Phased burst error-correcting array codes

Various aspects of single-phased burst-error-correcting array codes are explored. These codes are composed of two-dimensional arrays with row and column parities with a diagonally cyclic readout order; they are capable of correcting a single burst error along one diagonal. Optimal codeword sizes are found to have dimensions n1×n2 such that n2 is the smallest prime number larger than n1. These codes are capable of reaching the Singleton bound. A new type of error, approximate errors, is defined; in q-ary applications, these errors cause data to be slightly corrupted and therefore still close to the true data level. Phased burst array codes can be tailored to correct these codes with even higher rates than befor

Turbo-Coded Adaptive Modulation Versus Space-Time Trellis Codes for Transmission over Dispersive Channels

Decision feedback equalizer (DFE)-aided turbocoded wideband adaptive quadrature amplitude modulation (AQAM) is proposed, which is capable of combating the temporal channel quality variation of fading channels. A procedure is suggested for determining the AQAM switching thresholds and the specific turbo-coding rates capable of maintaining the target bit-error rate while aiming for achieving a highly effective bits per symbol throughput. As a design alternative, we also employ multiple-input/multiple-output DFE-aided space–time trellis codes, which benefit from transmit diversity and hence reduce the temporal channel quality fluctuations. The performance of both systems is characterized and compared when communicating over the COST 207 typical urban wideband fading channel. It was found that the turbo-coded AQAM scheme outperforms the two-transmitter space–time trellis coded system employing two receivers; although, its performance is inferior to the space–time trellis coded arrangement employing three receivers. Index Terms—Coded adaptive modulation, dispersive channels, space–time trellis codes

Quantum Block and Convolutional Codes from Self-orthogonal Product Codes

We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that the product construction cannot improve the rate in the classical case, we show that this can happen for quantum codes: we show that a code [[15,7,3]]_2 is obtained by the product of a code [[5,1,3]]_2 with a suitable code.Comment: 5 pages, paper presented at the 2005 IEEE International Symposium on Information Theor

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