Abstract In this paper, a communication system with digital burst‐mode transmission and distributed reception in the presence of carrier frequency offset and Additive White Gaussian Noise (AWGN) is considered. The distributed receiver consists of distributed nodes and a fusion center. Data‐aided frequency estimation at a receiving node can be performed using a preamble. However, accurate frequency estimation may not be achievable at nodes with low signal‐to‐noise ratio (SNR). The problem can be alleviated by collaboration between nodes. Low‐SNR nodes can improve their data‐aided frequency estimation by fetching already decoded symbols from the fusion center. This paper investigates deterministic and data dependent criteria for selecting and fetching of additional symbols. The mean‐square error (MSE) of frequency estimation errors achieved by different criteria are numerically compared via Monte‐Carlo simulations. The Cramer–Rao Lower Bounds (CRLB) for frequency estimation under the considered criteria are presented. The bit‐error‐rates (BER) of the distributed receiver across different symbol fetching schemes are numerically compared.

In this work, a hardware testbed is proposed to validate predistortion schemes designed to compensate for imperfections in a satellite channel. Such imperfection arise due to the nonlinear power amplifier and output channel filter and it is crucial to verify predistortion methods using satellite hardware. The testbed can be used to research novel state-of-the-art algorithms or for acceptance testing of existing algorithms prior to satellite launch. Using the custom-build testbed, various predistortion schemes were compared for a realistic setup consisting of an X-band travelling-wave tube amplifier and output channel filter. An improvement in SNR of 8 dB at the receiver was demonstrated using a Wiener predistortion system.

Distributed transmit beamforming (DTBF) is an efficient technique to increase the transmission coverage in a situation where distributed nodes have limited hardware capabilities such as transmit power or the number of equipped antennas. This scenario is quite typical in tactical communication systems. The DTBF precodes transmit signals based on feedback information. In practice, continuous channel phase information is quantized based on codebook to reduce feedback overhead. In this paper, we will analyze the effect of channel quantization in the DTBF and show a small number of bits are enough to encode channel feedback information to achieve comparable performance compared to the DTBF without channel quantization. We will also derive approximated probability density function of the received SNR, which is very useful to further derive the performance of the DTBF in terms of channel capacity, outage probability, and error rates.

Next generation satellite systems are required to perform robust frame synchronisation in the presence of large frequency offsets at low carrier‐to‐noise ratios. Differential correlation‐based frame acquisition is an appealing choice for these systems as it provides adequate performance with reasonable complexity. However, the theoretical characterisation of the multi‐span differential correlation metric is still an open problem due to the fact that the correlation outputs with multiple delays are correlated. In this study, the authors derived novel closed‐form approximations for the distribution of the multi‐span differential correlation metric as well as the probabilities of miss‐detection and false alarm. The close agreement between the simulated and theoretical receiver operating curves validates the analysis. This analysis can be used to characterise the performance of multi‐span differential correlation‐based frame synchroniser in terms of the number of delays without running computationally extensive Monte Carlo simulations.

Anytime codes are known to be useful for tracking and controlling unstable systems over noisy channels. Although practical anytime codes have been developed for point-to-point communication, to date no practical code constructions and tractable analysis of anytime codes are known to exist for relay networks. In this paper, we study the design and theoretical analysis of anytime codes for a three-terminal relay network. We propose bilayer codes for anytime transmission over the relay network and consider two transmission schemes for the relay-destination link. For both schemes, we analytically derive the delay-exponents and show that they closely match the corresponding numerical results obtained from density evolution. Through simulation, we also show the finite-length performance of the proposed bilayer anytime code.

This paper presents the design and analysis of spatially coupled low‐density parity‐check (SC‐LDPC) codes for Gaussian multiple access channel (GMAC). For two‐user GMAC, we consider that each user encodes their messages by SC‐LDPC codes while joint belief propagation decoding is considered at the receiver. We present low complexity density evolution analysis of SC‐LDPC GMAC codes and show simple optimisation procedure. For the asymptotic case, we observe that SC‐LDPC code‐based GMAC code outperforms existing irregular LDPC code‐based GMAC code.

This paper considers density evolution for low-density parity-check (LDPC) and multi-edge type LDPC (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three single-parameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely, at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus, single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared with full density evolution thereby making it more suitable for code design.

This paper studies the bilayer codes for anytime reliable transmission over three terminal relay networks. We propose an anytime code structure and provide a theoretical analysis of bilayer anytime transmission when uncoded relaying takes place over the relay-destination channel. Through asymptotic analysis, we show the anytime characteristics of the proposed relaying scheme. We find the theoretical delay exponent through the mathematical induction technique and compare it with the delay exponent obtained from numerical results. Through simulation results, we also show the finite-length performance of the proposed bilayer anytime code.

