An Iteratively Decodable Tensor Product Code with Application to Data Storage

The error pattern correcting code (EPCC) can be constructed to provide a syndrome decoding table targeting the dominant error events of an inter-symbol interference channel at the output of the Viterbi detector. For the size of the syndrome table to be manageable and the list of possible error events to be reasonable in size, the codeword length of EPCC needs to be short enough. However, the rate of such a short length code will be too low for hard drive applications. To accommodate the required large redundancy, it is possible to record only a highly compressed function of the parity bits of EPCC's tensor product with a symbol correcting code. In this paper, we show that the proposed tensor error-pattern correcting code (T-EPCC) is linear time encodable and also devise a low-complexity soft iterative decoding algorithm for EPCC's tensor product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a 1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor Product Code with Application to Data Storage

New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes

This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate structured codes with constant column weights 3 and higher. The proposed codes are efficiently encodable and exhibit good structural properties. Experimental results on decoding performance with the sum-product algorithm show that the novel codes offer substantial practical application potential, for instance, in high-speed applications in magnetic recording and optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications

Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes

In this paper, a simple, general-purpose and effective tool for the design of low-density parity-check (LDPC) codes for iterative correction of bursts of erasures is presented. The design method consists in starting from the parity-check matrix of an LDPC code and developing an optimized parity-check matrix, with the same performance on the memory-less erasure channel, and suitable also for the iterative correction of single bursts of erasures. The parity-check matrix optimization is performed by an algorithm called pivot searching and swapping (PSS) algorithm, which executes permutations of carefully chosen columns of the parity-check matrix, after a local analysis of particular variable nodes called stopping set pivots. This algorithm can be in principle applied to any LDPC code. If the input parity-check matrix is designed for achieving good performance on the memory-less erasure channel, then the code obtained after the application of the PSS algorithm provides good joint correction of independent erasures and single erasure bursts. Numerical results are provided in order to show the effectiveness of the PSS algorithm when applied to different categories of LDPC codes.Comment: 15 pages, 4 figures. IEEE Trans. on Communications, accepted (submitted in Feb. 2007