Coded Trace Reconstruction

Trace Reconstruction Revisited

The trace reconstruction problem is to reconstruct a string x of length n given m random subsequences where each subsequence is generated by deleting each character of x independently with probability p. Two natural questions are a) how large must m be as a function of n and p such that reconstruction is possible with high probability and b) how can this reconstruction be performed efficiently....

Real-time Trace Reconstruction (RTR)

Developers are using real-time analysis tools in the development stage, to debug real-time events either not observable during “run-stop” debug sessions, or limited by the requirements of the application; such as inherently not freezable systems like engine control or pace makers. Furthermore, engineers are using real-time analysis tools in their final development stage to do performance tuning...

Dynamic Reconstruction for Coded Aperture Imaging

trace reconstruction by parabolic radon transform

due to some difficulties during seismic data acquisition, like natural obstacles (high voltage electricity cable, bad coupling of geophones with the ground) some of the traces cannot be recorded. since bad traces make the final stack unclear, usually bad traces go mute while processing. the final image of the earth’s crust is highly dependent of the quality and resolution of acquired data and m...

Trace reconstruction with varying deletion probabilities

In the trace reconstruction problem an unknown string x = (x0, . . . , xn−1) ∈ {0, 1, ...,m − 1} is observed through the deletion channel, which deletes each xk with a certain probability, yielding a contracted string X̃. Earlier works have proved that if each xk is deleted with the same probability q ∈ [0, 1), then exp(O(n)) independent copies of the contracted string X̃ suffice to reconstruct x...