Joint Error Correction and Fading Channel Estimation Enhancement Leveraging GRAND

We present a novel method for error correction in the presence of fading channel estimation errors (CEE). When such errors are significant, considerable performance losses can be observed if the wireless transceiver is not adapted. Instead of refining the estimate by increasing the pilot sequence length or improving the estimation algorithm, we propose two new approaches based on Guessing Random Additive Noise Decoding (GRAND) decoders. The first method involves testing multiple candidates for the channel estimate located in the complex neighborhood around the original pilot-based estimate. All these candidates are employed in parallel to compute log-likelihood ratios (LLR). These LLRs are used as soft input to Ordered Reliability Bits GRAND (ORBGRAND). Posterior likelihood formulas associated with ORBGRAND are then computed to determine which channel candidate leads to the most probable codeword. The second method is a refined version of the first approach accounting for the presence of residual CEE in the LLR computation. The performance of these two techniques is evaluated for [128,112] 5G NR CA-Polar and CRC codes. For the considered settings, block error rate (BLER) gains of several dBs are observed compared to cases where CEE is ignored.