Enumerating and Counting Cycles in Bipartite Graphs (2008)
Thomas R. Halford, Keith M. Chugg
Exactly counting cycles and paths in arbitrary graphs is known to be hard [4]. Alon, Yuster and Zwick presented methods for counting cycles of length less than 8 in [1]; however, their methods are...
Thomas R. Halford, Alex J. Grant, Keith M. Chugg
Abstract — Let C be an [n, k, d] binary linear code with rate R = k/n and dual C ⊥. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pd ⊥ ≤
Spin foam models of Riemannian quantum gravity (2008)
John C. Baez, J. Daniel Christensen, Thomas R. Halford, C. Tsang
Abstract. Using numerical calculations, we compare three versions of the Barrett– Crane model of 4-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described...
Halford, Thomas R., Chugg, Keith M.
Generalized Tanner graphs have been implicitly studied by a number of authors under the rubric of generalized parity-check matrices. This work considers the conditioning of binary hidden variables in...
The Extraction and Complexity Limits of Graphical Models for Linear Codes (2006)
Halford, Thomas R., Chugg, Keith M.
Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive problems. The former class of problems concern the construction of a...
Which codes have 4cycle-free Tanner graphs (2006)
Thomas R. Halford, Alex J. Grant
Abstract — Let C be an [n, k, d] binary linear code with rate R = k/n and dual C ⊥. In this work, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pd ⊥ ≤ $r np(p...
Which codes have 4cycle-free Tanner graphs (2006)
Thomas R. Halford, Keith M. Chugg
Abstract — Let C be an [n, k, d] binary linear code with rate R = k/n and dual C ⊥. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pd ⊥...
Soft-in soft-out decoding of Reed-Solomon codes based on Vardy and Be’ery’s decomposition (2005)
Thomas R. Halford, Vishakan Ponnampalam, Alex J. Grant, Keith M. Chugg
Abstract — This correspondence presents an optimal soft-in soft-out (SISO) decoding algorithm for the binary image of Reed-Solomon codes that is based on Vardy and Be’ery’s optimal soft-in...
Spin Foam Models of Riemannian Quantum Gravity (2002)
Baez, John C., Christensen, J. Daniel, Halford, Thomas R., Tsang, David C.
Using numerical calculations, we compare three versions of the Barrett-Crane model of 4-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri,...
Spin Foam Models Of Riemannian Quantum Gravity (2002)
John C. Baez, J. Daniel Christensen, Thomas R. Halford, David C. Tsang
Using numerical calculations, we compare three versions of the Barrett{ Crane model of 4-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De...
Spin Foam Models Of Riemannian Quantum Gravity
John Baez Daniel, J. Daniel Christensen, Thomas R. Halford, C. Tsang
Using numerical calculations, we compare three versions of the Barrett{ Crane model of 4-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De...