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Showing papers in "IEEE Journal on Selected Areas in Communications in 1989"


Journal ArticleDOI
TL;DR: The authors discuss the major attributes desired in signal constellations, such as signal-to-noise ratio (SNR) efficiency, simplicity of mapping bits to points and vice versa, compatibility with coded modulation schemes, and compatibility with quadrature amplitude modulation (QAM).
Abstract: The authors discuss the major attributes desired in signal constellations, such as signal-to-noise ratio (SNR) efficiency, simplicity of mapping bits to points and vice versa, compatibility with coded modulation schemes, and compatibility with quadrature amplitude modulation (QAM). The capability of supporting a so-called opportunistic secondary channel, often used for internal control signaling, is considered. The gain in SNR efficiency of a multidimensional constellation (lattice code) consisting of the points from a lattice Lambda within a region R compared to a cubic constellation is shown to be approximately separable into the coding gain of Lambda and the shape gain of R, for large constellations. Similarly, the expansion of the associated constituent 2-D constellation is shown to be approximately separable into a constellation expansion ratio (CER) coding component CER/sub c/( Lambda ) and a shaping component CER/sub s/(R). The N sphere is the region R with the best shape gain, but N also has large constellation expansion. Bounds for the best possible shape gain versus CER/sub s/(R) or peak-to-average-power ratio (PAR) are given. Generalized cross constellations are discussed. These constellations yield a modest shape gain with very low CER/sub s/(R) or PAR, are easily implemented, are well suited for use with coded QAM modems, and can be readily adapted to support an opportunistic secondary channel. >

566 citations


Journal ArticleDOI
Hamid Ahmadi1, W.E. Denzel1
TL;DR: A survey of high-performance switch fabric architectures which incorporate fast packet switching as their underlying switching technique to handle various traffic types is presented.
Abstract: A survey of high-performance switch fabric architectures which incorporate fast packet switching as their underlying switching technique to handle various traffic types is presented. A descriptive overview of the major activities in this rapidly evolving field of telecommunications is given. The switch fabrics are classified into the following categories: banyan and buffered banyan-based fabrics, sort-banyan-based fabrics fabrics with disjoint-path topology and output queuing, crossbar-based fabrics, time division fabrics with common packet memory, and fabrics with shared medium. >

407 citations


Journal ArticleDOI
TL;DR: Two-layer conditional-replenishment coding of video signals over a variable-bit-rate (VBR) network is described and it is shown that the coder performs well for a guaranteed channel rate as low as 10-20% of the total bit rate.
Abstract: Two-layer conditional-replenishment coding of video signals over a variable-bit-rate (VBR) network is described. A slotted-ring network based on an Orwell protocol is assumed, where transmission of certain packets is guaranteed. The two-layer coder produces two output bit streams: the first bit stream contains all the important structural information in the image and is accommodated in the guaranteed capacity of the network, while the second adds the necessary quality finish. The performance of the coder is tested with CIF standard sequences and broadcast-quality pictures. The portion of the VBR channel allocated to the lower layer as guaranteed bandwidth is examined. Using broadcast-quality pictures, statistics were obtained on the performance of this system for different choices of bit rate in the lower layer. The effect of lost packets is shown on CIF standard picture sequences. It is shown that the coder performs well for a guaranteed channel rate as low as 10-20% of the total bit rate. >

386 citations


Journal ArticleDOI
TL;DR: The extensive empirical data indicate that path loss is dependent upon local surroundings and is log-normally distributed, temporal fading is Rician, and small-scale signal fluctuations due to receiver motion are primarily Rayleigh, although Rician and log-normal distributions fit some of the data.
Abstract: The authors detail the results of narrowband propagation measurements performed at five factories. The extensive empirical data indicate that path loss is dependent upon local surroundings and is log-normally distributed, temporal fading is Rician, and small-scale signal fluctuations due to receiver motion are primarily Rayleigh, although Rician and log-normal distributions fit some of the data. Shadowing effects of common factory equipment likely to obstruct indoor radio paths are also examined. >

