Grzegorz Dziwoki

GF(q) LDPC decoder design for FPGA implementation

The concept of Low Density Parity Check (LDPC) coding over Galois Fields GF (q = 2p) is a generalization of the industry standard binary LDPC coding. The performance for short block length codes is significantly higher for non-binary codes (over higher order GF fields), but on the other hand, the decoding complexity is increased. Therefore the hardware implementation of a decoder is still a challenging task. Most of the few implementations known from the literature use multiplierless computing units. In this article we present a different approach that does not exclude multiplier blocks from the decoder module. This approach is specifically intended for FPGA (Field Programmable Gate Array) implementation. We propose the decoding algorithm formulation that uses multiplications in the computation step of the Check Nodes and summations performed in the Bit Nodes. The main reason is to enable mapping a part of the algorithm to the multiplier cores available in the FPGA devices. In the article we present the decoder structure that has been developed and the construction of its building blocks. We also provide synthesis results for the Xilinx FPGAs and simulation results for a simple BPSK (Binary Phase Shift Keying) modulation model over AWGN (Additive White Gaussian Noise) channel.

Some remarks on the reduced constellation decision-directed blind phase correction

Phase offset recovery, besides channel equalization and timing synchronization, belongs to important task performed in physical layer of receivers. Correct information symbol detection is impossible without accurate phase estimation. The paper presents analysis of a decision-directed blind phase recovery schemes applied in communication systems with square QAM modulations. The cost function of the phase recovery scheme with a reduced constellation approach is considered as well as a way of its application in an adaptive algorithm. The algorithm operation is additionally controlled by an activation threshold. A comparison between different versions of decision-directed methods is made. The performed experiments show the influence of the activation threshold on the phase correction efficiency.

Transmission over UWB Channels with OFDM System using LDPC Coding

Hostile wireless environment requires use of sophisticated signal processing methods. The paper concerns on Ultra Wideband (UWB) transmission over Personal Area Networks (PAN) including MB-OFDM specification of physical layer. In presented work the transmission system with OFDM modulation was connected with LDPC encoder/decoder. Additionally the frame and bit error rate (FER and BER) of the system was decreased using results from the LDPC decoder in a kind of turbo equalization algorithm for better channel estimation. Computational block using evolutionary strategy, from genetic algorithms family, was also used in presented system. It was placed after SPA (Sum-Product Algorithm) decoder and is conditionally turned on in the decoding process. The result is increased effectiveness of the whole system, especially lower FER. The system was tested with two types of LDPC codes, depending on type of parity check matrices: randomly generated and constructed deterministically, optimized for practical decoder architecture implemented in the FPGA device.

Averaged Properties of the Residual Error in Sparse Signal Reconstruction

Greedy algorithms, like orthogonal matching pursuit (OMP), compressive sampling matching pursuit, and their modifications, are the popular methods of compressive sensing in sparse signal reconstruction. They are iterative in manner and often use a scaled value of the system noise energy as a reference threshold to decide when to stop the searching procedure. This letter presents an analytical analysis of the residual error and also of the difference of the successive residual errors in a general case of the greedy searching procedure, provided that the measurement error is an independent and identically distributed Gaussian stationary process. The obtained results show that the mean energy of the mentioned errors, just at the moment of perfect recovery of the signal support, depends only on the sparsity order and/or on the number of measurement samples. The results contributed to designing a practical stopping rule, which is a combination of those two errors. Numerical experiments with the new rule implemented in the OMP algorithm show that the number of executed iterations can be less spread around the true value of the signal sparsity in the mean sense. A quality of the sparse signal estimation is also preserved.

Iterative Identification of Sparse Mobile Channels for TDS-OFDM Systems

Spectral efficiency improvement is essential for mobile systems development in the light of growing demand for high data transmission rate. The Time-domain synchronous OFDM transmission system increases bandwidth utilization by time-domain channel estimation without any support from frequency-domain pilot signals. Channel identification methods use a training sequence, added at the beginning of every OFDM symbol. Sparse nature of the channel impulse response, which manifests itself during wireless broadband transmission, enables one to implement compressed sensing techniques for channel identification. Channel sparsity reduces the number of measurement samples required in channel reconstruction procedure, but they should be taken from the inter-block interference (IBI) free part of the received training sequence. If maximum delay spread of the channel is comparable with the length of the training sequence, the number of measurements within the IBI-free region may be insufficient for accurate channel identification. This paper discusses a new iterative approach to sparse channels estimation, which uses the measurements from outside the IBI-free region. The proposed solution is examined for simulated transmission over randomly generated doubly-selective channels when compared with the conventional CS technique and perfect channel state information condition. The experiments reveal an enhancement of the transmission quality in terms of SER for slow-time selective channels when both delays and gains of the channel impulse response are estimated with the orthogonal matching pursuit algorithm. Further improvement, also for transmission over moderate varying channels, is observed when the path delays are found in advance. A suitable frame structure is proposed to do so.

