In this paper, the reconstruction of the feedback polynomial as well as the initial state of a linear feedback shift register (LFSR) in a synchronous scrambler placed after a channel encoder is studied. The study is first based on the assumption that the channel is noiseless and then extended to the noisy channel condition. The dual words, which are orthogonal to the codewords generated by the channel encoder, are used in the reconstruction algorithm. The number of bits required by the new algorithm is compared with another recently proposed algorithm and results show that the number of bits required to do the reconstruction can be significantly reduced.

It is well known that in order to build linear scramblers and stream ciphers that are robust against correlation-based reconstruction, primitive polynomials which do not have sparse multiples of moderate degrees must be used. In this paper, the existence and density of such ‘good primitive polynomials’ are studied. Two theoretical lower bounds on the degree d of the primitive polynomial are derived. When d is larger than the first lower bound, there exists at least one primitive polynomial of degree d which does not have any sparse multiple of moderate degree and when d is larger than the second lower bound, it is almost guaranteed that a randomly chosen primitive polynomial of degree d does not have any sparse multiples of moderate degree. To make the lower bound tight, the distribution of the minimum degrees of sparse multiples of primitive polynomials is investigated in this paper. From comparison, it can be seen that the lower bounds obtained in this paper are much better than the previous results reported in the literature.

In this paper, the problem of reconstruction of the feedback polynomial in a linear scrambler is studied. Our work contains two parts. In the first part, schemes to improve the performance of an existing reconstruction algorithm are proposed. Simulation results show that both the detection capability and speed of the existing algorithm are significantly improved by using our proposed schemes. In the second part, the reconstruction of linear scramblers in the presence of channel noise is investigated. We consider flipped bits due to noise as well as insertion of bits in the scrambled bit sequence. For both cases, factors which affect the performance of the reconstruction algorithm are discussed.

The existing algorithm for reconstruction of the feedback polynomial in a linear scrambler relies on the assumption that the input sequence is produced by a biased memoryless source and the source bias is known and used for reconstruction. In this paper, the problem of reconstruction of the feedback polynomial in a linear scrambler without knowledge of the source bias is studied. An algorithm is proposed to reconstruct the scrambler without knowledge of the source bias and factors which affect the performance of this algorithm are discussed. A scheme which reduces the number of bits used in the reconstruction without affecting the detection capability of the reconstruction algorithm is also proposed in this paper.

A linear feedback shift register (LFSR) is a basic component of a linear scrambler and a stream cipher for a communication system. And primitive polynomials are used as the feedback polynomials of the LFSRs. In a non-cooperative context, the reverse-engineering of a linear scrambler and a stream cipher includes recovering the feedback polynomials and the LFSR's initial states (which are the secret keys in the case of stream ciphers). The problem of recovering the secret keys of stream ciphers has been extensively studied. For example, an effective approach for recovering a secret key is known as the correlation attack in the literature. The problem of reconstructing the feedback polynomials of a stream cipher and a linear scrambler has been studied recently. Both recovering the LFSR initial states by the above-mentioned correlation attack and reconstructing the feedback polynomials are highly dependent on an assumption, that is, they require that the feedback polynomials have sparse multiples of moderate degrees. Hence, in order to build linear scramblers and stream ciphers that are robust against reverse engineering, we should use primitive polynomials which do not have sparse multiples of moderate degrees. In this paper, we study the existence of primitive polynomials which do not have sparse multiples of moderate degrees, and the density of such primitive polynomials among all primitive polynomials. Our results on the existence and density of such primitive polynomials are better than the previous results in the literature.

The synchronization of clocks at physically separated network nodes requires timed signal exchanges between the nodes. Ultra-wideband (UWB) impulse signals potentially provide the means for doing this very accurately, but unlike narrowband signals, pulse signals are more naturally suited to time-division multiple-access (TDMA) schemes. In this work, we describe TDMA time-transfer schemes that estimate the mappings from a master node's clock time into slaves' clock times based on specific wireless measurements. We propose an optimal approach to distribution of UWB transmissions between those that perform alignment of nodes' clock rates and those that determine clock offsets. Analytical equations for the timing error variances are derived and our results suggest a possible lower bound for time-transfer error using UWB impulse signals.

This paper proposes a new method for steering a flexible needle in soft tissue according to an analogy of the swimming wave motion of fish locomotion. Assuming small deflection, the flexible needle is modeled as a linear beam. The governing equation for cantilever deflection is used to minimize the strain energy of the needle. Our simulation demonstrated that the repetitive motion has presented a more flexible agility to avoid obstacles, and possess better ability to find the appropriate path according to the external forces applied on the tissue during navigation. The motion of the needle can be tracked by comparing the desired deflection with needle position from x-ray images. Point-to-point algorithm is used to achieve real time control of the flexible needle.

This paper explores a correlation timing detector for tracking of Ultra-Wide-Band (UWB) monocycle signals. We seek to examine the optimal relationship between the received and reference UWB monocycle waveforms considering timing jitter and the ability to acquire lock. We modeled the received UWB monocycle waveform as the n/sup th/ order derivative of the Gaussian function. We are able to obtain a good fit using the UWB model with n=4 to both UWB impulses measured in an anechoic chamber and UWB impulses obtained in an indoor office environment. The UWB monocycle model, though an idealized representation, allows us to derive a closed form expression for the slope of the characteristic function of the TLL when both the received and reference monocycle are of arbitrary and different orders n and m. Using this compact formula, we can analyze the timing jitter of the error-tracking TLL in an additive white Gaussian noise (AWGN) channel. Computer simulation is also used to examine the dynamics of the tracking process when the loop is second order. Notably the phase plane plot is examined that gives us an indication of the ability of the TLL to acquire lock. The analysis allows us to make informed choices of the order of the monocycle waveform considering trades-off between timing error variance due to AWGN in the channel and the ability of the TLL to acquire lock. We conclude this paper by discussing a possible automatic gain control (AGC) scheme, whose main purpose is to remove the dependence of the TLL on variations in input signal amplitude.