In this paper we propose a computationally-efficient, iterative decoding algorithm that is well-suited for storage systems with very stringent reliability constraints and low redundancy/high code rate requirements. The proposed Dual-Scaling Min-Sum (DS-MSA) overcomes certain deficiencies of the Min-Sum approximation when used for decoding graph-based codes. We observe that a small but non-negligible fraction of check-to-variable messages is underestimated by the Normalized Min-Sum algorithm in the low error rate region. By carefully adjusting the scaling factor for the variable-to-check message with the smallest magnitude, we develop the DS-MSA algorithm characterized by two scaling parameters. The proposed algorithm (1) outperforms Sum-Product and (Normalized) Min-Sum algorithms in the very low error rate regime, (2) maintains the low-complexity feature of the Min-Sum, and (3) can be easily combined with existing decoder implementations.

This paper addresses an important problem in diffusion weighted MRI tractography -the estimation of the anatomical strength of reconstructed neuronal fibers. Our method incorporates information on the amount of white matter in voxels (small areas of brain) with diffusion data and estimates structural strength of fibers globally, by considering all the fibers and all the voxels simultaneously. We achieve this by using a message-passing optimization procedure, specially tailored for this problem, that operates on a bipartite graph with nodes corresponding to fibers and voxels. New estimates of fiber strength allow derivation of new measures for quantifying anatomical connections between large gray matter regions. In this paper we propose two: Anatomical Connection Weight (ACW) and Normalized Connection Weight (NCW). The proposed methodology was applied on human data and tested for convergence and consistency.

We discuss error floor asympotics and present a method for improving the performance of low-density parity-check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets from the original code. The advantages of the method are that it is universal, as it can be applied to any LDPC code/channel/decoding algorithm and it improves performance at the expense of increasing the code length, without losing the code regularity, without changing the decoding algorithm, and, under certain conditions, without lowering the code rate. The proposed method can be modified to construct convolutional LDPC codes also. The method is illustrated by modifying Tanner, MacKay and Margulis codes to improve performance on the binary symmetric channel (BSC) under the Gallager B decoding algorithm. Decoding results on AWGN channel are also presented to illustrate that optimizing codes for one channel/decoding algorithm can lead to performance improvement on other channels.

In this work we use a new approach to model error events in long-haul optical fiber transmission systems. Existing approaches for obtaining probability density functions (PDFs) rely on numerical simulations or analytical approximations. Numerical simulations make far tails of the PDFs difficult to obtain, while analytical approximations are often inaccurate, as they neglect nonlinear interaction between pulses and noise. Our approach combines the instanton method from statistical mechanics, to model far tails of the PDFs, with numerical simulations to refine the middle part of the PDFs. We combine the two methods by using an orthogonal polynomial expansion constructed specifically for this problem. We demonstrate the approach on an example of a specific submarine transmission system.

We present a method for lowering the error floor of low-density parity check (LDPC) codes. It is based on Tanner graph covers that do not have trapping sets from the original code. The advantages of the method are that it is universal, as it can be applied to any LDPC code/channel model/decoding algorithm and it improves performance at the expense of increasing the code length, without losing the code regularity, without changing the decoding algorithm, and, under certain conditions, without lowering the code rate. We illustrate the method by modifying Tanner, MacKay and Margulis codes to improve performance on the binary symmetric channel (BSC) under the Gallager B decoding algorithm.

In this paper, we analyze storage circuits constructed from unreliable memory components. We propose a memory construction, using low-density parity-check codes, based on a construction originally made by Taylor. The storage circuit consists of unreliable memory cells along with a correcting circuit. The correcting circuit is also constructed from unreliable logic gates along with a small number of perfect gates. The modified construction enables the memory device to perform better than the original construction. We present numerical results supporting our claims.

An iterative soft decoding scheme suitable for highspeed long-haul optical transmission is proposed. The approach is based on a combination of the method of optimal fluctuations (instantons) and a modification of a method, originally proposed in the context of magnetic media, which incorporates the BCJR algorithm and Low-Density Parity-Check (LDPC) codes. The proposed scheme can achieve target bit error rates at longer distances than conventional error correcting approaches.

In this paper we propose an analytical method to evaluate the performance of one step majority logic decoders constructed from faulty gates. We analyze the decoder under the assumption that the gates fail independently. We calculate the average bit error probability of such a decoder and apply the method to the special case of projective geometry codes. The method, however, applies to any regular low-density parity-check code of girth at least six but the calculations are much simpler for the projective geometry codes. We present results for the bit error rate performance of four codes from projective planes

A method for estimation of achievable information rates of high-speed optical transmission systems is proposed. This method consists of two steps: (i) approximating probability density functions for energy of pulses, which is done by instanton approach; (ii) estimating achievable information rates by a modification of a method originally proposed by Arnold and Pfitser. Numerical results for a specific optical transmission system (submarine system at transmission rate 40Gb/s) are reported.

This letter introduces a combinatorial construction of girth-eight high-rate low-density parity-check codes based on integer lattices. The parity-check matrix of a code is defined as a point-line incidence matrix of a 1-configuration based on a rectangular integer lattice, and the girth-eight property is achieved by a judicious selection of sets of parallel lines included in a configuration. A class of codes with a wide range of lengths and column weights is obtained. The resulting matrix of parity checks is an array of circulant matrices.