292 citations


Journal ArticleDOI
TL;DR: The traffic analysis of small-cell mobile networks with dynamic channel assignment is investigated to determine their blocking performance, using a hybrid method of analysis and simulation and significant improvement in network performance is established by numerical results.
Abstract: The traffic analysis of small-cell mobile networks with dynamic channel assignment is investigated to determine their blocking performance, using a hybrid method of analysis and simulation. The authors particularly focus on the performance problems presented by networks with heterogeneous cell traffic loads, the impact of traffic volatility among the cells, and the impact of multichannel traffic on the channel blocking probabilities. Significant improvement in network performance with dynamic channel assignment is established by numerical results. >

277 citations


Journal ArticleDOI
TL;DR: The authors apply a general method of bounding the event error probability of TCM (trellis-coded modulation) schemes to fading channels and use the effective length and the minimum-squared-product distance to replace theminimum-free-squaring-Euclidean distance as code design parameters for Rayleigh and Rician fading channels with a substantial multipath component.
Abstract: The authors apply a general method of bounding the event error probability of TCM (trellis-coded modulation) schemes to fading channels and use the effective length and the minimum-squared-product distance to replace the minimum-free-squared-Euclidean distance as code design parameters for Rayleigh and Rician fading channels with a substantial multipath component. They present 8-PSK (phase-shift-keying) trellis codes specifically constructed for fading channels that outperform equivalent codes designed for the AWGN (additive white Gaussian noise) channel when v>or=5. For quasiregular trellis codes there exists an efficient algorithm for evaluating event error probability, and numerical results which demonstrate the importance of the effective length as a code design parameter for fading channels with or without side information have been obtained. This is consistent with the case for binary signaling, where the Hamming distance remains the best code design parameter for fading channels. The authors show that the use of Reed-Solomon block codes with expanded signal sets becomes interesting only for large value of E/sub s//N/sub 0/, where they begin to outperform trellis codes. >

265 citations


Journal ArticleDOI
TL;DR: TCMP is a novel modulation strategy for Rician fading channels that multiplexes a time domain pilot sequence with trellis-coded data to permit coherent detection and is shown to provide remarkably robust performance in the presence of fading.
Abstract: The authors describe TCMP, a novel modulation strategy for Rician fading channels that multiplexes a time domain pilot sequence with trellis-coded data to permit coherent detection. This technique is shown to provide remarkably robust performance in the presence of fading. It is also shown that, when choosing trellis codes for fading channels, time diversity is of greater important than asymptotic coding gain. The motivation for studying this strategy is to find signaling schemes for transmitting data at a 4.8 kb/s rate over a mobile satellite channel with 5-kHz channel spacing. >

255 citations


Journal ArticleDOI
TL;DR: The authors extend earlier work in modeling video sources using interframe coding schemes and in carrying out buffer queueing analysis for the multiplexing of several such sources, and consider models for scenes with multiple activity levels which lead to sudden changes in the coder output bit rates.
Abstract: The authors extend earlier work (ibid., vol.36, p.834-44, Jul. 1988) in modeling video sources using interframe coding schemes and in carrying out buffer queueing analysis for the multiplexing of several such sources. The previous models and analysis were suitable for relatively uniform activity scenes. Here, models are considered for scenes with multiple activity levels which lead to sudden changes in the coder output bit rates. Such models apply to talker-listener alternating scenes, as well as to situations where there is a mix of dissimilar services, e.g., television and videotelephony. Correlated Markov models for the corresponding sources are given. A flow-equivalent queueing analysis is used to obtain common buffer queue distributions and probabilities of packet loss. The results demonstrate the efficiency of packet video on a single link, due to the smoothing effect of multiplexing several variable-bit-rate video sources. >

