Robust Turbo Analog Error Correcting Codes Based on Analog CRC Verification

In this paper, a new analog error correcting code with an iterative decoder is presented for real-valued signals corrupted by impulsive noises. In the proposed algorithm, a redundancy coding matrix is implemented as an analog version of the cyclic redundancy check (CRC) that is commonly used for data verification in digital communication. On the basis of this analog CRC, we propose an alternate decoding scheme with iterative decoding. In each iteration of the algorithm, the problem of decoding the long block code is decoupled into a set of parallel LP/LASSO subproblems. In the sparse noise model, this leads to a significant reduction in decoding complexity as compared to one-step convex programming decoding. The new code has improved correction capability compared to Zanko et al. In the almost sparse noise model, energy detectors are used to verify the decoding correctness of the inner code before transferring the result to the next iteration. In this case, the Turbo decoder shows little loss compared to the oracle bound based on least squares when the impulsive noises are perfectly known at the receiver.