Low-density parity-check codes have recently received much attention because of their excellent performance and the availability of a simple iterative decoder. The decoder, however, requires large amounts of memory, which causes problems with memory consumption. We investigate a new decoding scheme for low density parity check codes to address this problem. The basic idea is to define a reliability measure and a threshold, and stop updating the messages for a bit whenever its reliability is higher than the threshold. We also consider some modifications to this scheme, including a dynamic threshold more suitable for codes with cycles, and a scheme with soft thresholds which allow the possibility of removing a decision which have proved wrong. By exploiting the bits different rates of convergence we are able to achieve an efficiency of up to 50% at a bit error rate of less than 10^-5. The efficiency should roughly correspond to the power consumption of a hardware implementation of the algorithm.

Approved for public release, distribution is unlimited / This thesis discusses VHDL modeling and simulation of a full custom Application Specific Integrated Circuit (ASIC) for a Digital Image Synthesizer (DIS). The DIS synthesizes the characteristic echo signature of a pre-selected target. It is mainly used against Inverse Synthetic Aperture Radars as an electronic counter measure. The VHDL description of the DIS architecture was exported from Tanner S-Edit, modified, and simulated in Aldec Active HDLTM. Simulation results were compared with C++ and Matlab simulation results for verification. Main subcomponents, a single Range Bin Processor (RBP), a cascade of 4 RBP s and a cascade of 16 RBP s were tested and verified. The overhead control circuitry, including Self Test Circuitry and Phase Extractor, was tested separately. Finally overall DIS was tested and verified using the control circuitry and a cascade of 4 RBP s together, representing the actual 512 RBP s. As a result of this research, the majority of the DIS was functionally tested and verified. / First Lieutenant, Turkish Army

Two standard graph representations for linear codes are the Tanner graph and the tailbiting trellis. Such graph representations allow the decoding problem for a code to be phrased as a computational problem on the corresponding graph and yield graph theoretic criteria for good codes. When a Tanner graph for a code is used for communication across a binary erasure channel (BEC) and decoding is performed using the standard iterative decoding algorithm, the maximum number of correctable erasures is determined by the stopping distance of the Tanner graph. Hence the computational problem of determining the stopping distance of a Tanner graph is of interest. In this thesis it is shown that computing stopping distance of a Tanner graph is NP hard. It is also shown that there can be no (1 + є ) approximation algorithm for the problem for any є > 0 unless P = NP and that approximation ratio of 2(log n)1- є for any є > 0 is impossible unless NPCDTIME(npoly(log n)). One way to construct Tanner graphs of large stopping distance is to ensure that the graph has large girth. It is known that stopping distance increases exponentially with the girth of the Tanner graph. A new elementary combinatorial construction algorithm for an almost regular LDPC code family with provable Ώ(log n) girth and O(n2) construction complexity is presented. The bound on the girth is close within a factor of two to the best known upper bound on girth. The problem of linear time exact maximum likelihood decoding of tailbiting trellis has remained open for several years. An O(n) complexity approximate maximum likelihood decoding algorithm for tail-biting trellises is presented and analyzed. Experiments indicate that the algorithm performs close to the ideal maximum likelihood decoder.

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The aim of this essay is to examine the significance of the concept of sanctification in biblical theological reflection on economics through a comparative textual study. The theologians analyzed are Albino Barrera, Wayne Grudem, and Kathryn Tanner. In what way are their biblical and systematic theologies of economics related to their understanding of the concept of sanctification? What is the relationship between sanctification and the Bible’s words on economics? In a broader perspective, the essay aims to reflect on how the concept of sanctification can be viewed and enunciated in the light of a capitalist economic system. The theologians used in the essay all have their origins in disparate theological discourses, Christian communities, and academic disciplines. Barrera is a biblical scholar, economist and a priest in the Catholic Church. In Biblical Economic Ethics, Barrera writes an economic theology with an emphasis on social justice. Grudem is a Calvinist Baptist biblical scholar and systematic theologian, active in conservative evangelical theological discourse. In Politics according to the Bible, Grudem presents his biblical theology on politics and society. Tanner is a systematic theologian in the Episcopal Church, active in the disciplines of feminist and constructive theology. In Christianity and the New Spirit of Capitalism, she critiques the economic paradigm she describes as the new spirit of capitalism. Barrera, Grudem, and Tanner all make different readings of what the Bible has to say about economic life. Grudem actively endorses the economic system of today, while Barrera and Tanner have a more critical voice. Barrera sees sanctification as a gift of divine friendship from God. Grudem views sanctification as what comes after conversion from sin and the blessings granted by God. Tanner means that sanctification takes place through the work of the Spirit and by Jesus’ gift of a life in holiness. Through the essay a connection has been established between a person’s view on sanctification and their biblical theology on economics. Barrera’s, Grudem’s, and Tanner’s biblical theology on economics is closely connected to their understanding of the concept of sanctification. There seems to be a connection between the biblical material that is being analyzed, how it is analyzed, and what is being left out. A central finding in the essay is the connection between the understanding of sanctification as either a gift or a reward.

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In this effort, we consider the performance of a dedicated short range communication (DSRC) system for inter-vehicle communications (IVC). The DSRC standard employs convolutional codes for forward error correction (FEC). The performance of the DSRC system is evaluated in three different channels with convolutional codes, regular low density parity check (LDPC) codes and quasi-cyclic (QC) LDPC codes. In addition, we compare the complexity of these codes. It is shown that LDPC and QC-LDPC codes provide a significant improvement in performance compared to convolutional codes. / Graduate

We investigate into the limitations of the sum-product algorithm for binary low density parity check (LDPC) codes having isolated short cycles. Independence assumption among messages passed, assumed reasonable in all configurations of graphs, fails the most in graphical structures with short cycles. This research work is a step forward towards understanding the effect of short cycles on error floors of the sum-product algorithm. We propose a modified sum-product algorithm by considering the statistical dependency of the messages passed in a cycle of length 4. We also formulate a modified algorithm in the log domain which eliminates the numerical instability and precision issues associated with the probability domain. Simulation results show a signal to noise ratio (SNR) improvement for the modified sum-product algorithm compared to the original algorithm. This suggests that dependency among messages improves the decisions and successfully mitigates the effects of length-4 cycles in the Tanner graph. The improvement is significant at high SNR region, suggesting a possible cause to the error floor effects on such graphs. Using density evolution techniques, we analysed the modified decoding algorithm. The threshold computed for the modified algorithm is higher than the threshold computed for the sum-product algorithm, validating the observed simulation results. We also prove that the conditional entropy of a codeword given the estimate obtained using the modified algorithm is lower compared to using the original sum-product algorithm.