Improved closed-form bounds on the performance of convolutional codes with correlated Rayleigh fading

New bounds on the probability of bit error are presented for a coded communication system with binary antipodal modulation and soft-decision maximum-likelihood decoding over a correlated Rayleigh-fading channel. The bounds are closed-form expressions in terms of the code\u27s transfer function; they are illustrated by considering a system using convolutional encoding. A long-standing conjecture regarding the worst-case error event in correlated Rician fading is proven for the special case of correlated Rayleigh fading, and it is used in the development of some of the new bounds. The bounds are shown to be tighter than previously developed closed-form bounds for communications using convolutional codes in correlated Rayleigh fading

Near-Capacity Turbo Coded Soft-decision Aided DAPSK/Star-QAM for Amplify-and-Forward based Cooperative Communications

Multilevel Differential Amplitude and Phase-Shift Keying (DAPSK) schemes do not require any channel estimation, which results in low complexity. In this treatise we derive the soft-output probability formulas required for a soft-decision based demodulation of high-order DAPSK, in order to facilitate iterative detection by exchanging extrinsic information with an outer Turbo Code (TC). Furthermore, when the TC block size is increased, the system operates closer to the channel capacity. Compared to the identical-throughput TC assisted 64-ary Differential Phase-Shift Keying (64-DPSK) scheme, the 4-ring based TC assisted 64-ary DAPSK arrangement has a power-efficiency improvement of 2.3 dB at a bit error rate (BER) of 10-5 . Furthermore, when the TC block size is increased, the system operates closer to the channel capacity. More specifically, when using a TC block length of 400 modulated symbols, the 64 DAPSK (4, 16) scheme is 7.56 dB away from its capacity curve, while it had a reduced gap as low as 2.25 dB, when using a longer TC block length of 40 000 modulated symbols. Finally, as a novel application example, the soft-decision M-DAPSK scheme was incorporated into an Amplify-and-Forward (AF) based cooperative communication system, which attains another 4.5 dB SNR improvement for a TC block length of 40 000 modulated symbols

Self-concatenated coding for wireless communication systems

In this thesis, we have explored self-concatenated coding schemes that are designed for transmission over Additive White Gaussian Noise (AWGN) and uncorrelated Rayleigh fading channels. We designed both the symbol-based Self-ConcatenatedCodes considered using Trellis Coded Modulation (SECTCM) and bit-based Self- Concatenated Convolutional Codes (SECCC) using a Recursive Systematic Convolutional (RSC) encoder as constituent codes, respectively. The design of these codes was carried out with the aid of Extrinsic Information Transfer (EXIT) charts. The EXIT chart based design has been found an efficient tool in finding the decoding convergence threshold of the constituent codes. Additionally, in order to recover the information loss imposed by employing binary rather than non-binary schemes, a soft decision demapper was introduced in order to exchange extrinsic information withthe SECCC decoder. To analyse this information exchange 3D-EXIT chart analysis was invoked for visualizing the extrinsic information exchange between the proposed Iteratively Decoding aided SECCC and soft-decision demapper (SECCC-ID). Some of the proposed SECTCM, SECCC and SECCC-ID schemes perform within about 1 dB from the AWGN and Rayleigh fading channels’ capacity. A union bound analysis of SECCC codes was carried out to find the corresponding Bit Error Ratio (BER) floors. The union bound of SECCCs was derived for communications over both AWGN and uncorrelated Rayleigh fading channels, based on a novel interleaver concept.Application of SECCCs in both UltraWideBand (UWB) and state-of-the-art video-telephone schemes demonstrated its practical benefits.In order to further exploit the benefits of the low complexity design offered by SECCCs we explored their application in a distributed coding scheme designed for cooperative communications, where iterative detection is employed by exchanging extrinsic information between the decoders of SECCC and RSC at the destination. In the first transmission period of cooperation, the relay receives the potentially erroneous data and attempts to recover the information. The recovered information is then re-encoded at the relay using an RSC encoder. In the second transmission period this information is then retransmitted to the destination. The resultant symbols transmitted from the source and relay nodes can be viewed as the coded symbols of a three-component parallel-concatenated encoder. At the destination a Distributed Binary Self-Concatenated Coding scheme using Iterative Decoding (DSECCC-ID) was employed, where the two decoders (SECCC and RSC) exchange their extrinsic information. It was shown that the DSECCC-ID is a low-complexity scheme, yet capable of approaching the Discrete-input Continuous-output Memoryless Channels’s (DCMC) capacity.Finally, we considered coding schemes designed for two nodes communicating with each other with the aid of a relay node, where the relay receives information from the two nodes in the first transmission period. At the relay node we combine a powerful Superposition Coding (SPC) scheme with SECCC. It is assumed that decoding errors may be encountered at the relay node. The relay node then broadcasts this information in the second transmission period after re-encoding it, again, using a SECCC encoder. At the destination, the amalgamated block of Successive Interference Cancellation (SIC) scheme combined with SECCC then detects and decodes the signal either with or without the aid of a priori information. Our simulation results demonstrate that the proposed scheme is capable of reliably operating at a low BER for transmission over both AWGN and uncorrelated Rayleigh fading channels. We compare the proposed scheme’s performance to a direct transmission link between the two sources having the same throughput

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