The trellis complexity of convolutional codes

Convolutional codes have a natural, regular, trellis structure that facilitates the implementation of Viterbi's algorithm. Linear block codes also have a natural, though not in general a regular, “minimal” trellis structure, which allows them to be decoded with a Viterbi-like algorithm. In both cases, the complexity of an unenhanced Viterbi decoding algorithm can be accurately estimated by the number of trellis edge symbols per encoded bit. It would therefore appear that we are in a good position to make a fair comparison of the Viterbi decoding complexity of block and convolutional codes. Unfortunately, however, this comparison is somewhat muddled by the fact that some convolutional codes, the punctured convolutional codes, are known to have trellis representations which are significantly less complex than the conventional trellis. In other words, the conventional trellis representation for a convolutional code may not be the “minimal” trellis representation. Thus ironically, we seem to know more about the minimal trellis representation for block than for convolutional codes. We provide a remedy, by developing a theory of minimal trellises for convolutional codes. This allows us to make a direct performance-complexity comparison for block and convolutional codes. A by-product of our work is an algorithm for choosing, from among all generator matrices for a given convolutional code, what we call a trellis-canonical generator matrix, from which the minimal trellis for the code can be directly constructed. Another by-product is that in the new theory, punctured convolutional codes no longer appear as a special class, but simply as high-rate convolutional codes whose trellis complexity is unexpectedly small

Hybrid ARQ with parallel and serial concatenated convolutional codes for next generation wireless communications

This research focuses on evaluating the currently used FEC encoding-decoding schemes and improving the performance of error control systems by incorporating these schemes in a hybrid FEC-ARQ environment. Beginning with an overview of wireless communications and the various ARQ protocols, the thesis provides an in-depth explanation of convolutional encoding and Viterbi decoding, turbo (PCCC) and serial concatenated convolutional (SCCC) encoding with their respective MAP decoding strategies.;A type-II hybrid ARQ scheme with SCCCs is proposed for the first time and is a major contribution of this thesis. A vast improvement is seen in the BER performance of the successive individual FEC schemes discussed above. Also, very high throughputs can be achieved when these schemes are incorporated in an adaptive type-II hybrid ARQ system.;Finally, the thesis discusses the equivalence of the PCCCs and the SCCCs and proposes a technique to generate a hybrid code using both schemes

Physical-Layer Cooperation in Coded OFDM Relaying Systems

Mobile communication systems nowadays require ever-increasing data rate and coverage of wide areas. One promising approach to achieve this goal is the application of cooperative communications enabled by introducing intermediate nodes known as relays to support the transmission between terminals. By processing and forwarding the receive message at the relays, the path-loss effect between the source and the destination is mitigated. One major limit factor for relay assisted communications is that a relay cannot transmit and receive using the same physical resources. Therefore, a half-duplex constraint is commonly assumed resulting in halved spectral efficiency. To combat this drawback, two-way relaying is introduced, where two sources exchange information with each. On the other hand, due to the physical limitation of the relays, e.g., wireless sensor nodes, it's not possible to implement multiple antennas at one relay, which prohibits the application of multiple-input multiple-output (MIMO) techniques. However, when treating multiple relays as a cluster, a virtual antenna array is formed to perform MIMO techniques in a distributed manner. %This thesis aims at designing efficient one-way and two-way relaying schemes. Specifically, existing schemes from the literature are improved and new schemes are developed with the emphasis on coded orthogonal frequency division multiplexing (OFDM) transmissions. Of special interest is the application of physical-layer network coding (PLNC) for two-phase two-way relaying. In this case, a network coded message is estimated from the superimposed receive signal at the relay using PLNC schemes. The schemes are investigated based on a mutual information analysis and their performance are improved by a newly proposed phase control strategy. Furthermore, performance degradation due to system asynchrony is mitigated depending on different PLNC schemes. When multiple relays are available, novel cooperation schemes allowing information exchange within the relay cluster are proposed that facilitate distributed MIMO reception and transmission. Additionally, smart signaling approaches are presented to enable the cooperation at different levels with the cooperation overhead taken into account adequately in system performance evaluation