Anytime transmission was previously shown to be necessary and sufficient for tracking and controlling an unstable plant over a noisy channel. In this paper, we propose an efficient channel coding scheme for anytime transmission. We design this coding scheme based on spatially coupled codes and investigate its performance over binary erasure channels (BEC) and binary input additive white Gaussian noise (BIAWGN) channels. Through density evolution analysis, we asymptotically show the desired anytime properties of the proposed code. For the BEC, we derive the corresponding delay-exponent and numerically predict the finite-length performance of the proposed anytime code. We also propose adaptive window decoding techniques to ensure low complexity anytime receivers.

In this paper, we study the design and the delay-exponent of anytime codes over a three terminal relay network. We propose a bilayer anytime code based on anytime spatially coupled low-density parity-check (LDPC) codes and investigate the anytime characteristics through density evolution analysis. By using mathematical induction technique, we find analytical expressions of the delay-exponent for the proposed code. Through comparison, we show that the analytical delay-exponent has a close match with the delay-exponent obtained from numerical results.

In this paper, we study the performance of finite-length LDPC codes in the waterfall region. We propose an algorithm to predict the error performance of finite-length LDPC codes over various binary memoryless channels. Through numerical results, we find that our technique gives better performance prediction compared to existing techniques.

The authors propose the construction of spatially coupled low‐density parity‐check (SC‐LDPC) codes using a periodic time‐variant quasi‐cyclic (QC) algorithm. The QC‐based approach is optimised to obtain memory efficiency in storing the parity‐check matrix in the decoders. A hardware model of the parity‐check storage units has been designed for a Xilinx field‐programmable gate array (FPGA), to compare the logic and memory requirements for various approaches. It is shown that the proposed QC SC‐LDPC code (with optimisation) can be stored with reasonable logic resources and without the need of block memory in the FPGA. In addition, a significant improvement in the processing speed is also achieved. This study also proposes a new QC algorithm for constructing spatially coupled repeat‐accumulate (SC‐RA) codes. The proposed construction reduces the implementation complexity of the encoder and subsequently saves significant computational resources required for storing and accessing the circulants in the decoder. The performance of the proposed code is also compared with the standard RA codes through simulations.

This paper studies the three-user finite-field multi-way relay channel, where the users exchange messages via a relay. The messages are arbitrarily correlated, and the finite-field channel is linear and is subject to additive noise of arbitrary distribution. The problem is to determine the minimum achievable source-channel rate, defined as channel uses per source symbol needed for reliable communication. We combine Slepian-Wolf source coding and functional-decode-forward channel coding to obtain the solution for two classes of source and channel combinations. Furthermore, for correlated sources that have their common information equal their mutual information, we propose a new coding scheme to achieve the minimum source-channel rate.

We consider a multi-way relay network with an orthogonal uplink and correlated sources, and we characterise reliable communication (in the usual Shannon sense) with a single-letter expression. The characterisation is obtained using a joint source-channel random-coding argument, which is based on a combination of Wyner et al.'s Cascaded Slepian-Wolf Source Coding and Tuncel's Slepian-Wolf Coding over Broadcast Channels. We prove a separation theorem for the special case of two nodes; that is, we show that a modular code architecture with separate source and channel coding functions is (asymptotically) optimal. Finally, we propose a practical coding scheme based on low-density parity-check codes, and we analyse its performance using multi-edge density evolution.

Binary message passing decoders for low-density parity-check codes are studied by using extrinsic information transfer charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the log-likelihood ratio (L-value) domain. A hard decision results in the Gallager B algorithm and examples show that increasing the channel output alphabet to two bits gains more than 1.0 dB in signal to noise ratio when using optimized codes. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.

This paper studies coding schemes for theq-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet sizeq=2m,m∈N, thus complementing some recently proposed packet-based schemes requiring largeq. First, theoretical optimality of a simple layered scheme is shown; then, a practical coding scheme based on a simple modification of standard binary LDPC decoding is proposed. The decoder is derived from first principles and using a factor-graph representation of a front end that mapsq-ary symbols to groups ofmbits connected to a binary code. The front end can be processed with a complexity that is linear inm=log2q. An extrinsic information transfer chart analysis is carried out and used for code optimization. Finally, it is shown how the same decoder structure can also be applied to a larger class ofq-ary channels.

We consider the two-way relay network where two nodes communicate via a relay. We assume that the data at the nodes are correlated (e.g., measurements in a sensor network) and that there is no direct communication between the nodes. The nodes communicate via the relay using a two-phase protocol consisting of an uplink part over an orthogonal multiple access channel and a downlink part over a broadcast channel. The individual codes as well as the overall system can be represented by a joint factor graph consisting of a source code at each node, a channel code for the each uplink and a channel code for the downlink. The optimality of separation of source and channel coding implies that it is optimal to individually design these codes. We focus on low-density parity-check codes where code design corresponds to the optimisation of their degree distributions.

