Public key cryptography and error correcting codes as Ising models

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.

Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

Statistical mechanics of broadcast channels using low-density parity-check codes

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

A hierarchy of phase transitions in optimal neuronal coding:from binary to M-ary discrete optimal codes

We have investigated how optimal coding for neural systems changes with the time available for decoding. Optimization was in terms of maximizing information transmission. We have estimated the parameters for Poisson neurons that optimize Shannon transinformation with the assumption of rate coding. We observed a hierarchy of phase transitions from binary coding, for small decoding times, toward discrete (M-ary) coding with two, three and more quantization levels for larger decoding times. We postulate that the presence of subpopulations with specific neural characteristics could be a signiture of an optimal population coding scheme and we use the mammalian auditory system as an example.

Warfarin toxicity: do discharge ICD-10 codes and yellow cards accurately identify serious adverse drug reactions?

Focal points: ICD-10 codings and spontaneous yellow card reports for warfarin toxicity were compared retrospectively over a one-year period Eighteen cases of ICD-10 coded warfarin toxicity were identified from a total of 55,811 coded episodes More than three times as many ADRs to warfarin were found by screening ICD-10 codes as were reported spontaneously using the yellow card scheme Valuable information is being lost to regulatory authorities and as recognised reporters to the yellow card scheme, pharmacists are well placed to report these ADRs, enhancing their role in the safe and appropriate prescribing of warfarin