The Error-Pattern-Correcting Turbo Equalizer

The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By targeting the low Hamming-weight interleaved errors of the outer convolutional code, which are responsible for low Euclidean-weight errors in the Viterbi trellis, the turbo equalizer with an error-pattern correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications. A maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise ratio (SNR) gain for various channel conditions and design parameters. In addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is compared to demonstrate the present TE's superiority for short interleaver lengths and high coding rates.Comment: This work has been submitted to the special issue of the IEEE Transactions on Information Theory titled: "Facets of Coding Theory: from Algorithms to Networks". This work was supported in part by the NSF Theoretical Foundation Grant 0728676

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit

Performance of turbo coded DS-CDMA systems in correlated and uncorrelated satellite communication channels

Word processed copy.Includes bibliographical references (leaves 82-88).This thesis aims at presenting the perfonnance of turbo codes in the correlated and uncorrelated satellite fading channel. Turbo codes are known to give very good perfonnance results in A WGN channels, especially for very large input message length codes or interleaver sizes. It can be shown that good perfonnance of the turbo codes can be achieved with small interleaver sizes in a satellite channel

Low Density Graph Codes And Novel Optimization Strategies For Information Transfer Over Impaired Medium

Effective methods for information transfer over an imperfect medium are of great interest. This thesis addresses the following four topics involving low density graph codes and novel optimization strategies.Firstly, we study the performance of a promising coding technique: low density generator matrix (LDGM) codes. LDGM codes provide satisfying performance while maintaining low encoding and decoding complexities. In the thesis, the performance of LDGM codes is extracted for both majority-rule-based and sum-product iterative decoding algorithms. The ultimate performance of the coding scheme is revealed through distance spectrum analysis. We derive the distance spectral for both LDGM codes and concatenated LDGM codes. The results show that serial-concatenated LDGM codes deliver extremely low error-floors. This work provides valued information for selecting the parameters of LDGM codes. Secondly, we investigate network-coding on relay-assisted wireless multiple access (WMA) networks. Network-coding is an effective way to increase robustness and traffic capacity of networks. Following the framework of network-coding, we introduce new network codes for the WMA networks. The codes are constructed based on sparse graphs, and can explore the diversities available from both the time and space domains. The data integrity from relays could be compromised when the relays are deployed in open areas. For this, we propose a simple but robust security mechanism to verify the data integrity.Thirdly, we study the problem of bandwidth allocation for the transmission of multiple sources of data over a single communication medium. We aim to maximize the overall user satisfaction, and formulate an optimization problem. Using either the logarithmic or exponential form of satisfaction function, we derive closed-form optimal solutions, and show that the optimal bandwidth allocation for each type of data is piecewise linear with respect to the total available bandwidth. Fourthly, we consider the optimization strategy on recovery of target spectrum for filter-array-based spectrometers. We model the spectrophotometric system as a communication system, in which the information content of the target spectrum is passed through distortive filters. By exploiting non-negative nature of spectral content, a non-negative least-square optimal criterion is found particularly effective. The concept is verified in a hardware implemen

Error-correction coding for high-density magnetic recording channels.

Finally, a promising algorithm which combines RS decoding algorithm with LDPC decoding algorithm together is investigated, and a reduced-complexity modification has been proposed, which not only improves the decoding performance largely, but also guarantees a good performance in high signal-to-noise ratio (SNR), in which area an error floor is experienced by LDPC codes.The soft-decision RS decoding algorithms and their performance on magnetic recording channels have been researched, and the algorithm implementation and hardware architecture issues have been discussed. Several novel variations of KV algorithm such as soft Chase algorithm, re-encoded Chase algorithm and forward recursive algorithm have been proposed. And the performance of nested codes using RS and LDPC codes as component codes have been investigated for bursty noise magnetic recording channels.Future high density magnetic recoding channels (MRCs) are subject to more noise contamination and intersymbol interference, which make the error-correction codes (ECCs) become more important. Recent research of replacement of current Reed-Solomon (RS)-coded ECC systems with low-density parity-check (LDPC)-coded ECC systems obtains a lot of research attention due to the large decoding gain for LDPC-coded systems with random noise. In this dissertation, systems aim to maintain the RS-coded system using recent proposed soft-decision RS decoding techniques are investigated and the improved performance is presented

Synchronization for capacity -approaching coded communication systems

The dissertation concentrates on synchronization of capacity approaching error-correction codes that are deployed in noisy channels with very low signal-to-noise ratio (SNR). The major topics are symbol timing synchronization and frame synchronization.;Capacity-approaching error-correction codes, like turbo codes and low-density parity-check (LDPC) codes, are capable of reaching very low bit error rates and frame error rates in noisy channels by iterative decoding. To fully achieve the potential decoding capability of Turbo codes and LDPC codes, proper symbol timing synchronization, frame synchronization and channel state estimation are required. The dissertation proposes a joint estimator of symbol time delay and channel SNR for symbol timing recovery, and a maximum a posteriori (MAP) frame synchronizer for frame synchronization.;Symbol timing recovery is implemented by sampling and interpolation. The received signal is sampled multiple times per symbol period with unknown delay and unknown SNR. A joint estimator estimates the time delay and the SNR. The signal is rebuilt by interpolating available samples using estimated time delay. The intermediate decoding results enable decision-feedback estimation. The estimates of time delay and SNR are refined by iterative processing. This refinement improves the system performance significantly.;Usually the sampling rate is assumed to be a strict integer multiple of the symbol rate. However, in a practical system the local oscillators in the transmitter and the receiver may have random drifts. Therefore the sampling rate is no longer an exact multiple of the symbol rate, and the sampling time follows a random walk. This random walk may harm the system performance severely. The dissertation analyzes the effect of random time walks and proposes to mitigate the effect by overlapped sliding windows and iterative processing.;Frame synchronization is required to find the correct boundaries of codewords. MAP frame synchronization in the sense of minimizing the frame sync failure rate is investigated. The MAP frame synchronizer explores low-density parity-check attributes of the capacity-approaching codes. The accuracy of frame synchronization is adequate for considered coded systems to work reliably under very low SNR