TY - JOUR
T1 - Asymptotic enumeration methods for analyzing LDPC codes
AU - Burshtein, David
AU - Miller, Gadi
N1 - Funding Information:
Manuscript received April 22, 2002; revised January 25, 2004. This work was supported by the Israel Science Foundation under Grant 22/01-1. The material in this paper was presented at the 40th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, October 2002. The authors are with the School of Electrical Engineering, Tel-Aviv University, Ramat-Aviv 69978, Tel-Aviv, Israel (e-mail: [email protected]; [email protected]). Communicated by R. Koetter, Associate Editor for Coding Theory. Digital Object Identifier 10.1109/TIT.2004.828064
PY - 2004/6
Y1 - 2004/6
N2 - We show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low-density parity-check (LDPC) codes. In particular, we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular LDPC code ensembles. We then consider the binary erasure channel (BEC). Using these estimates we derive lower bounds on the error exponent, under iterative decoding, of LDPC codes used over the BEC. Both regular and irregular code structures are considered. These bounds are compared to the corresponding bounds when optimal (maximum-likelihood (ML)) decoding is applied.
AB - We show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low-density parity-check (LDPC) codes. In particular, we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular LDPC code ensembles. We then consider the binary erasure channel (BEC). Using these estimates we derive lower bounds on the error exponent, under iterative decoding, of LDPC codes used over the BEC. Both regular and irregular code structures are considered. These bounds are compared to the corresponding bounds when optimal (maximum-likelihood (ML)) decoding is applied.
KW - Binary erasure channel (BEC)
KW - Code ensembles
KW - Code spectrum
KW - Iterative decoding
KW - Low-density parity-check (LDPC) codes
UR - http://www.scopus.com/inward/record.url?scp=2942679339&partnerID=8YFLogxK
U2 - 10.1109/TIT.2004.828064
DO - 10.1109/TIT.2004.828064
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AN - SCOPUS:2942679339
SN - 0018-9448
VL - 50
SP - 1115
EP - 1131
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
ER -