios with L spatial diversity branches as well as scenarios with no diversity. Numerical simulation results show that the Fading-GRAND outperforms the traditional Berlekamp-Massey (B-M) decoder for decoding BCH code (127, 106) and BCH code (127, 113) by $0.5\sim 6.5\mathrm{dB}$ at a target FER of $10^{-7}$. Similarly, Fading-GRAND outperforms GRANDAB, the hard-input variation of GRAND, by $0.2\sim 8\mathbf{d B}$ at a target FER of $10^{-7}$ with CRC (128, 104) code and RLC (128,104). Furthermore the average complexity of Fading-GRAND, at $\frac{E_{b}}{N_{0}}$ corresponding to target FER of $10^{-7}$, is $\frac{1}{2}\times\sim\frac{1}{46}\times$ the complexity of GRANDAB.