Cryptanalysis of WG-7 : a lightweight stream cipher

WG-7 is a stream cipher based on WG stream cipher and has been designed by Luo et al. (2010). This cipher is designed for low cost and lightweight applications (RFID tags and mobile phones, for instance). This paper addresses cryptographic weaknesses of WG-7 stream cipher. We show that the key stream generated by WG-7 can be distinguished from a random sequence after knowing 213.5 keystream bits and with a negligible error probability. Also, we investigate the security of WG-7 against algebraic attacks. An algebraic key recovery attack on this cipher is proposed. The attack allows to recover both the internal state and the secret key with the time complexity about 2/27.

Practical attack on NLM-MAC scheme

The NLM stream cipher designed by Hoon Jae Lee, Sang Min Sung, Hyeong Rag Kim is a strengthened version of the LM summation generator that combines linear and non-linear feedback shift registers. In recent works, the NLM cipher has been used for message authentication in lightweight communication over wireless sensor networks and for RFID authentication protocols. The work analyses the security of the NLM stream cipher and the NLM-MAC scheme that is built on the top of the NLM cipher. We first show that the NLM cipher suffers from two major weaknesses that lead to key recovery and forgery attacks. We prove the internal state of the NLM cipher can be recovered with time complexity about nlog7×2, where the total length of internal state is 2⋅n+22⋅n+2 bits. The attack needs about n2n2 key-stream bits. We also show adversary is able to forge any MAC tag very efficiently by having only one pair (MAC tag, ciphertext). The proposed attacks are practical and break the scheme with a negligible error probability.

Gittins indices and constrained allocation in clinical trials

We explore the use of Gittins indices to search for near optimality in sequential clinical trials. Some adaptive allocation rules are proposed to achieve the following two objectives as far as possible: (i) to reduce the expected successes lost, (ii) to minimize the error probability at the end. Simulation results indicate the merits of the rules based on Gittins indices for small trial sizes. The rules are generalized to the case when neither of the response densities is known. Asymptotic optimality is derived for the constrained rules. A simple allocation rule is recommended for one-stage models. The simulation results indicate that it works better than both equal allocation and Bather's randomized allocation. We conclude with a discussion of possible further developments.

A non-orthogonal cooperative multiple access (NCMA) protocol and low ML decoding complexity codes

A half-duplex constrained non-orthogonal cooperative multiple access (NCMA) protocol suitable for transmission of information from N users to a single destination in a wireless fading channel is proposed. Transmission in this protocol comprises of a broadcast phase and a cooperation phase. In the broadcast phase, each user takes turn broadcasting its data to all other users and the destination in an orthogonal fashion in time. In the cooperation phase, each user transmits a linear function of what it received from all other users as well as its own data. In contrast to the orthogonal extension of cooperative relay protocols to the cooperative multiple access channels wherein at any point of time, only one user is considered as a source and all the other users behave as relays and do not transmit their own data, the NCMA protocol relaxes the orthogonality built into the protocols and hence allows for a more spectrally efficient usage of resources. Code design criteria for achieving full diversity of N in the NCMA protocol is derived using pair wise error probability (PEP) analysis and it is shown that this can be achieved with a minimum total time duration of 2N - 1 channel uses. Explicit construction of full diversity codes is then provided for arbitrary number of users. Since the Maximum Likelihood decoding complexity grows exponentially with the number of users, the notion of g-group decodable codes is introduced for our setup and a set of necesary and sufficient conditions is also obtained.

A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n(t) denote the number of transmit antennas and T the block interval. For any n(t) <= T, a unified construction of (n(t) x T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2(K)-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the S-ary case corresponding to constellations of size S-K. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.

Optimal Weighted Antenna Selection For Imperfect Channel Knowledge From Training

Receive antenna selection (AS) reduces the hardware complexity of multi-antenna receivers by dynamically connecting an instantaneously best antenna element to the available radio frequency (RF) chain. Due to the hardware constraints, the channels at various antenna elements have to be sounded sequentially to obtain estimates that are required for selecting the ``best'' antenna and for coherently demodulating data. Consequently, the channel state information at different antennas is outdated by different amounts. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, the channel estimates of different antennas should be weighted differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then derive an explicit formula for the optimal selection weights that minimize the SEP. We find that when selection weights are not used, the SEP need not improve as the number of antenna elements increases, which is in contrast to the ideal channel estimation case. However, the optimal selection weights remedy this situation and significantly improve performance.

