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

Space-Time Codes Concatenated with Turbo Codes over Fading Channels

The uses of space-time code (STC) and iterative processing have enabled robust communications over fading channels at previously unachievable signal-to-noise ratios. Maintaining desired transmission rate while improving the diversity from STC is challenging, and the performance of the STC suffers considerably due to lack of channel state information (CSI). This dissertation research addresses issues of considerable importance in the design of STC with emphasis on efficient concatenation of channel coding and STC with theoretical bound derivation of the proposed schemes, iterative space-time trellis coding (STTC), and differential space-time codes. First, we concatenate space-time block code (STBC) with turbo code for improving diversity gain as well as coding gain. Proper soft-information sharing is indispensable to the iterative decoding process. We derive the required soft outputs from STBC decoders for passing to outer turbo code. Traditionally, the performance of STBC schemes has been evaluated under perfect channel estimation. For fast time-varying channel, obtaining the CSI is tedious if not impossible. We introduce a scheme of calculating the CSI at the receiver from the received signal without the explicit channel estimation. The encoder of STTC, which is generally decoded using Viterbi like algorithm, is based on a trellis structure. This trellis structure provides an inherent advantage for the STTC scheme that an iterative decoding is feasible with the minimal addition computational complexity. An iteratively decoded space-time trellis coding (ISTTC) is proposed in this dissertation, where the STTC schemes are used as constituent codes of turbo code. Then, the performance upper bound of the proposed ISTTC is derived. Finally, for implementing STBC without channel estimation and maintaining trans- mission rate, we concatenate differential space-time block codes (DSTBC) with ISTTC. The serial concatenation of DSTBC or STBC with ISTTC offers improving performance, even without an outer channel code. These schemes reduce the system complexity com- pared to the standalone ISTTC and increase the transmission rate under the same SNR condition. Detailed design procedures of these proposed schemes are analyzed

Recent advances in coding theory for near error-free communications

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression

Self-concatenated code design and its application in power-efficient cooperative communications

In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions

Unified turbo/LDPC code decoder architecture for deep-space communications

Deep-space communications are characterized by extremely critical conditions; current standards foresee the usage of both turbo and low-density-parity-check (LDPC) codes to ensure recovery from received errors, but each of them displays consistent drawbacks. Code concatenation is widely used in all kinds of communication to boost the error correction capabilities of single codes; serial concatenation of turbo and LDPC codes has been recently proven effective enough for deep space communications, being able to overcome the shortcomings of both code types. This work extends the performance analysis of this scheme and proposes a novel hardware decoder architecture for concatenated turbo and LDPC codes based on the same decoding algorithm. This choice leads to a high degree of datapath and memory sharing; postlayout implementation results obtained with complementary metal-oxide semiconductor (CMOS) 90 nm technology show small area occupation (0.98 mm 2 ) and very low power consumption (2.1 mW)

Turbo space-time coded modulation : principle and performance analysis

A breakthrough in coding was achieved with the invention of turbo codes. Turbo codes approach Shannon capacity by displaying the properties of long random codes, yet allowing efficient decoding. Coding alone, however, cannot fully address the problem of multipath fading channel. Recent advances in information theory have revolutionized the traditional view of multipath channel as an impairment. New results show that high gains in capacity can be achieved through the use of multiple antennas at the transmitter and the receiver. To take advantage of these new results in information theory, it is necessary to devise methods that allow communication systems to operate close to the predicted capacity. One such method recently invented is space-time coding, which provides both coding gain and diversity advantage. In this dissertation, a new class of codes is proposed that extends the concept of turbo coding to include space-time encoders as constituent building blocks of turbo codes. The codes are referred to as turbo spacetime coded modulation (turbo-STCM). The motivation behind the turbo-STCM concept is to fuse the important properties of turbo and space-time codes into a unified design framework. A turbo-STCM encoder is proposed, which consists of two space-time codes in recursive systematic form concatenated in parallel. An iterative symbol-by-symbol maximum a posteriori algorithm operating in the log domain is developed for decoding turbo-STCM. The decoder employs two a posteriori probability (APP) computing modules concatenated in parallel; one module for each constituent code. The analysis of turbo-STCM is demonstrated through simulations and theoretical closed-form expressions. Simulation results are provided for 4-PSK and 8-PSK schemes over the Rayleigh block-fading channel. It is shown that the turbo-STCM scheme features full diversity and full coding rate. The significant gain can be obtained in performance over conventional space-time codes of similar complexity. The analytical union bound to the bit error probability is derived for turbo-STCM over the additive white Gaussian noise (AWGN) and the Rayleigh block-fading channels. The bound makes it possible to express the performance analysis of turbo-STCM in terms of the properties of the constituent space-time codes. The union bound is demonstrated for 4-PSK and 8-PSK turbo-STCM with two transmit antennas and one/two receive antennas. Information theoretic bounds such as Shannon capacity, cutoff rate, outage capacity and the Fano bound, are computed for multiantenna systems over the AWGN and fading channels. These bounds are subsequently used as benchmarks for demonstrating the performance of turbo-STCM