Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithms are special cases of two generic algorithms, the min-sum and sum-product algorithms, which also...

In the context of channel coding, the Generalized Belief Propagation (GBP) is an iterative algorithm used to recover the transmission bits sent through a noisy channel. To ensure a reliable transmission, we apply a map on the bits, that is called a code. This code induces artificial correlations between the bits to send, and it can be modeled by a graph whose nodes are the bits and the edges ar...

Tanner codes represent a broad class of graph-based coding schemes, including low-density parity-check (LDPC) and turbo codes. Whereas many different classes of LDPC and turbo codes have been proposed and studied in the past decade, very little work has been performed on the broader class of Tanner codes. In this paper we propose a design technique which leads to efficiently encodable quasi-cyc...

We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph wit...

We propose a joint network-channel coding scheme for the multiple-access relay channel. In this scenario, two users use a common relay which performs network coding. We show how a distributed Low-Density Parity-Check (LDPC) code can be applied as a joint network-channel code. The network-channel code is described by one single regular Tanner graph and is decoded with the iterative messagepassin...

One of the most important open problems in the communication society is to determine the performance of iterative message passing algorithms over loopy graphs. Some recent work addresses this problem for loopy Tanner graphs by introducing the concepts of stopping distance and stopping redundancy. By analyzing the eigenvalues and eigenvectors of the normalized incidence matrix representing a Tan...

Amber M. Makowicz,a Jessie C. Tanner,a,b Eric Dumas,a Cameron D. Siler,a,c and Ingo Schluppa aDepartment of Biology, University of Oklahoma, 730 Van Vleet Oval, Norman, OK 73019, USA, bCollege of Biological Sciences, University of Minnesota, 123 Snyder Hall, 1475 Gortner Ave, Saint Paul, MN 55108, USA and cSam Noble Oklahoma Museum of Natural History, University of Oklahoma, 2401 Chautauqua, No...

Abstract: Two different ways of obtaining generalized low-density parity-check codes are considered. Lower bounds on the minimum distance, stopping distance, and pseudodistance are derived for these codes using graph based analysis. These bounds are generalizations of Tanner’s bit-oriented and parity-oriented bound for simple LDPC codes. The new bounds are useful in predicting the performance o...

Abstract. We study a class of quasi-cyclic LDPC codes. We provide both a Gröbner basis approach, which leads to precise conditions on the code dimension, and a graph theoretic prospective, that lets us guarantee high girth in their Tanner graph. Experimentally, the codes we propose perform no worse than random LDPC codes with their same parameters, which is a significant achievement for algebra...

D. A. Wardle ([email protected]) and P. Kardol, Dept of Forest Ecology and Management, Swedish Univ. of Agricultural Sciences, SE901 83 Umeå, Sweden. – P. J. Bellingham, Landcare Research, PO Box 69040, Lincoln 7640, New Zealand. – R. Giesler, Climate Impacts Research Centre, Dept of Ecology and Environmental Sciences, Umeå Univ., Abisko, Sweden. – E. V. J. Tanner, Dept of Plant Sciences, Uni...