A Correlation-Breaking Interleaving of Polar Codes

It's known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. However, existing concatenation schemes of polar codes with other error correction codes rarely take this coupling effect into consideration. To achieve a better BER performance, a concatenation scheme, which divides all $N_l$ bits in a LDPC block into $N_l$ polar blocks to completely de-correlate the possible coupled errors, is first proposed. This interleaving is called the blind interleaving (BI) and can keep the simple SC polar decoding while achieving a better BER performance than the state-of-the-art (SOA) concatenation of polar codes with LDPC codes. For better balance of performance and complexity, a novel interleaving scheme, named the correlation-breaking interleaving (CBI), is proposed by breaking the correlation of the errors among the correlated bits of polar codes. This CBI scheme 1) achieves a comparable BER performance as the BI scheme with a smaller memory size and a shorter turnaround time; 2) and enjoys a performance robustness with reduced block lengths. Numerical results have shown that CBI with small block lengths achieves almost the same performance at BER=$10^{-4}$ compared with CBI with block lengths $8$ times larger.