Stopping Criteria Analysis of the OMP Algorithm for Sparse Channels Estimation

Wireless propagation environment utilised by broadband transmission systems usually has a sparse nature, i.e. only several isolated propagation paths are essential for information transfer. Receiver can recover the parameters of the particular paths using greedy, iterative algorithms that belong to the family of compressed sensing techniques. How to stop the iterative procedure, if no precise knowledge about the order of the channel sparsity is available in the receiver a priori, is a key question regarding a practical implementation of the method. The paper provides stopping criteria analysis of the Orthogonal Matching Pursuit (OMP) algorithm that is used as the core of the channel impulse response estimation method for Time-Domain Synchronous OFDM transmission system. There are investigated the residual error and the difference of successive residual errors of the OMP algorithm, as the possible metrics applied to stop the iteration procedure. Finally, a new heuristic stopping rule based on these two errors is proposed and numerically examined.

Time Domain Estimation of Mobile Radio Channels for OFDM Transmission

Time domain synchronous OFDM (TDS-OFDM) is a kind of orthogonal multicarrier transmission, where a guard period between consecutive parts of useful information is filled with a pseudorandom noise that acts as a training sequence. This sequence can be used both for synchronization and channel estimation. The paper presents a new estimation procedure for mobile channel recovery, that is based on the time domain training sequence and utilizes the compressive sensing approach. The proposed solution does not require any additional help from any deliberately deployed training information in the frequency domain (pilot tones). The method is experimentally explored in a simulated doubly selective sparse transmission environment. The quality metrics, obtained for an uncoded OFDM transmission system with implementation of the proposed estimation method, are compared to the ones that were obtained in case of ideal channel state information as well as the time-frequency training method.

OFDM Transmission with Non-binary LDPC Coding in Wireless Networks

High-quality information exchange between upper layers of the communication network (e.g. TCP, IP layers) requires reliable connection of communicating devices on the physical layer. Any non-corrected errors at this level force the upper layers to perform proper action to recover transmitted information. It reduces data throughput and increases delay to unacceptable level for some services. Among physical media, wireless one is the most hostile environment, due to its unpredictable behavior. In that case, OFDM (Orthogonal Frequency Division Multiplex) modulation and LDPC (Low Density Parity Check) error correction codes appear the best choice to provide high transmission quality on the physical layer. This paper presents the results of the authors’ simulation of a LDPC-coded OFDM system with particular emphasis on codes over high order Galois fields (non-binary) which are not commercialized yet.

A cost function analysis of a blind phase acquisition method

The Reduced Constellation Decision Directed (RCDD) blind phase correction is the simple method to remove a phase offset introduced in transmission system due to absence of carrier synchronization. This method can be used successfully for QAM signal constellations, but it can suffer convergence to a wrong phase solution. The paper presents a method to analyze static properties of the RCDD algorithm. The proposed approach, although limited to an ideal scenario with only a phase offset, allows to draw the RCDD cost function for the number of cases of QAM constellations. The investigation of the cost function properties in the case of the 16-, 32- and 64 point QAM constellations is presented in the paper.

The IEEE Wireless Standards as an Infrastructure of Smart Home Network

Home environment management systems, also known as smart home systems, become more and more popular subject in recent days. Such systems can be a support for elder or handicapped people as well as can save energy and decrease pollution emission. Although dedicated systems have been already presented on the market they are rather expensive and require major interference in existing building infrastructure. Therefore easy to use solutions are strongly demanded by modern home owners. The paper presents general requirements that should be fulfilled by the network of a smart home system and discusses some aspects of the application of wireless networks for that purpose. The main attention is put on the network operation on the level of the physical layer. The simulation and measurement results are also presented in order to evaluate usefulness of the proposed wireless approach.