242 citations


Journal ArticleDOI
TL;DR: The authors investigated the detection of trellis codes designed for channels that are intersymbol interference free when they operate in the presence of intersy symbol interference.
Abstract: The authors investigated the detection of trellis codes designed for channels that are intersymbol interference free when they operate in the presence of intersymbol interference. A well-structured reduced-state sequence estimation (RSSE) algorithm is described which can achieve the performance of maximum-likelihood sequence estimation (MLSE) with drastically reduced complexity. Well-defined reduced-state trellises are first constructed by merging the states of the ML supertrellis using set partitioning principles. Then the Viterbi algorithm is used to search these trellises. A special case of RSSE, called parallel decision-feedback decoding, uses the encoder trellis, yet on channels with large attenuation distortion it can provide a significantly better performance than linear equalization. The performance of RSSE is examined analytically and through simulation, and then compared to that of MLSE and ideal decision-feedback equalization. It is noted that the performance advantage of RSSE can be obtained without significantly increasing the decoding delay or complicating an adaptive implementation. >

237 citations


Journal ArticleDOI
G. K. Kaleh1
TL;DR: By using a pulse-amplitude-modulation representation of binary continuous-phase- modulation signals, the authors develop a novel optimum Viterbi sequence detector and a near-optimum Viterba receiver with low complexity.
Abstract: By using a pulse-amplitude-modulation representation of binary continuous-phase-modulation signals, the authors develops a novel optimum Viterbi sequence detector and a near-optimum Viterbi receiver with low complexity. For modulation index 0.5, where a linear receiver can be used, a minimum-mean-squared-error linear receiver filter is derived. The performance of all of these is analyzed, using the Gaussian minimum-shift-keying signal (GMSK) for illustration. It is shown that a GMSK receiver consisting of two matched filters and a four-state Viterbi algorithm performs with less than 0.24-dB degradation compared with the optimal receiver. The linear receiver is optimum for all values of E/sub b//N/sub 0/ (bit-energy-to-noise one-sided spectral density ratio). A design method for its filter is given. The filter is equivalent to a cascade of a matched filter and a Wiener filter estimator. Both upper and lower bounds for the bit-error probability are calculated. Simulation results which confirm the analysis are given. >

236 citations


Journal ArticleDOI
P. Harley1
TL;DR: The results show that at short distances from the antenna the signal attenuation slope is very much less than that predicted by extrapolating the results of Hata and Okumura et al. (1968).
Abstract: Short-distance, low-antenna-height signal attenuation measurements are presented in connection with their use in the design of future microcell cellular radio networks. Measurements presented are based on the propagation along busy city streets in a direction radial to a fixed antenna site. Antenna heights between 5 m and 20 m were chosen for the fixed site, while 1.5 m was chosen for the mobile vehicle. The signal strength was then measured out to a distance of 1 km in a line-of-sight path from the fixed site at both 870.15 MHz and 1.8 GHz. The measurements show that extrapolation of the M. Hata (1980) and Y. Okumura et al. (1968) formulas into the low-antenna-height, short-distance area is not valid and can lead to inaccuracies. The results show that at short distances from the antenna the signal attenuation slope is very much less than that predicted by extrapolating the results of Hata and Okumura et al. >

Journal ArticleDOI
TL;DR: Basic characteristics of variable-rate video coders applied to asynchronous transfer mode (ATM) transmission are described and burstiness of video information is evaluated for conference-type scenes using various coding algorithms.
Abstract: Basic characteristics of variable-rate video coders applied to asynchronous transfer mode (ATM) transmission are described Burstiness of video information is evaluated for conference-type scenes using various coding algorithms Three measures (distribution, autocorrelation, and coefficient of variation) are introduced to evaluate burstiness Video sources are modeled and characterized by the autoregressive process and coefficient of variation Video quality improvement achieved with variable rate transmission is evaluated using signal-to-noise ratio (SNR) and subjective ratings An improvement of 5-10 dB in temporal SNR and 1 rank in mean opinion score are reported >

