Short LDPC Codes with Low Undetected Frame Error Rate: Post-Decoding Error Detection Criteria

Kurzfassung

Low-density parity-check (LDPC) codes have become a standard in modern communication systems thanks to their near-optimal error correction performance, which approaches Shannon's channel capacity as block length increases. However, in scenarios requiring short block lengths with low undetected frame error rate (UFER)-such as command and control data transmission in satellite communications-using only iterative decoders fails to achieve a balance between undetected and total frame error rates (FERs). This thesis addresses these challenges by investigating post-decoding error detection methods that enhance iterative LDPC decoding to achieve target FERs for both total and undetected errors. Specifically, we work with (128, 64) LDPC codes and explore two novel post-decoding techniques: bounded angle iterative decoding and single bit flip (SBF) list decoding, a variation of SBF decoding. These methods are applied to the iterative LDPC decoder output to manage the trade-off between total and undetected FERs effectively. Our results demonstrate that bounded angle iterative decoding effectively reduces UFER in codes with a large minimum distance with maintaining an acceptable increase in total frame error rate (TFER). Meanwhile, SBF list decoding mitigates the UFER increase introduced by standard SBF decoding, while retaining the significant TFER improvement that SBF decoding offers.