Simple adaptive progressive edge-growth construction of LDPC codes for close(r)-to-optimal sensing in pulsed ToF

摘要

In pulsed Time-of-Flight (ToF) systems the pulse width establishes a tradeoff between depth resolution and range. Ideally, one would wish to emit a pulse that is as short as allowed by the hardware, while keeping the depth range arbitrarily large, being able to sense more than one return per pixel. This suggests the use of compressive sensing (CS) as sensing paradigm, in order to exploit the sparsity of the light echo, s. Unfortunately, the best CS sensing matrices are dense matrices of random nature, thus expensive to generate and store when the signal dimensionality n (desired range over desired depth resolution) is high. The computational cost of the recovery also becomes prohibitive for large n. Additionally, dense matrices lead to measurements with poor SNR if the ratio s/n is too low or, conversely, require prohibitive amplitudes of the nonzero components. Deterministically-generated low-density parity-check (LDPC) sensing matrices can leverage these problems, but perform worse than random matrices if the density is too low compared to the sparsity. In this paper we present a simple method for deterministic construction of LDPC sensing matrices that builds upon progressive edge-growth (PEG) methods and integrates adaptiveness, that is, each new LDPC code is generated using information on the sparse signal captured by the previously-generated codes. Sensing matrices constructed via our adaptive PEG (APEG) algorithm exhibit superior sparse recovery performance than their PEG counterparts. If the density is appropriately adjusted (still low), APEG-LDPC matrices outperform classical CS random matrices.