Journal ArticleDOI
TL;DR: Bounds on the shape gain of Voronoi constellations are given that depend on the depth and normalized informativity of Lambda /sub s/.
Abstract: For pt.I see ibid., vol.7, no.6, p.877-92 (1989). Voronoi constellations, also called Voronoi codes are implementable N-dimensional constellations based on partitions of N-dimensional lattices ( Lambda ) that can achieve good shape gains and that are inherently suited for use with coded modulation. Two methods are given for specifying Voronoi constellations on the basis of arbitrary lattice partitions Lambda / Lambda /sub s/, where Lambda /sub s/, the shaping lattice, is an N-dimensional sublattice of Lambda . One of the methods is conjectured to be optimum, and the other has desirable symmetries and naturally supports opportunistic secondary channels. When Lambda and Lambda /sub s/ are 2-D-symmetric, the constituent 2-D constellation is itself a Voronoi constellation. The shaping constellation expansion ratio and peak-to-average-power ratio are determined in general and for various Lambda /sub s/. Methods for labeling Voronoi constellations are given. Their complexity is shown to be dominated by that of decoding Lambda /sub s/. It is also shown that coding and shaping are separable and dual. Bounds on the shape gain of Voronoi constellations are given that depend on the depth and normalized informativity of Lambda /sub s/. These bounds suggest the use of lattices Lambda with depth 2 and normalized informativity less than 1, which can achieve near-optimal shape gains with reduced constellation expansion and implementation complexity. >

Journal ArticleDOI
Floyd E. Ross1
TL;DR: In this paper, the authors present an overview of fiber distributed data interface (FDDI) technology and explore the basis for its success, with particular emphasis on the technical specifications for an upwards compatible version of FDDI, which adds the capability for circuit-switched services to the packet services, thus creating an integrated services LAN.
Abstract: Updating earlier efforts in previously published work, the author presents an overview of fiber distributed data interface (FDDI) technology and explores the basis for its success. Particular emphasis is placed on the technical specifications for an upwards-compatible version of FDDI, FDDI-II, which adds the capability for circuit-switched services to the packet services of the basic FDDI, thus creating an integrated services LAN. >

Journal ArticleDOI
TL;DR: An ID-based cryptosystem based on the discrete logarithm problem is proposed which is one of the earliest realizations in Shamir's sense and the security against a conspiracy of some entities in the proposed system is considered, along with the possibility of establishing a more secure system.
Abstract: In a modern network system, data security technologies such as cryptosystems, signature schemes, etc., are indispensable for reliable data transmission. In particular, for a large-scale network, ID-based systems such as the ID-based cryptosystem, the ID-based signature scheme, or the ID-based key distribution system are among the better countermeasures for establishing efficient and secure data transmission systems. The concept of an ID-based cryptosystem has been proposed by A. S?hamir (1985), and it is advantageous to public-key cryptosystems because a large public-key file is not required for such a system. An ID-based cryptosystem based on the discrete logarithm problem is proposed which is one of the earliest realizations in Shamir's sense. The security against a conspiracy of some entities in the proposed system is considered, along with the possibility of establishing a more secure system. >

Journal ArticleDOI
TL;DR: In this selective recovery method, video signals are not stopped even if a long propagation delay exists, no additional information is transmitted to error recovery and conventional coding algorithms can be used.
Abstract: An efficient recovery method using error concealment is proposed for video packet loss in fast packet switching networks. In this method, the receiver detects the damaged picture area caused by packet loss from the structured picture data received, makes error concealments, notifies the transmitter, and continues decoding. The transmitter, having received the notice, calculates the affected picture area in the local decoded picture and continues encoding without using this affected area. In this selective recovery method, video signals are not stopped even if a long propagation delay exists, no additional information is transmitted to error recovery and conventional coding algorithms can be used. The proposed method is suitable for multipoint communication. Simulation results show the affected picture area is localized for a considerable time attesting to the method's effectiveness. >