Optimal Receive Antenna Selection in Time-Varying Fading Channels with Practical Training Constraints

Hardware constraints, which motivate receive antenna selection, also require that various antenna elements at the receiver be sounded sequentially to obtain estimates required for selecting the `best' antenna and for coherently demodulating data thereafter. Consequently, the channel state information at different antennas is outdated by different amounts and corrupted by noise. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, a preferable strategy is to linearly weight the channel estimates of different antennas differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then characterize explicitly the optimal selection weights that minimize the SEP. We also consider packet reception, in which multiple symbols of a packet are received by the same antenna. New suboptimal, but computationally efficient weighted selection schemes are proposed for reducing the packet error rate. The benefits of weighted selection are also demonstrated using a practical channel code used in third generation cellular systems. Our results show that optimal weighted selection yields a significant performance gain over conventional unweighted selection.

A Novel, Balanced, and Energy-Efficient Training Method for Receive Antenna Selection

In receive antenna selection (AS), only signals from a subset of the antennas are processed at any time by the limited number of radio frequency (RF) chains available at the receiver. Hence, the transmitter needs to send pilots multiple times to enable the receiver to estimate the channel state of all the antennas and select the best subset. Conventionally, the sensitivity of coherent reception to channel estimation errors has been tackled by boosting the energy allocated to all pilots to ensure accurate channel estimates for all antennas. Energy for pilots received by unselected antennas is mostly wasted, especially since the selection process is robust to estimation errors. In this paper, we propose a novel training method uniquely tailored for AS that transmits one extra pilot symbol that generates accurate channel estimates for the antenna subset that actually receives data. Consequently, the transmitter can selectively boost the energy allocated to the extra pilot. We derive closed-form expressions for the proposed scheme's symbol error probability for MPSK and MQAM, and optimize the energy allocated to pilot and data symbols. Through an insightful asymptotic analysis, we show that the optimal solution achieves full diversity and is better than the conventional method.

Low-Complexity Detection and Performance in Multi-Gigabit High Spectral Efficiency Wireless Systems

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in Lid. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i) We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where N-t, N-r -> infinity keeping N-t = N-r, where N-t and N-r are the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as N-t, N-r -> infinity keeping N-t = N-r ii) We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10(-3), the performance of the LAS detector in decoding 16 x 16 STBC from DA with N-t = = 16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and 19) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10(-4). Our results further show that providing asymmetry in number of antennas such that N-r > N-t keeping the total receiver array length same as that for N-r = N-t, the detector is able to pick up the extra receive diversity thereby significantly improving the BER performance.

X-Codes: A Low Complexity Full-Rate High-Diversity Achieving Precoder for TDD MIMO Systems

We consider a time division duplex multiple-input multiple-output (nt × nr MIMO). Using channel state information (CSI) at the transmitter, singular value decomposition (SVD) of the channel matrix is performed. This transforms the MIMO channel into parallel subchannels, but has a low overall diversity order. Hence, we propose X-Codes which achieve a higher diversity order by pairing the subchannels, prior to SVD preceding. In particular, each pair of information symbols is encoded by a fixed 2 × 2 real rotation matrix. X-Codes can be decoded using nr very low complexity two-dimensional real sphere decoders. Error probability analysis for X-Codes enables us to choose the optimal pairing and the optimal rotation angle for each pair. Finally, we show that our new scheme outperforms other low complexity precoding schemes.

