Paper accepted @ ISIT 2016
The paper “’Weight Distribution of the Syndrome of Linear Codes and Connections to Combinatorial Designs” by Christoph Pacher (AIT), Philipp Grabenweger (AIT) and Dimitris Simos (SBA Research) has been accepted for publication in the 2016 IEEE International Symposium on Information Theory (ISIT) which takes place from July, 10th-15th, 2016 in Barcelona, Spain. ISIT is one of the main venues for Information Theory.
Abstract: The expectation and the variance of the syndrome weight distribution of linear codes after transmission of codewords through a binary symmetric channel is derived exactly in closed form as functions of the code’s parity-check matrix and of the degree distributions of the associated Tanner graph. The influence of (check) regularity of the Tanner graph is studied. Special attention is payed to Tanner graphs that have no cycles of length four. We further study the equivalence of some classes of combinatorial designs and important classes of LDPC codes and apply our general results to those more specific structures. Simulations are performed to show the validity of the theoretical approach.