Journal ArticleDOI
TL;DR: Simulation results indicating practical solutions to some of the issues raised are presented for a hierarchical packet-video subband coding system and they can be made less dependent on network implementation and signal format.
Abstract: Packet video is investigated from a systems point of view. The most important issues relating to its transmission are identified and studied in the context of a layered network architecture model, leading to a better understanding of the interactions between network and signal handling. The functions at a particular layer can thereby be made less dependent on network implementation and signal format. In the layered network model, the higher layers provide format conversion, hierarchical source coding, error recovery, resynchronization, cost/quality arbitration, session setup and tear-down, packetization, and multiplexing. Provisions from the network layers pertain mainly to real-time transmission. Special consideration is given to hierarchical source coding, error recovery, statistical behavior, and timing aspects. Simulation results indicating practical solutions to some of the issues raised are presented for a hierarchical packet-video subband coding system. >

Journal ArticleDOI
TL;DR: A variable-bit-rate coding method for asynchronous transfer mode (ATM) networks is described that is capable of compensating for packet loss and the influence of packet loss on picture quality is discussed, and decoded pictures with packet loss are shown.
Abstract: Statistical characteristics of video signals for video packet coding, are clarified and a variable-bit-rate coding method for asynchronous transfer mode (ATM) networks is described that is capable of compensating for packet loss ATM capabilities are shown to be greatly affected by delay, delay jitter, and packet loss probability Packet loss has the greatest influence on picture quality Packets may be lost either due to random bit error in a cell header or to network control when traffic is congested A layered coding technique using discrete-cosine transform (DCT) coding is presented which is suitable for packet loss compensation The influence of packet loss on picture quality is discussed, and decoded pictures with packet loss are shown The proposed algorithm was verified by computer simulations >

Journal ArticleDOI
E. Okamoto1, K. Tanaka1
TL;DR: A key distribution system (KDS) based on identification information (ID-based KDS) is presented, which is founded on the Diffie-Hellman public key distribution scheme and has an identity authentication function.
Abstract: A key distribution system (KDS) based on identification information (ID-based KDS) is presented. The system is founded on the Diffie-Hellman public key distribution scheme and has an identity authentication function. It uses an individual user's identification information instead of the public file used in the Diffie-Hellman scheme. It does not require any services of a center to distribute work keys or users to keep directories of key-encrypting keys. Therefore, key management in cryptosystems can be simplified by adopting the ID-based KDS. Two kinds of identity-based key distribution system are proposed and applied to actual communication networks. One uses two-way (interactive) communication to distribute work keys, while the other uses one-way communication. Modular exponentiations of large numbers, used in the systems, are implemented with digital signal processors. >

Journal ArticleDOI
TL;DR: The teletraffic performance of a highway microcellular digital mobile radio system having an oversailing macrocell that spans many microcells is presented and a narrowband time-division-multiple-access arrangement supporting ten channels per carrier and one carrier per base station is used.
Abstract: The teletraffic performance of a highway microcellular digital mobile radio system having an oversailing macrocell that spans many microcells is presented. The microcellular cluster is composed of concatenated segments of the highway where each segment is a microcell, typically 500-2000 m in length, with the base stations located at lamp-post elevations. A narrowband time-division-multiple-access arrangement supporting ten channels per carrier and one carrier per base station is used. The teletraffic analysis assumes there are n-up and n-down lanes, and that the vehicular speeds conform to a truncated Gaussian distribution whose mean speed is 100 or 50 km/h when the vehicular traffic is free-flowing or in traffic-congested conditions, respectively. >

