TY - GEN
T1 - Upper bounding the performance of arbitrary finite LDPC codes on binary erasure channels
AU - Wang, Chih Chun
AU - Kulkarni, Sanjeev R.
AU - Vincent Poor, H.
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - 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) ≈ 1.67 × 1025 trials if a brute force approach is taken. These experiments indicate that this upper bound can be used both as an analytical tool and as a deterministic worst-performance (error floor) guarantee, the latter of which is crucial to optimizing LDPC codes for extremely low BER applications, e.g., optical/satellite communications.
AB - 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) ≈ 1.67 × 1025 trials if a brute force approach is taken. These experiments indicate that this upper bound can be used both as an analytical tool and as a deterministic worst-performance (error floor) guarantee, the latter of which is crucial to optimizing LDPC codes for extremely low BER applications, e.g., optical/satellite communications.
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U2 - 10.1109/ISIT.2006.261701
DO - 10.1109/ISIT.2006.261701
M3 - Conference contribution
AN - SCOPUS:39049117017
SN - 1424405041
SN - 9781424405046
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 411
EP - 415
BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Y2 - 9 July 2006 through 14 July 2006
ER -