No description available.

Since the rediscovery, LDPC codes attract a large amount of research efforts. In 1998, nonbinary LDPC codes were firstly investigated and the results shown that they are better than their binary counterparts in performance. Recently, there is always a requirement from the industry to design applied nonbinary LDPC codes. In this dissertation, we firstly propose a novel class of quasi-cyclic (QC) LDPC codes. This class of QC-LDPC codes embraces both linear encoding complexity and excellent compatibility in various degree distributions and nonbinary expansions. We show by simulation results that our proposed QC-LDPC codes perform as well as their comparable counterparts. However, this proposed code structure is more flexible in designing. This feature may show its power when we change the code length and rate adaptively. Further more, we present two algorithms to generate codes with short girth and better girth distribution. The two algorithms are designed based on progressive edge growth (PEG) algorithm and they are specifically designed for quasi-cyclic structure. The simulation results show the improvement they achieved. In this thesis, we also investigate the believe propagation based iterative algorithms for decoding of nonbinary LDPC codes. The algorithms include sum-product (SP) algorithm, SP algorithm using fast Fourier transform, min-sum (MS) algorithm and complexity reduced extended min-sum (EMS) algorithm. In particular, we present the proposed modified min-sum algorithm with threshold filtering which further reduces the computation complexity.

Since the rediscovery, LDPC codes attract a large amount of research efforts. In 1998, nonbinary LDPC codes were firstly investigated and the results shown that they are better than their binary counterparts in performance. Recently, there is always a requirement from the industry to design applied nonbinary LDPC codes. In this dissertation, we firstly propose a novel class of quasi-cyclic (QC) LDPC codes. This class of QC-LDPC codes embraces both linear encoding complexity and excellent compatibility in various degree distributions and nonbinary expansions. We show by simulation results that our proposed QC-LDPC codes perform as well as their comparable counterparts. However, this proposed code structure is more flexible in designing. This feature may show its power when we change the code length and rate adaptively. Further more, we present two algorithms to generate codes with short girth and better girth distribution. The two algorithms are designed based on progressive edge growth (PEG) algorithm and they are specifically designed for quasi-cyclic structure. The simulation results show the improvement they achieved. In this thesis, we also investigate the believe propagation based iterative algorithms for decoding of nonbinary LDPC codes. The algorithms include sum-product (SP) algorithm, SP algorithm using fast Fourier transform, min-sum (MS) algorithm and complexity reduced extended min-sum (EMS) algorithm. In particular, we present the proposed modified min-sum algorithm with threshold filtering which further reduces the computation complexity.

No description available.

No description available.

No description available.

Low density parity check (LDPC) codes are linear block codes constructed by pseudo-random parity check matrices. These codes are powerful in terms of error performance and, especially, have low decoding complexity. While infinite-length LDPC codes approach the capacity of communication channels, finite-length LDPC codes also perform well, and simultaneously meet the delay requirement of many communication applications such as voice and backbone transmissions. Therefore, finite-length LDPC codes are attractive to employ in low-latency communication systems. This thesis mainly focuses on the bandwidth-efficient communication systems using finite-length LDPC codes. Such bandwidth-efficient systems are realized by mapping a group of LDPC coded bits to a symbol of a high-order signal constellation. Depending on the systems' infrastructure and knowledge of the channel state information (CSI), the signal constellations in different coded modulation systems can be two-dimensional multilevel/multiphase constellations or multi-dimensional space-time constellations. In the first part of the thesis, two basic bandwidth-efficient coded modulation systems, namely LDPC coded modulation and multilevel LDPC coded modulation, are investigated for both additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. The bounds on the bit error rate (BER) performance are derived for these systems based on the maximum likelihood (ML) criterion. The derivation of these bounds relies on the union bounding and combinatoric techniques. In particular, for the LDPC coded modulation, the ML bound is computed from the Hamming distance spectrum of the LDPC code and the Euclidian distance profile of the two-dimensional constellation. For the multilevel LDPC coded modulation, the bound of each decoding stage is obtained for a generalized multilevel coded modulation, where more than one coded bit is considered for level. For both systems, the bounds are confirmed by the simulation results of ML decoding and/or the performance of the ordered-statistic decoding (OSD) and the sum-product decoding. It is demonstrated that these bounds can be efficiently used to evaluate the error performance and select appropriate parameters (such as the code rate, constellation and mapping) for the two communication systems.<p>The second part of the thesis studies bandwidth-efficient LDPC coded systems that employ multiple transmit and multiple receive antennas, i.e., multiple-input multiple-output (MIMO) systems. Two scenarios of CSI availability considered are: (i) the CSI is unknown at both the transmitter and the receiver; (ii) the CSI is known at both the transmitter and the receiver. For the first scenario, LDPC coded unitary space-time modulation systems are most suitable and the ML performance bound is derived for these non-coherent systems. To derive the bound, the summation of chordal distances is obtained and used instead of the Euclidean distances. For the second case of CSI, adaptive LDPC coded MIMO modulation systems are studied, where three adaptive schemes with antenna beamforming and/or antenna selection are investigated and compared in terms of the bandwidth efficiency. For uncoded discrete-rate adaptive modulation, the computation of the bandwidth efficiency shows that the scheme with antenna selection at the transmitter and antenna combining at the receiver performs the best when the number of antennas is small. For adaptive LDPC coded MIMO modulation systems, an achievable threshold of the bandwidth efficiency is also computed from the ML bound of LDPC coded modulation derived in the first part.

