Order Statistics Based List Decoding Techniques for Linear Binary Block Codes

The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics decoding is generalized by assuming segmentation of the most reliable independent positions of the received bits. The segmentation is shown to overcome several drawbacks of the original order statistics decoding. The complexity of the order statistics based decoding is further reduced by assuming a partial ordering of the received bits in order to avoid the complex Gauss elimination. The probability of the test error patterns in the decoding list is derived. The bit error rate performance and the decoding complexity trade-off of the proposed decoding algorithms is studied by computer simulations. Numerical examples show that, in some cases, the proposed decoding schemes are superior to the original order statistics decoding in terms of both the bit error rate performance as well as the decoding complexity.Comment: 17 pages, 2 tables, 6 figures, submitted to IEEE Transactions on Information Theor

Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on Information Theor

Distributed Turbo Product Coding Techniques Over Cooperative Communication Systems

In this dissertation, we propose a coded cooperative communications framework based on Distributed Turbo Product Code (DTPC). The system uses linear block Extended Bose-Chaudhuri-Hochquenghem (EBCH) codes as component codes. The source broadcasts the EBCH coded frames to the destination and nearby relays. Each relay constructs a product code by arranging the corrected bit sequences in rows and re-encoding them vertically using EBCH as component codes to obtain an Incremental Redundancy (IR) for source\u27s data. Under this frame, we have investigated a number of interesting and important issues. First, to obtain, independent vertical parities from each relay in the same code space, we propose circular interleaving of the decoded EBCH rows before reencoding vertically. We propose and derive a novel soft information relay for the DTPC over cooperative network based on EBCH component codes. The relay generates Log-Likelihood Ratio (LLR) values for the decoded rows are used to construct a product code by re-encoding the matrix along the columns using a novel soft block encoding technique to obtain soft parity bits with different reliabilities that can be used as soft IR for source\u27s data which is forwarded to the destination. To minimize the overall decoding errors, we propose a power allocation method for the distributed encoded system when the channel attenuations for the direct and relay channels are known. We compare the performance of our proposed power allocation method with the fixed power assignments for DTPC system. We also develop a power optimization algorithm to check the validity of our proposed power allocation algorithm. Results for the power allocation and the power optimization prove on the potency of our proposed power allocation criterion and show the maximum possible attainable performance from the DTPC cooperative system. Finally, we propose new joint distributed Space-Time Block Code (STBC)-DTPC by generating the vertical parity on the relay and transmitting it to the destination using STBC on the source and relay. We tested our proposed system in a fast fading environment on the three channels connecting the three nodes in the cooperative network

Adaptive Methods for Linear Programming Decoding

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we make a first step in studying this method, and show that it can significantly reduce the complexity of the problem, which was originally exponential in the maximum check-node degree. We further show that adaptively adding new constraints, e.g. by combining parity checks, can provide large gains in the performance.Comment: 22 pages, 8 figures. Submitted to IEEE Transactions on Information Theor