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 The performance curve of Low Density Parity Check (LDPC) code consists of water fall region and error floor region. The error floor region performance is difficult to obtained because the Frame Error Rate (FER) is very low. The traditional methods of predicting the error performance are not useful due to the iterative decoding. T.J. Richardson proposed a method to estimate the error floor region using trapping sets. We extend the Richardson's method of error floor prediction to obtain bounds on the FER of LDPC coded bit interleaved coded modulation.
We first find as many trapping sets as possible, and then evaluate the contribution towards the FER of each trapping set. By noticing that different directions and magnitudes of noise to different modulated symbols will give different errors, we classify the modulated symbols into classes according to noise levels. In each class, we select a representative and evaluate the its error probability by importance sampling. To evaluate the overall error performance, we multiple the representative error probability by a factor decided by the number of representatives. We give a good estimation of error probability at high SNR region.
By the insight we gained from the prediction techniques, we design the interleaver to lower the error probability at high SNR for modulated systems. We reduce the frame error rate in 8-PAM, 16-QAM and 8-PSK modulated systems.
 In our work, we consider the problem of transmitting a document to multiple terminals using network coding from multiple sources. Our goal is to minimize the transmission and storage cost.
By establishing the connection between measure theory and information theory, we facilitate the multicast optimization problem with the constraints that guarantee the sources only store a subset of total information set.
We also reformulate the case when network coding is allowed at the sources. By comparing the two cases when network coding is allowed or not allowed at the sources, we give a simpler formulation to compute the upper bound of the cost gap, and then propose a greedy algorithm which can be done in polynomial time. We also specify the case when there are three sources.
 We consider the multiple unicast problem under network coding over directed acyclic networks with unit capacity edges. There is a set of n source-terminal (s_i, t_i) pairs that wish to communicate at unit rate over this network. The connectivity between the s_i-t_i pairs is quantited by means of a connectivity level vector, [k_1 k_2 . . . k_n] such that there exist k_i edge-disjoint paths between si and ti. Our main aim is to characterize the feasibility of achieving this for different values of n and [k_1 . . . k_n]. For 3 unicast connections (n = 3), we characterize several achievable and unachievable values of the connectivity 3- tuple. In addition, in this work, we have found certain network topologies, and capacity characterizations that are useful in understanding the case of general n.