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Information Theory Workshop, 2005 IEEE

Date Aug. 29 2005-Sept. 1 2005

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  • Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity

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  • Copyright

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  • Welcome from the co-chairs

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  • Committee members

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  • Finite-length scaling of irregular LDPC code ensembles

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    We investigate the finite-length scaling methodology for irregular LDPC code ensembles when transmission takes place over the binary erasure channel (BEC). We first show how the necessary computations, namely the covariance evolution and the computation of the finite-length shift, can be accomplished in the irregular case. We then investigate how the obtained approximation can be used to predict the performance of irregular code ensembles and to optimize the degree distributions for finite-length codes. View full abstract»

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  • BEAST decoding - asymptotic complexity

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    BEAST is a bidirectional efficient algorithm for searching trees that performs soft-decision maximum-likelihood (ML) decoding of block codes. The decoding complexity of BEAST is significantly reduced compared to the Viterbi algorithm. An analysis of the asymptotic BEAST decoding complexity verifies BEAST's high efficiency compared to other algorithms. The best of the obtained asymptotic upper bounds on the BEAST decoding complexity is better than previously known bounds for ML decoding in a wide range of code rates. View full abstract»

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  • Table of contents

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  • Symbol-by-symbol detection of space-time coded continuous phase modulated signals over fast Rayleigh fading channels

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    We investigate the detection of space time coded (STC) signals modulated using continuous phase modulation (CPM) in fast Rayleigh fading channels. A symbol-by-symbol iterative detector with an optimum front-end is derived, and its practical implementation using the concept of principal component analysis (PCA) is considered. To assess the performance, numerical examples for different STC-CPM schemes are presented. According to the simulation results, the proposed detector obtains very good power efficiencies. Moreover, the bit error rate (BER) performance of the proposed detector is in the range of 0.5-1 dB from the case without fading, highlighting its effectiveness to mitigate fading. View full abstract»

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  • Author list

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  • Rate-compatible path-pruned convolutional codes and their applications on channels with insertion, deletion and substitution errors

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    A concatenated system is presented to achieve unequal error protection (UEP) on a channel with insertion/deletion/substitution (IDS) errors. By using a feedback-mapping encoder scheme, the path-pruning of a convolutional code is achieved to periodically generate a specific block code, which can be exploited to correct insertion or deletion errors. This paper presents a general means to obtain a path-pruned convolutional code with specific trellis structure by using the puncturing and pruning processes. One application combining the rate-compatible path-pruned convolutional code, partial interleaving, and Reed-Solomon code was implemented to evaluate its performance on the IDS channel. View full abstract»

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  • Duality between packings and coverings of the Hamming space

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    We investigate the packing and covering densities of linear and nonlinear binary codes, and establish a number of duality relationships between the packing and covering problems. Specifically, we prove that if almost all codes are good packings, then only a vanishing fraction of codes are good coverings, and vice versa: if almost all codes are good coverings, then at most a vanishing fraction of codes are good packings. We also show that any specific maximal binary code is either a good packing or a good covering, in a certain well-defined sense. View full abstract»

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  • Interference management via capacity-achieving codes for the deterministic broadcast channel

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    We motivate the consideration of deterministic broadcast channel coding as an interference management technique in wireless scenarios. We address practical coding strategies for such channels and discuss two approaches. The first relies upon enumerative source coding and can be applied for any deterministic broadcast channel problem as the first step in pipelined encoding for vertex rates. The second approach addresses a wireless interference management scenario and is a complete, practical, capacity-achieving strategy that dualizes the Luby transform code construction and encoding/decoding algorithms. This results in the first practical, nontrivial, capacity achieving code construction for the deterministic broadcast channel. View full abstract»

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  • Fisher information matrix and hyperbolic geometry

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    The Fisher information matrix induces a metric on parametric spaces of families of probability density functions. We analyse here the family of normal distributions showing how hyperbolic geometry arises naturally from the Fisher information metric. View full abstract»

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  • Periodic Oppermann sequences for spread spectrum systems

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    In this paper we introduce periodic Oppermann sequences, which constitute a special class of polyphase sequences. The properties of these sequences are presented, and indicate that periodic Oppermann sequences are suitable for combination to generate families of longer sequences. Numerical examples show that periodic Oppermann sequences can be designed for ranging or synchronisation applications or for supporting multiple access spread spectrum communication systems. View full abstract»

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  • Steepest descent as message passing

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    It is shown how steepest descent (or steepest ascent) may be viewed as a message passing algorithm with "local" message update rules. For example, the well-known backpropagation algorithm for the training of feedforward neural networks may be viewed as message passing on a factor graph. The factor graph approach with its emphasis on "local" computations makes it easy to combine steepest descent with other message passing algorithms such as the sum/max-product algorithms, expectation maximization, Kalman filtering/smoothing, and particle filters. As an example, parameter estimation in a state space model is considered. For this example, it is shown how steepest descent can be used for the maximization step in expectation maximization. View full abstract»

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  • Bounds on the performance of sphere decoding of linear block codes

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    A sphere decoder searches for the closest lattice point within a certain search radius. The search radius provides a tradeoff between performance and complexity. We derive tight upper bounds on the performance of sphere decoding of linear block codes. The performance of soft-decision sphere decoding on AWGN channels as well as that of hard-decision sphere decoding on binary symmetric channels is analyzed. View full abstract»

