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 coding techniques with bit-interleaved coded modulations for MIMO block-fading channels

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January 2006 - First review: June 200

Iterative Detection of Three-Stage Concatenated FFH-MFSK

Serially concatenated and iteratively decoded Irregular Variable Length Coding (IrVLC) combined with precoded Fast Frequency Hopping (FFH) M-ary Frequency Shift Keying (MFSK) is considered. We employ EXtrinsic Information Transfer (EXIT) charts to investigate the 3-stage concatenation of the FFH-MFSK demodulator, the rate-1 decoder and the outer IrVLC decoder. The proposed joint source and channel coding scheme is capable of operating at low Signal-to-Noise Ratio (SNR) in Rayleigh fading channels contaminated by Partial Band Noise Jamming (PBNJ). The IrVLC scheme is comprised of a number of component Variable Length Coding (VLC) codebooks employing different coding rates for encoding particular fractions of the input source symbol stream. These fractions may be chosen with the aid of EXIT charts in order to shape the inverted EXIT curve of the IrVLC codec so that it can be matched with the EXIT curve of the inner decoder. We demonstrate that using the proposed scheme an infinitesimally low bit error ratio may be achieved at low SNR values

Design and analysis of iteratively decodable codes for ISI channels

Recent advancements in iterative processing have allowed communication systems to perform close to capacity limits withmanageable complexity.For manychannels such as the AWGN and flat fading channels, codes that perform only a fraction of a dB from the capacity have been designed in the literature. In this dissertation, we will focus on the design and analysis of near-capacity achieving codes for another important class of channels, namely inter-symbol interference (ISI)channels. We propose various coding schemes such as low-density parity-check (LDPC) codes, parallel and serial concatenations for ISI channels when there is no spectral shaping used at the transmitter. The design and analysis techniques use the idea of extrinsic information transfer (EXIT) function matching and provide insights into the performance of different codes and receiver structures. We then present a coding scheme which is the concatenation of an LDPC code with a spectral shaping block code designed to be matched to the channel??s spectrum. We will discuss how to design the shaping code and the outer LDPC code. We will show that spectral shaping matched codes can be used for the parallel concatenation to achieve near capacity performance. We will also discuss the capacity of multiple antenna ISI channels. We study the effects of transmitter and receiver diversities and noisy channel state information on channel capacity

Reduced complexity receivers for trellis coded modulations via punctured trellis codes

We introduce a new concept, called matched punctured trellis encoding, that simplifies the complexity of Maximum Likelihood Sequence Estimation (MLSE) receivers for combined trellis encoding and modulations with memory. Matched punctured trellis encoding is applied to tamed frequency modulation (TFM) which is a bandwidth efficient correlative - FM scheme. TFM finds applications in satellite, microwave radio, and mobile communications. Our approach is based on puncturing a rate - 1/2 matched convolutional code to obtain a rate - 2/3 mismatched code. A matched code is one that produces trellis coded modulations of minimum complexity. Puncturing these codes to obtain mismatched codes of higher rates increases the complexity of the trellis coded modulations and in return one can achieve greater coding gains. However, the main idea here is that using suboptimum MLSE receivers, with just the complexity of the matched codes, good coding gains can still be achieved. Furthermore, we conclude that the new rate - 2/3 coded modulations obtained with our approach achieve greater coding gains (for same complexity comparisons) than previously published work. The new codes are obtained by exhaustive computer search techniques and coding gains of up to 5.73 dB for 32 decoder states are achieved. These new codes are good for use with TFM modulation in an AWGN channel

Iterative equalization and decoding using reduced-state sequence estimation based soft-output algorithms

We study and analyze the performance of iterative equalization and decoding (IED) using an M-BCJR equalizer. We use bit error rate (BER), frame error rate simulations and extrinsic information transfer (EXIT) charts to study and compare the performances of M-BCJR and BCJR equalizers on precoded and non-precoded channels. Using EXIT charts, the achievable channel capacities with IED using the BCJR, M-BCJR and MMSE LE equalizers are also compared. We predict the BER performance of IED using the M-BCJR equalizer from EXIT charts and explain the discrepancy between the observed and predicted performances by showing that the extrinsic outputs of the $M$-BCJR algorithm are not true logarithmic-likelihood ratios (LLR's). We show that the true LLR's can be estimated if the conditional distributions of the extrinsic outputs are known and finally we design a practical estimator for computing the true LLR's from the extrinsic outputs of the M-BCJR equalizer

Channel Estimation in Coded Modulation Systems

With the outstanding performance of coded modulation techniques in fading channels, much research efforts have been carried out on the design of communication systems able to operate at low signal-to-noise ratios (SNRs). From this perspective, the so-called iterative decoding principle has been applied to many signal processing tasks at the receiver: demodulation, detection, decoding, synchronization and channel estimation. Nevertheless, at low SNRs, conventional channel estimators do not perform satisfactorily. This thesis is mainly concerned with channel estimation issues in coded modulation systems where different diversity techniques are exploited to combat fading in single or multiple antenna systems. First, for single antenna systems in fast time-varying fading channels, the thesis focuses on designing a training sequence by exploiting signal space diversity (SSD). Motivated by the power/bandwidth efficiency of the SSD technique, the proposed training sequence inserts pilot bits into the coded bits prior to constellation mapping and signal rotation. This scheme spreads the training sequence during a transmitted codeword and helps the estimator to track fast variation of the channel gains. A comprehensive comparison between the proposed training scheme and the conventional training scheme is then carried out, which reveals several interesting conclusions with respect to both error performance of the system and mean square error of the channel estimator. For multiple antenna systems, different schemes are examined in this thesis for the estimation of block-fading channels. For typical coded modulation systems with multiple antennas, the first scheme makes a distinction between the iteration in the channel estimation and the iteration in the decoding. Then, the estimator begins iteration when the soft output of the decoder at the decoding iteration meets some specified reliability conditions. This scheme guarantees the convergence of the iterative receiver with iterative channel estimator. To accelerate the convergence process and decrease the complexity of successive iterations, in the second scheme, the channel estimator estimates channel state information (CSI) at each iteration with a combination of the training sequence and soft information. For coded modulation systems with precoding technique, in which a precoder is used after the modulator, the training sequence and data symbols are combined using a linear precoder to decrease the required training overhead. The power allocation and the placement of the training sequence to be precoded are obtained based on a lower bound on the mean square error of the channel estimation. It is demonstrated that considerable performance improvement is possible when the training symbols are embedded within data symbols with an equi-spaced pattern. In the last scheme, a joint precoder and training sequence is developed to maximize the achievable coding gain and diversity order under imperfect CSI. In particular, both the asymptotic performance behavior of the system with the precoded training scheme under imperfect CSI and the mean square error of the channel estimation are derived to obtain achievable diversity order and coding gain. Simulation results demonstrate that the joint optimized scheme outperforms the existing training schemes for systems with given precoders in terms of error rate and the amount of training overhead