Quasi-Orthogonal Design and Performance Analysis of Amplify-And-Forward Relay Networks with Multiple-Antennas

This paper is on the design and performance analysis of practical distributed space-time codes for wireless relay networks with multiple antennas terminals. The amplify-andforward scheme is used in a way that each relay transmits a scaled version of the linear combination of the received symbols. We propose distributed generalized quasi-orthogonal space-time codes which are distributed among the source antennas and relays, and valid for any number of relays. Assuming M-PSK and M-QAM signals, we derive a formula for the symbol error probability of the investigated scheme over Rayleigh fading channels. For sufficiently large SNR, this paper derives closed-form average SER expression. The simplicity of the asymptotic results provides valuable insights into the performance of cooperative networks and suggests means of optimizing them. Our analytical results have been confirmed by simulation results, using full-rate full-diversity distributed codes.

Training and Voids in Receive Antenna Subset Selection in Time-Varying Channels

Receive antenna selection (AS) provides many benefits of multiple-antenna systems at drastically reduced hardware costs. In it, the receiver connects a dynamically selected subset of N available antennas to the L available RF chains. Due to the nature of AS, the channel estimates at different antennas, which are required to determine the best subset for data reception, are obtained from different transmissions of the pilot sequence. Consequently, they are outdated by different amounts in a time-varying channel. We show that a linear weighting of the estimates is necessary and optimum for the subset selection process, where the weights are related to the temporal correlation of the channel variations. When L is not an integer divisor of N , we highlight a new issue of ``training voids'', in which the last pilot transmission is not fully exploited by the receiver. We then present new ``void-filling'' methods that exploit these voids and greatly improve the performance of AS. The optimal subset selection rules with void-filling, in which different antennas turn out to have different numbers of estimates, are also explicitly characterized. Closed-form equations for the symbol error probability with and without void-filling are also developed.

Performance analysis of TCM with generalized selection combining on Rayleigh fading channels

We derive the computational cutoff rate, R-o, for coherent trellis-coded modulation (TCM) schemes on independent indentically distributed (i.i.d.) Rayleigh fading channels with (K, L) generalized selection combining (GSC) diversity, which combines the K paths with the largest instantaneous signal-to-noise ratios (SNRs) among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. We also derive the union bound on the bit error probability of TCM schemes with (K, L) GSC in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.

Fault-Tolerant Average Execution Time Optimization for General Purpose Multi-Processor System-on Chips

Fault-tolerance is due to the semiconductor technology development important, not only for safety-critical systems but also for general-purpose (non-safety critical) systems. However, instead of guaranteeing that deadlines always are met, it is for general-purpose systems important to minimize the average execution time (AET) while ensuring fault-tolerance. For a given job and a soft (transient) error probability, we define mathematical formulas for AET that includes bus communication overhead for both voting (active replication) and rollback-recovery with checkpointing (RRC). And, for a given multi-processor system-on-chip (MPSoC), we define integer linear programming (ILP) models that minimize AET including bus communication overhead when: (1) selecting the number of checkpoints when using RRC, (2) finding the number of processors and job-to-processor assignment when using voting, and (3) defining fault-tolerance scheme (voting or RRC) per job and defining its usage for each job. Experiments demonstrate significant savings in AET.

A Low ML-Decoding Complexity, Full-Diversity, Full-Rate MIMO Precoder

Precoding for multiple-input multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For two transmit antennas and QAM constellations, a real-valued precoder which is approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) among real-valued precoders based on the singular value decomposition (SVD) of the channel is proposed. The proposed precoder is obtainable easily for arbitrary QAM constellations, unlike the known complex-valued optimal precoder by Collin et al. for two transmit antennas which is in existence for 4-QAM alone and is extremely hard to obtain for larger QAM constellations. The proposed precoding scheme is extended to higher number of transmit antennas on the lines of the E - d(min) precoder for 4-QAM by Vrigneau et al. which is an extension of the complex-valued optimal precoder for 4-QAM. The proposed precoder's ML-decoding complexity as a function of the constellation size M is only O(root M)while that of the E - d(min) precoder is O(M root M)(M = 4). Compared to the recently proposed X- and Y-precoders, the error performance of the proposed precoder is significantly better while being only marginally worse than that of the E - d(min) precoder for 4-QAM. It is argued that the proposed precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for 2 x 2, 4 x 4 and 8 x 8 systems.