Algebraic superposition of LDGM codes for cooperative diversity

Abstract-This paper presents a technique for achieving cooperative spatial diversity using serially concatenated low density generator matrix (LDGM) codes. Specifically, we consider a scenario in which a pair of transceivers employ algebraic superposition of error control codes to effect spatial diversity at their common destination. The construction of LDGM codes from a sparse generator matrix makes them a natural fit for such a cooperative diversity scheme. The simple decoder structure for graph based codes reduces the complexity at the destination compared with previously-proposed schemes using algebraic superposition of convolutional codes and turbo-like decoding. The result is a system with low encoding and decoding complexity and improved error performance

Low Density Graph Codes And Novel Optimization Strategies For Information Transfer Over Impaired Medium

Effective methods for information transfer over an imperfect medium are of great interest. This thesis addresses the following four topics involving low density graph codes and novel optimization strategies.Firstly, we study the performance of a promising coding technique: low density generator matrix (LDGM) codes. LDGM codes provide satisfying performance while maintaining low encoding and decoding complexities. In the thesis, the performance of LDGM codes is extracted for both majority-rule-based and sum-product iterative decoding algorithms. The ultimate performance of the coding scheme is revealed through distance spectrum analysis. We derive the distance spectral for both LDGM codes and concatenated LDGM codes. The results show that serial-concatenated LDGM codes deliver extremely low error-floors. This work provides valued information for selecting the parameters of LDGM codes. Secondly, we investigate network-coding on relay-assisted wireless multiple access (WMA) networks. Network-coding is an effective way to increase robustness and traffic capacity of networks. Following the framework of network-coding, we introduce new network codes for the WMA networks. The codes are constructed based on sparse graphs, and can explore the diversities available from both the time and space domains. The data integrity from relays could be compromised when the relays are deployed in open areas. For this, we propose a simple but robust security mechanism to verify the data integrity.Thirdly, we study the problem of bandwidth allocation for the transmission of multiple sources of data over a single communication medium. We aim to maximize the overall user satisfaction, and formulate an optimization problem. Using either the logarithmic or exponential form of satisfaction function, we derive closed-form optimal solutions, and show that the optimal bandwidth allocation for each type of data is piecewise linear with respect to the total available bandwidth. Fourthly, we consider the optimization strategy on recovery of target spectrum for filter-array-based spectrometers. We model the spectrophotometric system as a communication system, in which the information content of the target spectrum is passed through distortive filters. By exploiting non-negative nature of spectral content, a non-negative least-square optimal criterion is found particularly effective. The concept is verified in a hardware implemen

A Unified Ensemble of Concatenated Convolutional Codes

We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes. We show that for each of the original classes of TCs, it is possible to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. We also derive the density evolution (DE) equations for this ensemble over the binary erasure channel. The thresholds obtained from the DE indicate that the TC ensembles from the unified ensemble have similar asymptotic behavior to the original TC ensembles

Graph Concatenation for Quantum Codes

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complementation." Our method applies to both binary and non-binary concatenated quantum codes as well as their generalizations.Comment: 26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]] are added. Submitted to JM