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Usage of polar codes for fixed and random length error bursts correction
Error correction during data storage, processing, and transmission allows for ensuring data integrity. Channel coding
techniques are used to counteract these errors. Noise in real systems is often correlated, whereas traditional coding
and decoding approaches are based on decorrelation which in turn reduces the performance limits of channel coding.
Polar codes, adopted as a coding scheme in the modern fifth-generation communication standard, demonstrate low
error probabilities during decoding in memoryless channels. The current task is to investigate the suitability of polar
codes for channels with memory, analyze their burst error-correcting capabilities, and compare them with known error-
correcting coding methods. To evaluate burst error-correcting capability, the method of calculating the ranks of each
submatrix of the parity-check matrix of a fixed-size polar code is used. The burst error-correcting capability of polar
codes can be improved through a proposed interleaving procedure. The analysis of the burst error-correcting capability is carried out for short-length polar codes. An analysis of the burst error-correcting capability of polar codes has been performed. A comparison of burst error-correcting capabilities of polar codes with codes defined by random generator matrix, Gilbert codes and low-density parity-check codes was conducted. An analysis of the decoding error probability shows that standard polar code decoding algorithms do not achieve low error probabilities. The same decoding error probability 0.01 as for Gilbert channel is achieved by polar code in binary symmetric channel with an unconditional error probability two times as high. From the analysis, it can be concluded that the burst error-correcting capability of standard polar codes is low. The proposed interleaving approach improves the burst error-correcting capability and allows achieving values close to the Reiger bound. Further research directions may include developing decoding algorithms for polar codes adapted for channels with variable packet lengths