CRC error correction for energy-constrained transmission

In this paper, we investigate the application of iterative decoding algorithms to error correction of cyclic redundancy check (CRC) codes widely used in low-energy communication standards. We consider the case when traditional error correction codes are not available due to energy constraints at the transmitter. Using the CRC-24 code adopted by the Bluetooth Low Energy standard as an example, we show how two iterative techniques traditionally used for decoding of low-density parity check codes - Belief Propagation (BP) and the Alternating Direction Method of Multipliers (ADMM) - can be applied to the high-density parity check matrix of the code. The performance of both techniques is evaluated through simulation, and it is demonstrated that a gain of up to 1.7 dB in terms of the SNR per bit and a total reduction of the packet error rate by more than 70% can be achieved compared with the non-correction scenario, at no extra cost for the transmitter. We also compare the two techniques and use the standard syndrome look-up method as a benchmark. Both schemes enable the correction of multiple errors, with the ADMM-based decoder demonstrating better overall performance than BP.