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. |