Erasure model | ||
Our erasure model depends on four parameters, | ||
p _{1} | - | the relative signal corruption of the first half of coordinates, |
p _{2} | - | the relative signal corruption of the second half of coordinates, |
q _{1} | - | the corruption factor of one half of the signals and |
q _{2} | - | the corruption factor of the other half of the signals. |
Based on these parameters, we generate a random erasure mask as follows. First, we choose q∈{q _{1},q _{2}} uniformly at random and determine for every entry the probability of being non-zero as η _{ j }=q p _{1} for j≤d/2 and η _{ j }=q p _{2} for j>d/2. We then generate a mask as a realisation of the independent Bernoulli variables M(j,j)∼B(η _{ j }), that is P(M(j,j)=1)=η _{ j }. | ||
Burst error model | ||
Our burst error model depends on four parameters, | ||
p _{ T } | - | the probability of a burst of length T, |
p _{2T } | - | the probability of a burst of length 2T, |
T | - | the burst length and |
q | - | the probability of the burst starting in the first half of the coordinates. |
Based on these parameters, we generate a burst error mask as follows. First, we choose a burstlength τ∈{0,T,2T} according to the probability distribution prescribed by {p _{0},p _{ T },p _{2T }}, where p _{0}=1−p _{ T }−p _{2T }. We then decide according to the probability q whether the burst start t occurs among the first half of coordinates, t≤d/2, or the second half, t>d/2. Finally, we draw the burst start t uniformly at random from the chosen half of coordinates and in a cyclic fashion set M(j,j)=0 whenever t≤j<t+τ or j<t+τ−d and M(j,j)=1 else. |