On Maximum Contention-Free Interleavers and Permutation Polynomials over Integer Rings

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contention-free interleavers have been recently shown to be suitable for parallel decoding of turbo codes. In this correspondence, it is shown that permutation polynomials generate maximum contention-free interleavers, i.e., every factor of the interleaver length becomes a possible degree of parallel processing of the decoder. Further, it is shown by computer simulations that turbo codes using these interleavers perform very well for the 3rd Generation Partnership Project (3GPP) standard.Comment: 13 pages, 2 figures, submitted as a correspondence to the IEEE Transactions on Information Theory, revised versio

On Quadratic Inverses for Quadratic Permutation Polynomials over Integer Rings

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and Takeshita have recently shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes. In this correspondence, a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial for a quadratic permutation polynomial over an integer ring. Further, a simple construction is given for the quadratic inverse. All but one of the quadratic interleavers proposed earlier by Sun and Takeshita are found to admit a quadratic inverse, although none were explicitly designed to do so. An explanation is argued for the observation that restriction to a quadratic inverse polynomial does not narrow the pool of good quadratic interleavers for turbo codes.Comment: Submitted as a Correspondence to the IEEE Transactions on Information Theory Submitted : April 1, 2005 Revised : Nov. 15, 200

Pruned Bit-Reversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures

A mathematical characterization of serially-pruned permutations (SPPs) employed in variable-length permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct to coding for error correction. Typically only a small set of discrete permuter lengths are supported. Serial pruning is a simple technique to alter the length of a permutation to support a wider range of lengths, but results in a serial processing bottleneck. In this paper, parallelizing SPPs is formulated in terms of recursively computing sums involving integer floor and related functions using integer operations, in a fashion analogous to evaluating Dedekind sums. A mathematical treatment for bit-reversal permutations (BRPs) is presented, and closed-form expressions for BRP statistics are derived. It is shown that BRP sequences have weak correlation properties. A new statistic called permutation inliers that characterizes the pruning gap of pruned interleavers is proposed. Using this statistic, a recursive algorithm that computes the minimum inliers count of a pruned BR interleaver (PBRI) in logarithmic time complexity is presented. This algorithm enables parallelizing a serial PBRI algorithm by any desired parallelism factor by computing the pruning gap in lookahead rather than a serial fashion, resulting in significant reduction in interleaving latency and memory overhead. Extensions to 2-D block and stream interleavers, as well as applications to pruned fast Fourier transforms and LTE turbo interleavers, are also presented. Moreover, hardware-efficient architectures for the proposed algorithms are developed. Simulation results demonstrate 3 to 4 orders of magnitude improvement in interleaving time compared to existing approaches.Comment: 31 page

A Novel Seed Based Random Interleaving for OFDM System and Its PHY Layer Security Implications

Wireless channels are characterized by multipath and fading that can often cause long burst of errors. Even though, to date, many very sophisticated error correcting codes have been designed, yet none can handle long burst of errors efficiently. An interleaver, a device that distributes a burst of errors, possibly caused by a deep fade, and makes them appear as simple random errors, therefore, proves to a very useful technique when used in conjunction with an efficient error correcting code. In this work, a novel near optimal seed based random interleaver is designed. An optimal interleaver scatters a given burst of errors uniformly over a fixed block of data - a property that is measured by so called ‘spread’. The design makes use of a unique seed based pseudo-random sequence generator or logistic map based chaotic sequence generator to scramble the given block of data. Since the proposed design is based on a seed based scrambler, the nature of input is irrelevant. Therefore, the proposed interleaver can interleave either the bits or the symbols or the packets or even the frames. Accordingly, in this work, we analyze the suitability of interleaver when introduced before or after the modulation in single carrier communication systems and show that interleaving the bits before modulation or interleaving the symbols after modulation has same advantage. We further show that, in an orthogonal frequency division multiplexing (OFDM) systems, the position of interleaver, whether before or after constellation mapper, has no significance, and is interchangeable. However, scrambling symbols is computationally less expensive than scrambling bits. For the purpose of analyzing the performance of the proposed seed based random interleaver, simulations are carried out in MATLAB®. Results show that our proposed seed based random interleaver has near optimal properties of ‘spread’ and ‘dispersion’. Furthermore, the proposed interleaver is evaluated in terms of bit error rate (BER) versus length of burst error in a single carrier system both before and after modulation. The proposed interleaver out-performs the built in RANDINTLV in MATLAB® when used in the same system. It shows that proposed interleaver can convert greater amount of burst errors into simple random errors than that of MATLAB® interleaver. The proposed interleaver is also tested in IEEE 802.16e based WiMAX system with Stanford University Interim (SUI) channels to compare the performance of average BER versus SNR for both pre modulation and post modulation interleaver. Results show that pre modulation interleaver and post modulation has same performance. There is also a side advantage of this seed based interleaver, in that it generates a variety of unique random-looking interleaving sequences. Only a receiver that has the knowledge of the input seed can generate this sequence and no one else. If the interleaving patterns are kept secure then it can possibly be used to introduce an extra layer of security at physical (PHY) layer. In that way, at PHY layer, one builds an additional entry barrier to break through and it comes with no extra cost. This property has been investigated by carrying out key sensitivity analysis to show that the attacks to guess key can be very futile, as difference at 4th decimal place in the initial condition can lead to entirely different scrambling