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  • Asymptotically optimum detection for large wireless networks with fading

    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (363 KB) |  | HTML iconHTML  

    This paper proves that CDMA with beam forming single user detection (SUD-CDMA) is asymptotically optimum, even if it is done on a user by user basis (naive CDMA), for many large wireless networks in the presence of unknown fading. The paper models the transmitters and receivers as uniformly distributed over a grid in a 3-D, 2-D or 1-D universe and allows every transmitter to broadcast to all receivers with a power inversely proportional to the second, third or the fourth power of its distance from the receiver. The channel between the transmitters and the receivers is a fading channel where the receivers do not have any knowledge of the fading realizations. The introduction of unknown fading (even if very slow) and interference from all the transmitters make the model and hence the result of this paper fundamentally different from previous results. The paper proves that, when the number of users increases while keeping the network expanse constant SUD-CDMA is optimal irrespective of the geometry of the network or the path loss exponent. When the number of users increases while keeping the network density constant SUD-CDMA is optimal for most geometries when the path loss exponent is low. View full abstract»

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  • The multivariate merit factor of a Boolean function

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    A new metric, the multivariate merit factor (MMF) of a Boolean function, is presented, and various infinite recursive quadratic sequence constructions are given for which both univariate and multivariate merit factors can be computed exactly. In some cases these constructions lead to merit factors with non-vanishing asymptotes. A formula for the average value of 1/MMF is derived and a characterisation of the MMF in terms of cryptographic differentials is discussed. View full abstract»

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  • Bounds on signature coding for fast frequency hopping with asynchronous access

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    Signature coding for fast frequency hopped channel is studied, where the bandwidth is partitioned into frequency subbands. A frequency hopping pattern is assigned to each user that specifies the sequence of frequency subbands in which the user can transmit a sinus waveform during a time slot. Partial activity is considered where only a small fraction of the potential users may be active simultaneously. We prove that in frame asynchronous case the upper bound on the minimum code length via random coding is asymptotically the same as in the case of synchronous access. View full abstract»

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  • Maximum entropy and the Edgeworth expansion

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    For sums of i.i.d. random variables the maximum entropy distribution with respect to the first moments fixed is compared with the Edgeworth expansion. It is demonstrated that the Edgeworth expansion can and shall be considered as a linear extrapolation of the maximum entropy distribution. The coefficients in the Edgeworth expansion can be used as a first approximation for numerical calculation of the maximum entropy distribution. View full abstract»

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  • New monomial bent functions over the finite fields of odd characteristic

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    We consider p-ary bent functions having the form f(x) = Trn (axd). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. We also discuss the (weak) regularity of our new as well as of known monomial bent functions and give the first example of a not weakly regular bent function. View full abstract»

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  • A finite-field transform domain construction of binary low-density parity-check codes

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    A new method of finding binary cyclic codes from the finite-field transform domain is presented. These cyclic codes have sparse parity-check matrix and thus are suitable for iterative decoding. Some interesting properties of the proposed construction method include the knowledge of the minimum distance and the ability to trade the increase in code dimension with a reduction in the parity-check matrix sparsity. By means of simulations, we show that the error correcting performance of the codes under iterative decoding is very close to the sphere-packing-bound constrained for binary transmission. View full abstract»

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  • Correlation analysis of random number sequences based on pseudo random binary sequence generation

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    In this paper, the hardware structural correlation effects associated with digit pick-off positions on a maximal length linear feedback shift register (LFSR) in random number (RN) generation, based on a pseudorandom binary sequence (PRBS), are examined using the RN autocorrelation function (ACF). The ACF of the RN codeword sequence is derived analytically from the known noise-like autocorrelation property of the parent PRBS and is then employed to elucidate any structural deficiencies in the choice of digit pickoff points made from the underlying LFSR. Various permutations of the LFSR pickoff selection in the binary code weight assignment for RN construction are examined in the search of an optimal RN spike-like ACF akin to that for a PRBS. Results are presented for ACF evaluation for different binary weight pickoff topologies using RN simulation from a parent PRBS stream, which are in excellent agreement with theoretical calculations. View full abstract»

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  • Capacity of M-ary 2-D RLL constraints for optical recording channels

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    A new class of M-ary two-dimensional (2-D) run-length limited (RLL) constraints is introduced in this paper. In particular, only RLL d constraints on 2D m × n arrays with limited height m are considered. Column vectors of 2-D arrays are used as states in a directed graph. The transfer matrix of the graph is obtained with consideration of non-binary alphabet, and the largest eigenvalue of the transfer matrix is used to calculate the capacity of 2-D (M, d, ∞) RLL constraints on 2-D arrays. Some numerical results are derived for RLL d = 1 and d = 2 constraints. We also present an example of efficient finite-state encoder for d = 1 constraint by state splitting and merging algorithm. The 2-D (M, d, ∞) constrained codes have potential to be applied in advanced 2-D optical recording channels. View full abstract»

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  • Iterative list decoding

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    We analyze the relation between iterative decoding and the properties of the extended parity check matrix. By considering a modified version of bit flipping, which produces a list of decoded words, we derive several relations between decodable error patterns and parameters of the code. By developing a tree of codewords at minimal distance form the received vector, we also obtain new information about the code. View full abstract»

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