Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Intraoperative prediction of refractive error using a prototype surgical aberrometer

Purpose: To ascertain the agreement level between intra-operative refraction using a prototype surgical Hartmann-Shack aberrometer and subjective refraction a month later. Methods: Fifty-four consecutive patients had their pseudophakic refractive measured with the aberrometer intra-operatively at the end of their cataract surgery. A masked optometrist performed subjective refraction 4 weeks later. The two sets of data were then analysed for correlation. Results: The mean spherical equivalent was −0.14 ± 0.37 D (Range: −1.41 to +1.72 D) with the prototype aberrometer and −0.34 ± 0.32 (−1.64 to +1.88 D) with subjective refraction. The measurements positively correlated to a very high degree (r =+0.81, p < 0.01). In 84.3% of cases the two measurements were within 0.50D of each other. Conclusion: The aberrometer can verify the aimed refractive status of the eye intraoperatively to avoid a refractive surprise. The aberrometer is a useful tool for real time assessment of the ocular refractive status.