Low density parity check (LDPC) codes are linear block codes constructed by pseudo-random parity check matrices. These codes are powerful in terms of error performance and, especially, have low decoding complexity. While infinite-length LDPC codes approach the capacity of communication channels, finite-length LDPC codes also perform well, and simultaneously meet the delay requirement of many communication applications such as voice and backbone transmissions. Therefore, finite-length LDPC codes are attractive to employ in low-latency communication systems. This thesis mainly focuses on the bandwidth-efficient communication systems using finite-length LDPC codes. Such bandwidth-efficient systems are realized by mapping a group of LDPC coded bits to a symbol of a high-order signal constellation. Depending on the systems' infrastructure and knowledge of the channel state information (CSI), the signal constellations in different coded modulation systems can be two-dimensional multilevel/multiphase constellations or multi-dimensional space-time constellations. In the first part of the thesis, two basic bandwidth-efficient coded modulation systems, namely LDPC coded modulation and multilevel LDPC coded modulation, are investigated for both additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. The bounds on the bit error rate (BER) performance are derived for these systems based on the maximum likelihood (ML) criterion. The derivation of these bounds relies on the union bounding and combinatoric techniques. In particular, for the LDPC coded modulation, the ML bound is computed from the Hamming distance spectrum of the LDPC code and the Euclidian distance profile of the two-dimensional constellation. For the multilevel LDPC coded modulation, the bound of each decoding stage is obtained for a generalized multilevel coded modulation, where more than one coded bit is considered for level. For both systems, the bounds are confirmed by the simulation results of ML decoding and/or the performance of the ordered-statistic decoding (OSD) and the sum-product decoding. It is demonstrated that these bounds can be efficiently used to evaluate the error performance and select appropriate parameters (such as the code rate, constellation and mapping) for the two communication systems.<p>The second part of the thesis studies bandwidth-efficient LDPC coded systems that employ multiple transmit and multiple receive antennas, i.e., multiple-input multiple-output (MIMO) systems. Two scenarios of CSI availability considered are: (i) the CSI is unknown at both the transmitter and the receiver; (ii) the CSI is known at both the transmitter and the receiver. For the first scenario, LDPC coded unitary space-time modulation systems are most suitable and the ML performance bound is derived for these non-coherent systems. To derive the bound, the summation of chordal distances is obtained and used instead of the Euclidean distances. For the second case of CSI, adaptive LDPC coded MIMO modulation systems are studied, where three adaptive schemes with antenna beamforming and/or antenna selection are investigated and compared in terms of the bandwidth efficiency. For uncoded discrete-rate adaptive modulation, the computation of the bandwidth efficiency shows that the scheme with antenna selection at the transmitter and antenna combining at the receiver performs the best when the number of antennas is small. For adaptive LDPC coded MIMO modulation systems, an achievable threshold of the bandwidth efficiency is also computed from the ML bound of LDPC coded modulation derived in the first part.

International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Soft-decision correlation decoding with retransmission requests for block codes is proposed and the resulting performance is analyzed. The correlation decoding rule is modified to allow retransmission requests when the received word is rendered unreliable by the channel noise. The modification is realized by a reduction in the volume in Euclidean space of the decoding region corresponding to each codeword. The performance analysis reveals the typical throughput - reliability trade-off characteristic of error control systems which employ retransmissions. Performance comparisons with hard-decision decoding reveal performance improvements beyond those attainable with hard-decision decoding algorithms. The proposed soft-decision decoding rule permits the use of a simplified codeword searching algorithm which reduces the complexity of the correlation decoder to the point where practical implementation is feasible.

This thesis investigates four FEC (forward error correction) coding schemes for their suitability for a broadcast system where there is one energy-rich transmitter and many energy-constrained receivers with a variety of channel conditions. The four coding schemes are: repetition codes (the baseline scheme); Reed-Solomon (RS) codes; Luby-Transform (LT) codes; and a type of RS and LT concatenated codes. The schemes were tested in terms of their ability to achieve both high average data reception success probability and short data reception time at the receivers (due to limited energy). The code rate (Rc) is fixed to either 1/2 or 1/3. Two statistical channel models were employed: the memoryless channel and the Gilbert-Elliott channel. The investigation considered only the data-link layer behaviour of the schemes. During the course of the investigation, an improvement to the original LT encoding process was made, the name LTAM (LT codes with Added Memory) was given to this improved coding method. LTAM codes reduce the overhead needed for decoding short-length messages. The improvement can be seen for decoding up to 10000 number of user packets. The maximum overhead reduction is as much as 10% over the original LT codes. The LT-type codes were found to have the property that can both achieve high success data reception performance and flexible switch off time for the receivers. They are also adaptable to different channel characteristics. Therefore it is a prototype of the ideal coding scheme that this project is looking for. This scheme was then further developed by applying an RS code as an inner code to further improve the success probability of packet reception. The results show that LT&RS code has a significant improvement in the channel error tolerance over that of the LT codes without an RS code applied. The trade-off is slightly more reception time needed and more decoding complexity. This LT&RS code is then determined to be the best scheme that fulfils the aim in the context of this project which is to find a coding scheme that both has a high overall data reception probability and short overall data reception time. Comparing the LT&RS code with the baseline repetition code, the improvement is in three aspects. Firstly, the LT&RS code can keep full success rate over channels have approximately two orders of magnitude more errors than the repetition code. This is for the two channel models and two code rates tested. Secondly, the LT&RS code shows an exceptionally good performance under burst error channels. It is able to maintain more than 70% success rate under the long burst error channels where both the repetition code and the RS code have almost zero success probability. Thirdly, while the success rates are improved, the data reception time, measured in terms of number of packets needed to be received at the receiver, of the LT&RS codes can reach a maximum of 58% reduction for Rc = 1=2 and 158% reduction for Rc = 1=3 compared with both the repetition code and the RS code at the worst channel error rate that the LT&RS code maintains almost 100% success probability.