Finite connectivity systems as error-correcting codes

We investigate the performance of parity check codes using the mapping onto spin glasses proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C parity checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K?8 when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The analogy between statistical physics methods and decoding by belief propagation is also discussed.

Statistical physics of low density parity check error correcting codes

We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomly-constructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.

Visual acuity measures do not reliably detect childhood refractive error - an epidemiological study

Purpose To investigate the utility of uncorrected visual acuity measures in screening for refractive error in white school children aged 6-7-years and 12-13-years. Methods The Northern Ireland Childhood Errors of Refraction (NICER) study used a stratified random cluster design to recruit children from schools in Northern Ireland. Detailed eye examinations included assessment of logMAR visual acuity and cycloplegic autorefraction. Spherical equivalent refractive data from the right eye were used to classify significant refractive error as myopia of at least 1DS, hyperopia as greater than +3.50DS and astigmatism as greater than 1.50DC, whether it occurred in isolation or in association with myopia or hyperopia. Results Results are presented from 661 white 12-13-year-old and 392 white 6-7-year-old school-children. Using a cut-off of uncorrected visual acuity poorer than 0.20 logMAR to detect significant refractive error gave a sensitivity of 50% and specificity of 92% in 6-7-year-olds and 73% and 93% respectively in 12-13-year-olds. In 12-13-year-old children a cut-off of poorer than 0.20 logMAR had a sensitivity of 92% and a specificity of 91% in detecting myopia and a sensitivity of 41% and a specificity of 84% in detecting hyperopia. Conclusions Vision screening using logMAR acuity can reliably detect myopia, but not hyperopia or astigmatism in school-age children. Providers of vision screening programs should be cognisant that where detection of uncorrected hyperopic and/or astigmatic refractive error is an aspiration, current UK protocols will not effectively deliver.

Information-theory analysis of skewed coding for suppression of pattern-dependent errors in digital communications

We present information-theory analysis of the tradeoff between bit-error rate improvement and the data-rate loss using skewed channel coding to suppress pattern-dependent errors in digital communications. Without loss of generality, we apply developed general theory to the particular example of a high-speed fiber communication system with a strong patterning effect. © 2007 IEEE.

Effective video content distribution by combining TCP with adaptive FEC coding

This paper will look at the benefits and limitations of content distribution using Forward Error Correction (FEC) in conjunction with the Transmission Control Protocol (TCP). FEC can be used to reduce the number of retransmissions which would usually result from a lost packet. The requirement for TCP to deal with any losses is then greatly reduced. There are however side-effects to using FEC as a countermeasure to packet loss: an additional requirement for bandwidth. When applications such as real-time video conferencing are needed, delay must be kept to a minimum, and retransmissions are certainly not desirable. A balance, therefore, between additional bandwidth and delay due to retransmissions must be struck. Our results show that the throughput of data can be significantly improved when packet loss occurs using a combination of FEC and TCP, compared to relying solely on TCP for retransmissions. Furthermore, a case study applies the result to demonstrate the achievable improvements in the quality of streaming video perceived by end users.

Suppression of patterning effects in digital communications by an adaptive constrained coding

We quantify the error statistics and patterning effects in a 5x 40 Gbit/s WDM RZ-DBPSK SMF/DCF fibre link using hybrid Raman/EDFA amplification. We propose an adaptive constrained coding for the suppression of errors due to patterning effects. It is established, that this coding technique can greatly reduce the bit error rate (BER) value even for large BER (BER > 101). The proposed approach can be used in the combination with the forward error correction schemes (FEC) to correct the errors even when real channel BER is outside the FEC workspace.