On the Convergence Speed of Turbo Demodulation with Turbo Decoding

Iterative processing is widely adopted nowadays in modern wireless receivers for advanced channel codes like turbo and LDPC codes. Extension of this principle with an additional iterative feedback loop to the demapping function has proven to provide substantial error performance gain. However, the adoption of iterative demodulation with turbo decoding is constrained by the additional implied implementation complexity, heavily impacting latency and power consumption. In this paper, we analyze the convergence speed of these combined two iterative processes in order to determine the exact required number of iterations at each level. Extrinsic information transfer (EXIT) charts are used for a thorough analysis at different modulation orders and code rates. An original iteration scheduling is proposed reducing two demapping iterations with reasonable performance loss of less than 0.15 dB. Analyzing and normalizing the computational and memory access complexity, which directly impact latency and power consumption, demonstrates the considerable gains of the proposed scheduling and the promising contributions of the proposed analysis.Comment: Submitted to IEEE Transactions on Signal Processing on April 27, 201

Low-complexity soft-decision feedback turbo equalization for multilevel modulations

This dissertation proposes two new decision feedback equalization schemes suitable for multilevel modulation systems employing turbo equalization. One is soft-decision feedback equalization (SDFE) that takes into account the reliability of both soft a priori information and soft decisions of the data symbols. The proposed SDFE exhibits lower signal to noise ratio (SNR) threshold that is required for water fall bit error rate (BER) and much faster convergence than the near-optimal exact minimum mean square error linear equalizer (Exact-MMSE-LE) for high-order constellation modulations. The proposed SDFE also offers a low computational complexity compared to the Exact-MMSE-LE. The drawback of the SDFE is that its coefficients cannot reach the matched filter bound (MFB) and therefore after a large number of iterations (e.g. 10), its performance becomes inferior to that of the Exact-MMSE-LE. Therefore, soft feedback intersymbol interference (ISI) canceller-based (SIC) structure is investigated. The SIC structure not only exhibits the same low complexity, low SNR threshold and fast convergence as the SDFE but also reaches the MFB after a large number of iterations. Both theoretical analysis and numerical simulations demonstrate why the SIC achieves MFB while the SDFE cannot. These two turbo equalization structures are also extended from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and applied in high data-rate underwater acoustic (UWA) communications --Abstract, page iv

Adaptive iterative detection for expediting the convergence of a serially concatenated unary error correction decoder, turbo decoder and an iterative demodulator

Unary Error Correction (UEC) codes constitute a recently proposed Joint Source and Channel Code (JSCC) family, conceived for alphabets having an infinite cardinality, whilst out-performing previously used Separate Source and Channel Codes (SSCCs). UEC based schemes rely on an iterative decoding process, which involves three decoding blocks when concatenated with a turbo code. Owing to this, following the activation of one of the three blocks, the next block to be activated must be chosen from the other two decoding block options. Furthermore, the UEC decoder offers a number of decoding options, allowing its complexity and error correction capability to be dynamically adjusted. It has been shown that iterative decoding convergence can be expedited by activating the specific decoding option that offers the highest Mutual Information (MI) improvement to computational complexity ratio. This paper introduces an iterative demodulator, which is shown to improve the associated error correction performance, while reducing the overall iterative decoding complexity. The challenge is that the iterative demodulator has to forward its soft-information to the other two iterative decoding blocks, and hence the corresponding MI improvements cannot be compared on a like-for-like basis. Additionally, we also propose a method of eliminating the logarithmic calculations from the adaptive iterative decoding algorithm, hence further reducing its implementational complexity without impacting its error correcting performance

Exploiting diversity in wireless channels with bit-interleaved coded modulation and iterative decoding (BICM-ID)

