Upper Bounding the Performance of Arbitrary Finite LDPC Codes on Binary Erasure Channels

Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be evaluated for all operating erasure probabilities, including both the waterfall and the error floor regions. This upper bound can also be viewed as a narrowing search of stopping sets, which is an approach different from the stopping set enumeration used for lower bounding the error floor. When combined with optimal leaf-finding modules, this upper bound is guaranteed to be tight in terms of the asymptotic order. The Boolean framework proposed herein further admits a composite search for even tighter results. For comparison, a refinement of the algorithm is capable of exhausting all stopping sets of size 13 for irregular LDPC codes of length n 500, which requires `500 13

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Chih-Chun Wang, Sanjeev R. Kulkarni, H. Vincent Poor
• Keywords: Binary Erasure Channels, CORR 2006, Education, Error Floor, Upper Bound