#VERIFY QUANTUM PENDANT SERIAL NUMBER CODE#

A comparison with a standard BOTDA sensor is realized and validates the theoretical coding gain.

#VERIFY QUANTUM PENDANT SERIAL NUMBER CODE#

Compared to traditional intensity-modulated cyclic codes, the code presents an additional gain of ГўЛ†ЕЎ2 while keeping the same number of sequences as for a colour coding. Le Floch, SГѓВ©bastien Sauser, Florian Llera, Miguel Rochat, EtienneДЇor the first time, a colour cyclic coding (CCC) is theoretically and experimentally demonstrated for Brillouin optical time-domain analysis (BOTDA) distributed sensors. Decoding uses the RS error-correcting procedures for the m-tuple codes for m = 4, 5, and 6.Д¬olour cyclic code for Brillouin distributed sensors For low rates, a second shift-register encoding operation may be invoked. Encoding is systematic and involves a two-stage procedure consisting of the usual linear feedback register (using the division or check polynomial) and a small table lookup. The binary (m - j)-tuples are identified with a subgroup of the binary m-tuples which represents the field GF(2 exp m). The code rates are very close to Reed-Solomon (RS) codes and are much better than Bose-Chaudhuri-Hocquenghem (BCH) codes (a former alternative).

These codes can be systematically encoded and decoded algebraically. New cyclic group codes of length 2(exp m) - 1 over (m - j)-bit symbols are introduced. Error Correction using Quantum Quasi- Cyclic Low-Density Parity-Check(LDPC) Codes. This makes these codes promising as storage blocks in fault-tolerant quantum computation. Our results show that this code family can perform reasonably well even at high code rates, thus considerably reducing the overhead compared to concatenated and surface codes. From the rates of uncorrectable errors under different error weights we can extrapolate the BER to any small error probability. We simulated this system for depolarizing noise on USC's High Performance Computing Cluster, and obtained the block error rate (BER) as a function of the error weight and code rate. The submatrix of Hc is used to correct Pauli X errors, and the submatrix of Hd to correct Pauli Z errors. Using submatrices obtained from Hc and Hd by deleting rows, we can alter the code rate. Two distinct, orthogonal matrices Hc and Hd are used.

Manabu Hagiwara et al., 2007 presented a method to calculate parity check matrices with high girth. Quasi- cyclic LDPC codes can approach the Shannon capacity and have efficient decoders. Jing, Lin Brun, Todd Quantum Research Team Error Correction using Quantum Quasi- Cyclic Low-Density Parity-Check(LDPC) Codes

Verify quantum pendant serial number