This dissertation studies a state-of-the-art bandwidth-efficient coded modulation technique, known as bit interleaved coded modulation with iterative decoding (BICM-ID), together with various diversity techniques to dramatically improve the performance of digital communication systems over wireless channels. For BICM-ID over a single-antenna frequency non-selective fading channel, the problem of mapping over multiple symbols, i.e., multi-dimensional (multi-D) mapping, with 8-PSK constellation is investigated. An explicit algorithm to construct a good multi-D mapping of 8-PSK to improve the asymptotic performance of BICM-ID systems is introduced. By comparing the performance of the proposed mapping with an unachievable lower bound, it is conjectured that the proposed mapping is the global optimal mapping. The superiority of the proposed mapping over the best conventional (1-dimensional complex) mapping and the multi-D mapping found previously by computer search is thoroughly demonstrated. In addition to the mapping issue in single-antenna BICM-ID systems, the use of signal space diversity (SSD), also known as linear constellation precoding (LCP), is considered in BICM-ID over frequency non-selective fading channels. The performance analysis of BICM-ID and complex N-dimensional signal space diversity is carried out to study its performance limitation, the choice of the rotation matrix and the design of a low-complexity receiver. Based on the design criterion obtained from a tight error bound, the optimality of the rotation matrix is established. It is shown that using the class of optimal rotation matrices, the performance of BICM-ID systems over a frequency non-selective Rayleigh fading channel approaches that of the BICM-ID systems over an additive white Gaussian noise (AWGN) channel when the dimension of the signal constellation increases. Furthermore, by exploiting the sigma mapping for any M-ary quadrature amplitude modulation (QAM) constellation, a very simple sub-optimal, yet effective iterative receiver structure suitable for signal constellations with large dimensions is proposed. Simulation results in various cases and conditions indicate that the proposed receiver can achieve the analytical performance bounds with low complexity. The application of BICM-ID with SSD is then extended to the case of cascaded Rayleigh fading, which is more suitable to model mobile-to-mobile communication channels. By deriving the error bound on the asymptotic performance, it is first illustrated that for a small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the Rayleigh and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. In the next step, the use of SSD in BICM-ID over frequency selective Rayleigh fading channels employing a multi-carrier modulation technique known as orthogonal frequency division multiplexing (OFDM) is studied. Under the assumption of correlated fading over subcarriers, a tight bound on the asymptotic error performance for the general case of applying SSD over all N subcarriers is derived and used to establish the best achievable asymptotic performance by SSD. It is then shown that precoding over subgroups of at least L subcarriers per group, where L is the number of channel taps, is sufficient to obtain this best asymptotic error performance, while significantly reducing the receiver complexity. The optimal joint subcarrier grouping and rotation matrix design is subsequently determined by solving the Vandermonde linear system. Illustrative examples show a good agreement between various analytical and simulation results. Further, by combining the ideas of multi-D mapping and subcarrier grouping, a novel power and bandwidth-efficient bit-interleaved coded modulation with OFDM and iterative decoding (BI-COFDM-ID) in which multi-D mapping is performed over a group of subcarriers for broadband transmission in a frequency selective fading environment is proposed. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multi-D mapping for BICM-ID in frequency non-selective Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with SSD. Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using SSD and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth and receiver complexity. Finally, the investigation is extended to the application of BICM-ID over a multiple-input multiple-output (MIMO) system equipped with multiple antennas at both the transmitter and the receiver to exploit both time and spatial diversities, where neither the transmitter nor the receiver knows the channel fading coefficients. The concentration is on the class of unitary constellation, due to its advantages in terms of both information-theoretic capacity and error probability. The tight error bound with respect to the asymptotic performance is also derived for any given unitary constellation and mapping rule. Design criteria regarding the choice of unitary constellation and mapping are then established. Furthermore, by using the unitary constellation obtained from orthogonal design with quadrature phase-shift keying (QPSK or 4-PSK) and 8-PSK, two different mapping rules are proposed. The first mapping rule gives the most suitable mapping for systems that do not implement iterative processing, which is similar to a Gray mapping in coherent channels. The second mapping rule yields the best mapping for systems with iterative decoding. Analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs, the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

Code optimization and analysis for multiple-input and multiple-output communication systems

Design and analysis of random-like codes for various multiple-input and multiple-output communication systems are addressed in this work. Random-like codes have drawn significant interest because they offer capacity-achieving performance. We first consider the analysis and design of low-density parity-check (LDPC) codes for turbo multiuser detection in multipath CDMA channels. We develop techniques for computing the probability density function (pdf) of the extrinsic messages at the output of the soft-input soft-output (SISO) multiuser detectors as a function of the pdf of input extrinsic messages, user spreading codes, channel impulse responses, and signal-to-noise ratios. Using these techniques, we are able to accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. We then apply the tools of density evolution with mixture Gaussian approximations to optimize irregular LDPC codes and to compute minimum operational signal-to-noise ratios for ergodic MIMO OFDM channels. In particular, the optimization is done for various MIMO OFDM system configurations which include different number of antennas, different channel models and different demodulation schemes. We also study the coding-spreading tradeoff in LDPC coded CDMA systems employing multiuser joint decoding. We solve the coding-spreading optimization based on the extrinsic information SNR evolution curves for the SISO multiuser detectors and the SISO LDPC decoders. Both single-cell and multi-cell scenarios will be considered. For each of these cases, we will characterize the extrinsic information for both finite-size systems and the so-called large systems where asymptotic performance results must be evoked. Finally, we consider the design optimization of irregular repeat accumulate (IRA) codes for MIMO communication systems employing iterative receivers. We present the density evolution-based procedure with Gaussian approximation for optimizing the IRA code ensemble. We adopt an approximation method based on linear programming to design an IRA code with the extrinsic information transfer (EXIT) chart matched to that of the soft MIMO demodulator

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

Signal mapping designs for bit-interleaved coded modulation with iterative decoding (BICM-ID)

Bit-interleaved coded modulation with iterative decoding (BICM-ID)is a spectral efficient coded modulation technique to improve the performance of digital communication systems. It has been widely known that for fixed signal constellation, interleaver and error control code, signal mapping plays an important role in determining the error performance of a BICM-ID system. This thesis concentrates on signal mapping designs for BICM-ID systems. To this end, the distance criteria to find the best mapping in terms of the asymptotic performance are first analytically derived for different channel models. Such criteria are then used to find good mappings for various two-dimensional 8-ary constellations. The usefulness of the proposed mappings of 8-ary constellations is verified by both the error floor bound and simulation results. Moreover, new mappings are also proposed for BICM-ID systems employing the quadrature phase shift keying (QPSK) constellation. The new mappings are obtained by considering many QPSK symbols over a multiple symbol interval, which essentially creates hypercube constellations. Analytical and simulation results show that the use of the proposed mappings together with very simple convolutional codes can offer significant coding gains over the conventional BICM-ID systems for all the channel models considered. Such coding gains are achieved without any bandwidth nor power expansion and with a very small increase in the system complexity