Recent information theoretical results indicate that dirty-paper coding (DPC) achieves the entire capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This thesis presents practical code designs for Gaussian BCs based on DPC. To simplify our designs, we assume constraints on the individual rates for each user instead of the customary constraint on transmitter power. The objective therefore is to minimize the transmitter power such that the practical decoders of all users are able to operate at the given rate constraints. The enabling element of our code designs is a practical DPC scheme based on nested turbo codes. We start with Cover's simplest two-user Gaussian BC as a toy example and present a code design that operates 1.44 dB away from the capacity region boundary at the transmission rate of 1 bit per sample per dimension for each user. Then we consider the case of the multiple-input multiple-output BC and develop a practical limit-approaching code design under the assumption that the channel state information is available perfectly at the receivers as well as at the transmitter. The optimal precoding strategy in this case can be derived by invoking duality between the MIMO BC and MIMO multiple access channel (MAC). However, this approach requires transformation of the optimal MAC covariances to their corresponding counterparts in the BC domain. To avoid these computationally complex transformations, we derive a closed-form expression for the optimal precoding matrix for the two-user case and use it to determine the optimal precoding strategy. For more than two users we propose a low-complexity suboptimal strategy, which, for three transmit antennas at the base station and three users (each with a single receive antenna), performs only 0.2 dB worse than the optimal scheme. Our obtained results are only 1.5 dB away from the capacity limit. Moreover simulations indicate that our practical DPC based scheme significantly outperforms the prevalent suboptimal strategies such as time division multiplexing and zero forcing beamforming. The drawback of DPC based designs is the requirement of channel state information at the transmitter. However, if the channel state information can be communicated back to the transmitter effectively, DPC does indeed have a promising future in code designs for MIMO BCs.

In this thesis, we discuss the implementation of a low latency decoding algorithm for turbo codes and repeat accumulate codes and compare the implementation results in terms of maximum available clock speed, resource consumption, error correction performance, and the data (information bit) rate. In order to decrease the latency a parallelized decoder structure is introduced for these mentioned codes and the results are obtained by implementing the decoders on a field programmable gate array. The memory collision problem is avoided by using collision-free interleavers. Through a proposed quantization scheme and normalization approximations, computational issues are handled for overcoming the overflow and underflow issues in a fixed point arithmetic. Also, the effect of different implementation styles are observed.

Dans ce travail, nous nous intéressons au problème du codage canal, dont le but est de corriger les erreurs dûes au canal lors d'une transmission numérique. En particulier, les turbo codes constituent la dernière avancée dans ce domaine et atteignent la borne prédite par C.E. Shannon en 1948. Nous présentons une simplification de la mise en oeuvre du turbo décodeur de R. Pyndiah, ainsi que des systèmes de synchronisation profitant des informations apportées par le turbo décodeur.

This Diploma thesis aims to explain the data coding using turbo codes. These codes belong to the group of error correction codes. We can reach the high efficiency using these codes. The first part describes process of encoding and decoding. There are describes parts of encoder and decoder. Principle of encoding and decoding demonstrate a simple example. The end of this part contains description of two most frequently used decoding algorithms (SOVA and MAP). The second part contains description of computer program that was made for using as teaching aid. This program was created in Matlab GUI. This program enables to browse error correction process step by step. This program contains graphic interface with many options and display results. In the third part is described program created in Matlab Simulink that was implemented into the TMS320C6713 kit and there is description of measuring procedure. For verification of efficiency of turbo codes was measured any parameters. Some of these parameters are: number of decoding iterations, generating polynoms and using of puncturing. The last part contains measured value and result evaluation.

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Parallel concatenated convolutional codes (PCCCs), called "turbo codes" by their discoverers, have been shown to perform close to the Shannon bound at bit error rates (BERs) between 1e-4 and 1e-6. Serial concatenated convolutional codes (SCCCs), which perform better than PCCCs at BERs lower than 1e-6, were developed borrowing the same principles as PCCCs, including code concatenation, pseudorandom interleaving and iterative decoding. The first part of this dissertation introduces the fundamentals of concatenated convolutional codes. The theoretical and simulated BER performance of PCCC and SCCC are discussed. Encoding and decoding structures are explained, with emphasis on the Log-MAP decoding algorithm and the general soft-input soft-output (SISO) decoding module. Sliding window techniques, which can be employed to reduce memory requirements, are also briefly discussed. The second part of this dissertation presents four major contributions to the field of concatenated convolutional coding developed through this research. First, the effects of quantization and fixed point arithmetic on the decoding performance are studied. Analytic bounds and modular renormalization techniques are developed to improve the efficiency of SISO module implementation without compromising the performance. Second, a new stopping criterion, SDR, is discovered. It is found to perform well with lowest cost when evaluating its complexity and performance in comparison with existing criteria. Third, a new type-II code combining automatic repeat request (ARQ) technique is introduced which makes use of the related PCCC and SCCC. Fourth, a new code-assisted synchronization technique is presented, which uses a list approach to leverage the simplicity of the correlation technique and the soft information of the decoder. In particular, the variant that uses SDR criterion achieves superb performance with low complexity. Finally, the third part of this dissertation discusses the FPGA-based implementation of the turbo decoder, which is the fruit of cooperation with fellow researchers. / Ph. D.

Since the 1950s, hidden Markov models (HMMS) have seen widespread use in electrical engineering. Foremost has been their use in speech processing, pattern recognition, artificial intelligence, queuing theory, and communications theory. However, recent years have witnessed a renaissance in the application of HMMs to the analysis and simulation of digital communication systems. Typical applications have included signal estimation, frequency tracking, equalization, burst error characterization, and transmit power control. Of special significance to this thesis, however, has been the use of HMMs to model fading channels typical of wireless communications. This variegated use of HMMs is fueled by their ability to model time-varying systems with memory, their ability to yield closed form solutions to otherwise intractable analytic problems, and their ability to help facilitate simple hardware and/or software based implementations of simulation test-beds. The aim of this thesis is to employ and exploit hidden Markov fading models within an iterative (turbo) decoding framework. Of particular importance is the problem of channel estimation, which is vital for realizing the large coding gains inherent in turbo coded schemes. This thesis shows that a Markov fading channel (MFC) can be conceptualized as a trellis, and that the transmission of a sequence over a MFC can be viewed as a trellis encoding process much like convolutional encoding. The thesis demonstrates that either maximum likelihood sequence estimation (MLSE) algorithms or maximum <I> a posteriori</I> (MAP) algorithms operating over the trellis defined by the MFC can be used for channel estimation. Furthermore, the thesis illustrates sequential and decision-directed techniques for using the aforementioned trellis based channel estimators <I>en masse</I> with an iterative decoder. / Master of Science