Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor. © 2004 Elsevier B.V.

Performance of low density parity check codes as a function of actual and assumed noise levels

We investigate how sensitive Gallager's codes are, when decoded by the sum-product algorithm, to the assumed noise level. We have found a remarkably simple function that fits the empirical results as a function of the actual noise level at both high and low noise levels. © 2004 Elsevier B.V.

Performance of low density parity check codes as a function of actual and assumed noise levels

We investigate how sensitive Gallager's codes are, when decoded by the sum-product algorithm, to the assumed noise level. We have found a remarkably simple function that fits the empirical results as a function of the actual noise level at both high and low noise levels. ©2003 Published by Elsevier Science B. V.

Weaknesses of margulis and ramanujan-margulis low-density parity-check codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor. ©2003 Published by Elsevier Science B. V.

Permeability and stiffness of sands at very low effective stresses

Loose saturated sandy soils may undergo liquefaction under cyclic loading, generating positive excess pore pressures due to their contractile nature and inability to dissipate pore pressures rapidly during earthquake loading. These liquefied soils have a near-zero effective stress state, and hence have very low strength and stiffness, causing severe damage to structures founded upon them. The duration for which this near-zero effective stress state persists is a function of the rate of reconsolidation of the liquefied soil, which in turn is a function of the permeability and stiffness of the soil at this very low effective stress. Existing literature based on observation of physical model tests suggests that the consolidation coefficient C v associated with this reconsolidation of liquefied sand is significantly lower than that of the same soil at moderate stress levels. In this paper, the results of a series of novel fluidisation tests in which permeability k and coefficient of consolidation C v were independently measured will be presented. These results allow calculation of the variation of stiffness E 0 and permeability k with effective stress. It is shown that while permeability increases markedly at very low effective stresses, the simultaneous drop in stiffness measured results in a decrease in consolidation coefficient and hence an increase in the duration for which the soil remains liquefied.