The problem of loss less joint source-channel coding for the two-way relay network with an orthogonal multiple access channel is studied. Necessary and sufficient conditions for reliable communication are given, and a separation theorem for source and channel coding is proved.

The three-user finite field multi-way relay channel with correlated sources is considered. The three users generate possibly correlated messages, and each user is to transmit its message to the two other users reliably in the Shannon sense. As there is no direct link among the users, communication is carried out via a relay, and the link from the users to the relay and those from the relay to the users are finite field adder channels with additive noise of arbitrary distribution. The problem is to determine the set of all possible achievable rates, defined as channel uses per source symbol for reliable communication. For two classes of source/channel combinations, the solution is obtained using Slepian-Wolf source coding combined with functional-decode-forward channel coding.

We consider the design of bilayer-expurgated low density parity-check (BE-LDPC) codes as part of a decode and-forward protocol for use over the full-duplex relay channel. A new ensemble of codes, termed multi-edge-type bilayer expurgated LDPC (MET-BE-LDPC) codes, is introduced where the BE-LDPC code design problem is transformed into the problem of optimizing the multinomials of a multi-edge-type LDPC code. We propose two design strategies for optimizing MET-BE-LDPC codes; the bilayer approach is preferred when the difference in SNR between the source-to-relay and the source to-destination channels is small, while the bilayer approach with intermediate rates is preferred when this difference is large. In both proposed design strategies multi-edge-type density evolution is used for code optimization. The resulting MET-BE-LDPC codes exhibit improved threshold and bit-error-rate performance as compared to previously reported bilayer LDPC codes.

We study the error probability of LDPC codes in delay-limited block-fading channels with channel state information (CSI) at the transmitter and the receiver. We derive the optimal power allocation algorithms for LDPC codes with specific degree distributions using multi-edge-type density evolution error boundaries. The resulting performance approaches the outage probability for a number of power constraints. Furthermore, we adapt the algorithm for finite-length codes and show that the proposed algorithm enables gains larger than 10 dB over uniform power allocation. The method is valid for general, possibly correlated, fading distributions. This represents the first analysis of specific LDPC codes over block-fading channels with full CSI.

A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable node decoders use the binary check node decoders multiple times; each single use is referred to as a sub-iteration. To process the sequences of binary messages in each iteration, the variable node decoders employ pre-computed look-up tables. These look-up tables as well as the number of sub-iterations per iteration are dynamically adapted during the decoding process based on the decoder state, represented by the mutual information between the current messages and the syndrome bits. The look-up tables and the number of sub-iterations per iteration are determined and optimized using density evolution. The performance and the complexity of the proposed adaptive decoding algorithm is exemplified by simulations.

Modern wireless communication systems employ MIMO and feedback-two properties that make it especially difficult to measure the performance of such systems with reasonable effort in actual outdoor scenarios. In this paper, we will present a time, cost, and manpower efficient measurement approach to evaluate the throughput achieved by such systems. Summer/winter, large distance outdoor-toindoor/outdoor, urban/alpine measurements have been carried out to successfully test this approach. Exemplarily, we report on the throughput gains (over TX power and base-station-antennarotation) of standard compliant 2 × 2 MIMO HSDPA and IEEE 802.16-2004 WiMAX when for example employing improved channel coding methods.

Binary message-passing decoders for LDPC codes are analyzed using EXIT charts. For the analysis, the variable node decoder performs all computations in the L-value domain. For the special case of a hard decision channel, this leads to the well-know Gallager B algorithm, while the analysis can be extended to channels with larger output alphabets. By increasing the output alphabet from hard decisions to four symbols, a gain of more than 1.0 dB is achieved using optimized codes. For this code optimization, the mixing property of EXIT functions has to be modified to the case of binary message-passing decoders.

The degree distribution of low-density parity-check (LDPC) codes is optimized for systems that iterate over the receiver frontend, e.g., soft detector, demodulator, equalizer, etc., and the LDPC decoder. The overall extrinsic information transfer (EXIT) function of an iterative LDPC decoder is computed, based on the code's own EXIT chart, under the Gaussian assumption. While the optimization of the variable node distribution is a nonlinear problem, the optimization of the check node distribution is shown to be a linear problem. This fact is exploited to design codes where both the variable and the check node distributions are optimized, resulting in more robust constructions. The technique presented requires only knowledge of the measured EXIT function of the receiver frontend

We present a high performance implementation of a belief propagation decoder for decoding low-density parity-check (LDPC) codes on a fixed point digital signal processor. A simplified decoding algorithm was used and a stopping criteria for the iterative decoder was implemented to reduce the average number of required iterations. This leads to an implementation with increased throughput compared to other implementations of LDPC codes or turbo codes. This decoder is able to decode at 5.4 Mbps on a Texas Instruments TMS320C64xx DSP running at 600 MHz.