Journal ArticleDOI
TL;DR: In this paper, an approach to analyzing encryption protocols using machine-aided formal verification techniques is presented, where the properties that the protocol should preserve are expressed as state invariants, and the theorems that must be proved to guarantee that the cryptographic facility satisfies the invariants are automatically generated by the verification system.
Abstract: An approach to analyzing encryption protocols using machine-aided formal verification techniques is presented. The properties that the protocol should preserve are expressed as state invariants, and the theorems that must be proved to guarantee that the cryptographic facility satisfies the invariants are automatically generated by the verification system. A formal specification of an example system is presented, and several weaknesses that were revealed by attempting to verify and test the specification formally are discussed. >

Journal ArticleDOI
TL;DR: Key-stream generators are discussed in which shift registers are clocked in a quasi-random manner under the control of other shift registers, and it is shown how large periods and linear equivalences can readily be obtained.
Abstract: Key-stream generators are discussed in which shift registers are clocked in a quasi-random manner under the control of other shift registers. They are a promising practical alternative to those using nonlinear combining functions on the outputs from regularly stepped shift registers and are now almost as well understood. Some World War II ciphers using stuttered rotors are briefly described as natural predecessors, including one cryptanalyzed on the Colossus machines. The algebraic theory is discussed, from which it is shown how large periods and linear equivalences can readily be obtained. The work of a number of authors on cascades is reviewed; these are linear hierarchies in which each register except the first is clock controlled by its predecessor. Other schemes are considered. Results on statistical properties and autocorrelation functions are quoted. >

Journal ArticleDOI
TL;DR: The authors present a simulation study of an adaptive receiver, based on the concept of maximum-likelihood sequence estimation (MLSE), which compensates for the heavy selective distortions caused by multipath propagation.
Abstract: The authors present a simulation study of an adaptive receiver, based on the concept of maximum-likelihood sequence estimation (MLSE), which compensates for the heavy selective distortions caused by multipath propagation. The receiver includes a matched filter and a modified Viterbi processor and is suitable for implementation in a digital form. It operates adaptively, in a training mode at the beginning of each burst, as well as in a tracking mode during message detection. This makes the receiver robust both to fast Doppler shifts and to a large frequency offset. Simulation results are presented which show the performance in different multipath environments, with echo delay in excess of 20 mu s and vehicle speed up to 250 km/h. >

Journal ArticleDOI
TL;DR: A prototype model of a video codec was developed that demonstrates the feasibility of both variable bit rate (VBR) coding and user-selectable picture quality.
Abstract: The bandwidth flexibility offered by the asynchronous transfer mode (ATM) technique makes it possible to select picture quality and bandwidth over a wide range in a simple and straightforward manner. A prototype model of a video codec was developed that demonstrates the feasibility of both variable bit rate (VBR) coding and user-selectable picture quality. The VBR coding algorithm is discussed and it is shown how a stabilized quality is achieved and how this quality and associated bandwidth can be selected by the user. How error propagation is limited to reduce the visibility of cell losses is also discussed. Interfaces with the ATM network are analyzed, with emphasis on decoder synchronization and absorption of cell delay jitter. The VBR codec offers very good picture quality for videophony applications at an equivalent load of 5.9 Mb/s. Picture quality remains relatively constant, even for heavy motion. >

Journal ArticleDOI
TL;DR: An algorithm to compute the distance spectrum of linear, regular, and quasiregular trellis codes is presented, derived from a bidirectional stack algorithm, although it could also be based on the Viterbi algorithm.
Abstract: A class of quasiregular codesis defined for which the distance spectrum can be calculated from the codeword corresponding to the all-zero information sequence. Convolutional codes and regular codes are both quasiregular, as well as most of the best known trellis codes. An algorithm to compute the distance spectrum of linear, regular, and quasiregular trellis codes is presented. In particular, it can calculate the weight spectrum of convolutional (linear trellis) codes and the distance spectrum of most of the best known trellis codes. The codes do not have to be linear or regular, and the signals do not have to be used with equal probabilities. The algorithm is derived from a bidirectional stack algorithm, although it could also be based on the Viterbi algorithm. The algorithm is used to calculate the beginning of the distance spectrum of some of the best known trellis codes and to compute tight estimates on the first-event-error probability and on the bit-error probability. >