ERROR CORRECTION CODE-BASED EMBEDDING IN ADAPTIVE RATE WIRELESS COMMUNICATION SYSTEMS

In this dissertation, we investigated the methods for development of embedded channels within error correction mechanisms utilized to support adaptive rate communication systems. We developed an error correction code-based embedding scheme suitable for application in modern wireless data communication standards. We specifically implemented the scheme for both low-density parity check block codes and binary convolutional codes. While error correction code-based information hiding has been previously presented in literature, we sought to take advantage of the fact that these wireless systems have the ability to change their modulation and coding rates in response to changing channel conditions. We utilized this functionality to incorporate knowledge of the channel state into the scheme, which led to an increase in embedding capacity. We conducted extensive simulations to establish the performance of our embedding methodologies. Results from these simulations enabled the development of models to characterize the behavior of the embedded channels and identify sources of distortion in the underlying communication system. Finally, we developed expressions to define limitations on the capacity of these channels subject to a variety of constraints, including the selected modulation type and coding rate of the communication system, the current channel state, and the specific embedding implementation.Commander, United States NavyApproved for public release; distribution is unlimited

Collaborative HARQ Schemes for Cooperative Diversity Communications in Wireless Networks

Wireless technology is experiencing spectacular developments, due to the emergence of interactive and digital multimedia applications as well as rapid advances in the highly integrated systems. For the next-generation mobile communication systems, one can expect wireless connectivity between any devices at any time and anywhere with a range of multimedia contents. A key requirement in such systems is the availability of high-speed and robust communication links. Unfortunately, communications over wireless channels inherently suffer from a number of fundamental physical limitations, such as multipath fading, scarce radio spectrum, and limited battery power supply for mobile devices. Cooperative diversity (CD) technology is a promising solution for future wireless communication systems to achieve broader coverage and to mitigate wireless channels’ impairments without the need to use high power at the transmitter. In general, cooperative relaying systems have a source node multicasting a message to a number of cooperative relays, which in turn resend a processed version message to an intended destination node. The destination node combines the signal received from the relays, and takes into account the source’s original signal to decode the message. The CD communication systems exploit two fundamental features of the wireless medium: its broadcast nature and its ability to achieve diversity through independent channels. A variety of relaying protocols have been considered and utilized in cooperative wireless networks. Amplify and forward (AAF) and decode and forward (DAF) are two popular protocols, frequently used in the cooperative systems. In the AAF mode, the relay amplifies the received signal prior to retransmission. In the DAF mode, the relay fully decodes the received signal, re-encodes and forwards it to the destination. Due to the retransmission without decoding, AAF has the shortcoming that noise accumulated in the received signal is amplified at the transmission. DAF suffers from decoding errors that can lead to severe error propagation. To further enhance the quality of service (QoS) of CD communication systems, hybrid Automatic Repeat-reQuest (HARQ) protocols have been proposed. Thus, if the destination requires an ARQ retransmission, it could come from one of relays rather than the source node. This thesis proposes an improved HARQ scheme with an adaptive relaying protocol (ARP). Focusing on the HARQ as a central theme, we start by introducing the concept of ARP. Then we use it as the basis for designing three types of HARQ schemes, denoted by HARQ I-ARP, HARQ II-ARP and HARQ III-ARP. We describe the relaying protocols, (both AAF and DAF), and their operations, including channel access between the source and relay, the feedback scheme, and the combining methods at the receivers. To investigate the benefits of the proposed HARQ scheme, we analyze its frame error rate (FER) and throughput performance over a quasi-static fading channel. We can compare these with the reference methods, HARQ with AAF (HARQ-AAF) and HARQ with perfect distributed turbo codes (DTC), for which correct decoding is always assumed at the relay (HARQ-perfect DTC). It is shown that the proposed HARQ-ARP scheme can always performs better than the HARQ-AAF scheme. As the signal-to-noise ratio (SNR) of the channel between the source and relay increases, the performance of the proposed HARQ-ARP scheme approaches that of the HARQ-perfect DTC scheme