System capacity enhancement for 5G network and beyond

A thesis submitted to the University of Bedfordshire, in fulfilment of the requirements for the degree of Doctor of PhilosophyThe demand for wireless digital data is dramatically increasing year over year. Wireless communication systems like Laptops, Smart phones, Tablets, Smart watch, Virtual Reality devices and so on are becoming an important part of people’s daily life. The number of mobile devices is increasing at a very fast speed as well as the requirements for mobile devices such as super high-resolution image/video, fast download speed, very short latency and high reliability, which raise challenges to the existing wireless communication networks. Unlike the previous four generation communication networks, the fifth-generation (5G) wireless communication network includes many technologies such as millimetre-wave communication, massive multiple-input multiple-output (MIMO), visual light communication (VLC), heterogeneous network (HetNet) and so forth. Although 5G has not been standardised yet, these above technologies have been studied in both academia and industry and the goal of the research is to enhance and improve the system capacity for 5G networks and beyond by studying some key problems and providing some effective solutions existing in the above technologies from system implementation and hardware impairments’ perspective. The key problems studied in this thesis include interference cancellation in HetNet, impairments calibration for massive MIMO, channel state estimation for VLC, and low latency parallel Turbo decoding technique. Firstly, inter-cell interference in HetNet is studied and a cell specific reference signal (CRS) interference cancellation method is proposed to mitigate the performance degrade in enhanced inter-cell interference coordination (eICIC). This method takes carrier frequency offset (CFO) and timing offset (TO) of the user’s received signal into account. By reconstructing the interfering signal and cancelling it afterwards, the capacity of HetNet is enhanced. Secondly, for massive MIMO systems, the radio frequency (RF) impairments of the hardware will degrade the beamforming performance. When operated in time duplex division (TDD) mode, a massive MIMO system relies on the reciprocity of the channel which can be broken by the transmitter and receiver RF impairments. Impairments calibration has been studied and a closed-loop reciprocity calibration method is proposed in this thesis. A test device (TD) is introduced in this calibration method that can estimate the transmitters’ impairments over-the-air and feed the results back to the base station via the Internet. The uplink pilots sent by the TD can assist the BS receivers’ impairment estimation. With both the uplink and downlink impairments estimates, the reciprocity calibration coefficients can be obtained. By computer simulation and lab experiment, the performance of the proposed method is evaluated. Channel coding is an essential part of a wireless communication system which helps fight with noise and get correct information delivery. Turbo codes is one of the most reliable codes that has been used in many standards such as WiMAX and LTE. However, the decoding process of turbo codes is time-consuming and the decoding latency should be improved to meet the requirement of the future network. A reverse interleave address generator is proposed that can reduce the decoding time and a low latency parallel turbo decoder has been implemented on a FPGA platform. The simulation and experiment results prove the effectiveness of the address generator and show that there is a trade-off between latency and throughput with a limited hardware resource. Apart from the above contributions, this thesis also investigated multi-user precoding for MIMO VLC systems. As a green and secure technology, VLC is achieving more and more attention and could become a part of 5G network especially for indoor communication. For indoor scenario, the MIMO VLC channel could be easily ill-conditioned. Hence, it is important to study the impact of the channel state to the precoding performance. A channel state estimation method is proposed based on the signal to interference noise ratio (SINR) of the users’ received signal. Simulation results show that it can enhance the capacity of the indoor MIMO VLC system

A Novel Seed Based Random Interleaving for OFDM System and Its PHY Layer Security Implications

Wireless channels are characterized by multipath and fading that can often cause long burst of errors. Even though, to date, many very sophisticated error correcting codes have been designed, yet none can handle long burst of errors efficiently. An interleaver, a device that distributes a burst of errors, possibly caused by a deep fade, and makes them appear as simple random errors, therefore, proves to a very useful technique when used in conjunction with an efficient error correcting code. In this work, a novel near optimal seed based random interleaver is designed. An optimal interleaver scatters a given burst of errors uniformly over a fixed block of data - a property that is measured by so called ‘spread’. The design makes use of a unique seed based pseudo-random sequence generator or logistic map based chaotic sequence generator to scramble the given block of data. Since the proposed design is based on a seed based scrambler, the nature of input is irrelevant. Therefore, the proposed interleaver can interleave either the bits or the symbols or the packets or even the frames. Accordingly, in this work, we analyze the suitability of interleaver when introduced before or after the modulation in single carrier communication systems and show that interleaving the bits before modulation or interleaving the symbols after modulation has same advantage. We further show that, in an orthogonal frequency division multiplexing (OFDM) systems, the position of interleaver, whether before or after constellation mapper, has no significance, and is interchangeable. However, scrambling symbols is computationally less expensive than scrambling bits. For the purpose of analyzing the performance of the proposed seed based random interleaver, simulations are carried out in MATLAB®. Results show that our proposed seed based random interleaver has near optimal properties of ‘spread’ and ‘dispersion’. Furthermore, the proposed interleaver is evaluated in terms of bit error rate (BER) versus length of burst error in a single carrier system both before and after modulation. The proposed interleaver out-performs the built in RANDINTLV in MATLAB® when used in the same system. It shows that proposed interleaver can convert greater amount of burst errors into simple random errors than that of MATLAB® interleaver. The proposed interleaver is also tested in IEEE 802.16e based WiMAX system with Stanford University Interim (SUI) channels to compare the performance of average BER versus SNR for both pre modulation and post modulation interleaver. Results show that pre modulation interleaver and post modulation has same performance. There is also a side advantage of this seed based interleaver, in that it generates a variety of unique random-looking interleaving sequences. Only a receiver that has the knowledge of the input seed can generate this sequence and no one else. If the interleaving patterns are kept secure then it can possibly be used to introduce an extra layer of security at physical (PHY) layer. In that way, at PHY layer, one builds an additional entry barrier to break through and it comes with no extra cost. This property has been investigated by carrying out key sensitivity analysis to show that the attacks to guess key can be very futile, as difference at 4th decimal place in the initial condition can lead to entirely different scrambling