Journal ArticleDOI
TL;DR: In this paper, the effects of capture on the average system throughput and delay performance of slotted ALOHA were analyzed for slow and fast Rayleigh fading radio channels for a short-range multipoint-to-base station packet radio network.
Abstract: The effects of capture on the average system throughput and delay performance of slotted ALOHA were analyzed for slow and fast Rayleigh fading radio channels. A short-range multipoint-to-base station packet radio network is considered. It is shown that larger capture effects and thus improved network performance can be achieved with proper choice of modulation. It is also shown that the use of simple error-correcting codes improves capture. The use of selection diversity also improves the capture effect both for fast and slow fading. It is concluded that the inverse distance variability of the received signal is the main reason for the capture effect. The Rayleigh fading alone yields a very small contribution in terms of throughput; nonetheless, it helps to stabilize the system. Numerical results are presented for a slotted ALOHA system with 50 users. It is found that the maximum average throughput can be increased from about 36% to almost 60% by using channel coding and space diversity. >

Journal ArticleDOI
TL;DR: It is shown that for some test cases the congestion measure is substantially reduced with respect to the values obtained when the embedded topology is kept identical to the backbone topology.
Abstract: The design of a P/S network embedded into a backbone facility network is discussed. The problem is formulated as a network optimization problem where a congestion measure based on the average packet delay is minimized, subject to capacity constraints posed by the underlying facility trunks. The variables in this problem are the routing on the express pipes (i.e. the channels that interconnect the P/S modes) and the allocation of bandwidth to such pipes. An efficient algorithm is presented for the solution of the above problem and it is applied to some representative examples. It is shown that for some test cases the congestion measure is substantially reduced with respect to the values obtained when the embedded topology is kept identical to the backbone topology. Dynamic reconfiguration schemes where the embedded topology is periodically adjusted to track the fluctuations in traffic requirements are discussed. >

Journal ArticleDOI
R. de Buda1
TL;DR: It is demonstrated that optimal codes need not be random, but rather that some of them have structure, e.g. the structure of a lattice code.
Abstract: The techniques of the geometry of numbers, especially the Minkowski-Hlawka theorem, are used to modify Shannon's existence proof for optimal channel codes, so that the modified proof applies specifically to lattice codes. The resulting existence proof states that there exist lattice codes which satisfy Shannon's bound to within the factor 4, and hence match the reliability exponent and critical rate bounds which Shannon derived for optimal codes with unspecified structure. Therefore, it is demonstrated that optimal codes need not be random, but rather that some of them have structure, e.g. the structure of a lattice code. >

Journal ArticleDOI
TL;DR: Methods of implementing public key algorithms based on modular integer arithmetic (RSA) and finite-field arithmetic (Diffie-Hellman, El Gamal) and architecture for VLSI implementations are examined.
Abstract: Methods of implementing public key algorithms based on modular integer arithmetic (RSA) and finite-field arithmetic (Diffie-Hellman, El Gamal) are examined. Architectures for VLSI implementations are emphasized. >

Journal ArticleDOI
TL;DR: A 24-dimensional block code based on the Leech lattice is described for use in a 19200-b/s modem and encoding plus decoding was successfully programmed for an ADSP2100 signal processor requiring altogether slightly less than one half the processing capability.
Abstract: A 24-dimensional block code based on the Leech lattice is described for use in a 19200-b/s modem. Encoding (the process of converting binary data into message point coordinates) and detection (conversion of the received coordinates into the coordinates of the nearest code point of the lattice) are described. Decoding (the further conversion of these into binary data) is not described, since it consists of an easily achieved reversal of the encoding process. Block (1000-bit-length) error rates in the presence of white noise for baud rates of 2400 and 2743, the two baud rates at which the modem can operate, are presented. Encoding plus decoding was successfully programmed for an ADSP2100 signal processor requiring altogether slightly less than one half the processing capability. >