TY - GEN

T1 - Linear-programming decoding of Tanner codes with local-optimality certificates

AU - Halabi, Nissim

AU - Even, Guy

PY - 2012

Y1 - 2012

N2 - Given a channel observation y and a codeword x, we are interested in a one-sided error test that answers the questions: is x optimal with respect to y? is it unique? A positive answer for such a test is called a certificate for the optimality of a codeword. We present new certificates that are based on combinatorial characterization for local-optimality of a codeword in irregular Tanner codes. The certificate is based on weighted normalized trees in computation trees of the Tanner graph. These trees may have any finite height h (even greater than the girth of the Tanner graph). In addition, the degrees of local-code nodes are not restricted to two (i.e., skinny trees). We prove that local-optimality in this new characterization implies ML-optimality and LP-optimality, and show that a certificate can be computed efficiently. We apply the new local-optimality characterization to regular Tanner codes, and prove lower bounds on the noise thresholds of LP-decoding in MBIOS channels. When the noise is below these lower bounds, the probability that LP-decoding fails decays doubly exponentially in the girth of the Tanner graph.

AB - Given a channel observation y and a codeword x, we are interested in a one-sided error test that answers the questions: is x optimal with respect to y? is it unique? A positive answer for such a test is called a certificate for the optimality of a codeword. We present new certificates that are based on combinatorial characterization for local-optimality of a codeword in irregular Tanner codes. The certificate is based on weighted normalized trees in computation trees of the Tanner graph. These trees may have any finite height h (even greater than the girth of the Tanner graph). In addition, the degrees of local-code nodes are not restricted to two (i.e., skinny trees). We prove that local-optimality in this new characterization implies ML-optimality and LP-optimality, and show that a certificate can be computed efficiently. We apply the new local-optimality characterization to regular Tanner codes, and prove lower bounds on the noise thresholds of LP-decoding in MBIOS channels. When the noise is below these lower bounds, the probability that LP-decoding fails decays doubly exponentially in the girth of the Tanner graph.

UR - http://www.scopus.com/inward/record.url?scp=84867500687&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2012.6284007

DO - 10.1109/ISIT.2012.6284007

M3 - פרסום בספר כנס

AN - SCOPUS:84867500687

SN - 9781467325790

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2686

EP - 2690

BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012

Y2 - 1 July 2012 through 6 July 2012

ER -