We consider communication over binary memoryless symmetric channels using random elements from irregular low density parity check code (LDPC) ensembles, and belief propagation (BP) decoding. Under the assumption that the corresponding Tanner graph includes a non-vanishing fraction of degree 2 variable nodes, we determine the large blocklength behavior of the bit error rate for noise levels belo...

This paper presents a novel approach for constructing structured regular QC-LDPC codes based on a special type of combinatorial designs,known as the balanced incomplete block design (BIBD).The code design approach based on the technology of block cyclic shift and dispertion (BCSD) for correcting erasure-bursts over the binary bursts erasure channel (BBEC). Furthermore, the Tanner graph of the c...

In a digital communication system, information is sent from one place to another over a noisy communication channel using binary symbols (bits). Original information is encoded by adding redundant bits, which are then used by low–density parity–check (LDPC) codes to detect and correct errors that may have been introduced during transmission. Error correction capability of an LDPC code is severe...

The parity-check matrix of a linear code is used to define a bipartite code constraint (Tanner) graph in which bit nodes are connected to parity check nodes. The connectivity properties of this graph are analyzed using both local connectivity and the eigenvalues of the associated adjacency matrix. A simple lower bound on minimum distance of the code is expressed in terms of the two largest eige...

We introduce sequential and parallel decoders for quantum Tanner codes. When the code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain family of asymptotically good low-density parity-check In this case, our provably correct arbitrary errors weight linear in length, respectively or logarithmic time. The same are easily adapted expander lifted...

In this paper, a method to design regular (2, dc)-LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping...

Bipartite graphs of bit nodes and parity check nodes arise as Tanner graphs corresponding to low density parity check codes. Given graph parameters such as the number of check nodes, the maximum check-degree, the bit-degree, and the girth, we consider the problem of constructing bipartite graphs with the largest number of bit nodes, that is, the highest rate. We propose a simple-to-implement he...

OBJECTIVES Little is known about the relation of pubertal development on endothelial function and arterial elasticity in children and adolescents; therefore, we compared brachial artery flow-mediated dilation and carotid artery elasticity across Tanner (pubertal) stages in children and adolescents. STUDY DESIGN Blood pressure, fasting lipids, glucose and insulin, body fat, insulin sensitivity...

CONTEXT Peripubertal obesity is associated with abnormal sex steroid concentrations, but the timing of onset and degree of these abnormalities remain unclear. OBJECTIVE The objective of the study was to assess the degree of hyperandrogenemia across puberty in obese girls and assess overnight sex steroid changes in Tanner stage 1-3 girls. DESIGN This was a cross-sectional analysis. SETTING...

OBJECTIVES We assessed the agreement of body fat and fat-free mass measured by simpler methods against the four-compartment model (4C). METHODS In 60 obese schoolchildren (body mass index ≥95th percentile) between the ages of 8 and 13 y who were recruited from one school in Chile, multicompartmental body composition was estimated with the use of isotopic dilution, plethysmography (BodPod), ra...