Sparse Graph Codes for Quantum Error-Correction

We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse graph codes keep the number of quantum interactions associated with the quantum error correction process small: a constant number per quantum bit, independent of the blocklength. Third, sparse graph codes often offer great flexibility with respect to blocklength and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.Comment: Version 7.3e: 42 pages. Extended version, Feb 2004. A shortened version was resubmitted to IEEE Transactions on Information Theory Jan 20, 200

Mutually Uncorrelated Primers for DNA-Based Data Storage

We introduce the notion of weakly mutually uncorrelated (WMU) sequences, motivated by applications in DNA-based data storage systems and for synchronization of communication devices. WMU sequences are characterized by the property that no sufficiently long suffix of one sequence is the prefix of the same or another sequence. WMU sequences used for primer design in DNA-based data storage systems are also required to be at large mutual Hamming distance from each other, have balanced compositions of symbols, and avoid primer-dimer byproducts. We derive bounds on the size of WMU and various constrained WMU codes and present a number of constructions for balanced, error-correcting, primer-dimer free WMU codes using Dyck paths, prefix-synchronized and cyclic codes.Comment: 14 pages, 3 figures, 1 Table. arXiv admin note: text overlap with arXiv:1601.0817

Image transmission over Gilbert-Elliot and ITU fading channels using DVB-T2 channel coding and QPSK-OFDM

In this work, a concatenated forward error correction (FEC) scheme together with Orthogonal Frequency Division Multiplexing (OFDM) have been used for effective transmission of data/images over additive and fading channels. With a Bose Chaudhuri Hocquenghem (BCH) code as the outer code and a Low Density Parity Check (LDPC) code as the inner code, the transmission has been simulated over both the Gilbert-Elliot and ITU Rayleigh fading channels. The FEC parameters assumed throughout the simulations were obtained from the DVB-T2 standard and the Base Band (BB) frames were created by making use of shortening and zero-padding concepts. The results which have been presented in terms of BER and psycho-visual performances show the resilience of the FEC schemes and OFDM to channel impairments. The BER performances attained over the Gilbert-Elliot Channel (a channel that introduces burst errors when in the bad state) using LDPC only and BCH-LDPC concatenated coding indicated that the outer BCH coding will start to achieve a much lower BER after an SNR of 5 dB. Over the ITU-A Rayleigh fading channel it was observed that the performance increment due to the outer BCH encoder only become apparent after 6 dB when compared to the rate ¼ LDPC only coded system BER performance. Over the Gilbert-Elliot channel a BCH-LDPC coded QPSK-OFDM system would provide a BER of 3×10-4 at 6 dB while the same BER for the ITU Vehicular-A channel was possible at 6.6 dB