TY - GEN

T1 - Lower bounds on the spectrum and error rate of LDPC code ensembles

AU - Barak, Ohad

AU - Burshtein, David

PY - 2005

Y1 - 2005

N2 - We consider the ensemble of regular LDPC codes and obtain an expression for the second moment of the distance spectrum. We show how this expression can be used to derive a lower bound on the probability that the growth rate of a randomly chosen code from the ensemble is equal to the growth rate of the average distance spectrum, when the block length is sufficiently large. In particular, when the connectivity of the code is sufficiently large, the distance spectrum of a code in the ensemble is concentrated. We then derive a lower bound on the probability (confidence level) that the minimum distance and error rate, respectively, of a randomly chosen code from the ensemble are upper and lower bounded by some values (which depend on the confidence level).

AB - We consider the ensemble of regular LDPC codes and obtain an expression for the second moment of the distance spectrum. We show how this expression can be used to derive a lower bound on the probability that the growth rate of a randomly chosen code from the ensemble is equal to the growth rate of the average distance spectrum, when the block length is sufficiently large. In particular, when the connectivity of the code is sufficiently large, the distance spectrum of a code in the ensemble is concentrated. We then derive a lower bound on the probability (confidence level) that the minimum distance and error rate, respectively, of a randomly chosen code from the ensemble are upper and lower bounded by some values (which depend on the confidence level).

UR - http://www.scopus.com/inward/record.url?scp=33749442802&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2005.1523289

DO - 10.1109/ISIT.2005.1523289

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AN - SCOPUS:33749442802

SN - 0780391519

SN - 9780780391512

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 42

EP - 46

BT - Proceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05

T2 - 2005 IEEE International Symposium on Information Theory, ISIT 05

Y2 - 4 September 2005 through 9 September 2005

ER -