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This paper studies the diversity benefit of different interference alignment solutions. While most research about interference alignment was aiming at deriving or realizing the maximum achievable multiplexing gain, the symbol error rate performance, which can be characterized by the diversity gain is of equal importance. Different interference alignment solutions are classified into two categories called diversity interference alignment and zero-forcing interference alignment. Although these two types of solutions are not distinguishable in terms of the multiplexing gain, this paper will show their difference lies in the fact that they have different diversity gains. In this paper, a K-user (M\timesN) interference channel is used, with each user sending 1 degree of freedom of information by using interference alignment precoding and receiving filters but without space-time codes. The feasibility conditions for diversity interference alignment to be achieved are analyzed and the diversity orders different solutions can provide are compared. The results imply that diversity interference alignment solutions offer both multiplexing and diversity gains simultaneously. It also tells us two important rules about the interference alignment precoding filters design: an optimal design has to take both desired and interference channel matrices into consideration and the separation of interference alignment precoding filters design and space-time codes design may not be optimal in general. [ABSTRACT FROM PUBLISHER]

This paper focuses on conditional optimization as a decoding primitive for high rate space-time codes that are obtained by multiplexing in the spatial and code domains. The approach is a crystallization of the work of Hottinen et al. which applies to space-time codes that are assisted by quasi-orthogonality. It is independent of implementation and is more general in that it can be applied to space-time codes such as the Golden Code and perfect space-time block codes, that are not assisted by quasi-orthogonality, to derive fast decoders with essentially maximum likelihood (ML) performance. The conditions under which conditional optimization leads to reduced complexity ML decoding are captured in terms of the induced channel at the receiver. These conditions are then translated back to the transmission domain leading to codes that are constructed by multiplexing orthogonal designs. The methods are applied to several block space-time codes obtained by multiplexing Alamouti blocks where it leads to ML decoding with complexity O (N²) where N is the size of the underlying QAM signal constellation. A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML. The two design principles for perfect space-time codes are nonvanishing determinant of pairwise differences and cubic shaping, and it is cubic shaping that restricts the possible multiplexing structures. The new code shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity. [ABSTRACT FROM AUTHOR]

This paper introduces a new rate-2, full-diversity space-time code for four transmit antennas and one receive antenna. The 4 x 4 codeword matrix consists of four 2 x 2 Alamouti blocks with entries from Q (i, √5), and these blocks can be viewed as quaternions which in turn represent rotations in R3. The Alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron. This algebraic structure is different from the Golden code, but the complex entries are taken from a common underlying field. The minimum determinant is bounded below by a constant that is independent of the signal constellation, and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the E8 lattice. [ABSTRACT FROM AUTHOR]

We consider the "one-shot frame synchronization problem," where a decoder wants to locate a sync pattern at the output of a memoryless channel on the basis of sequential observations. The sync pattern of length N starts being emitted at a random time within some interval of size A, where A characterizes the asynchronism level. We show that a sequential decoder can optimally locate the sync pattern, i.e., exactly, without delay, and with probability approaching one as N → ∞, if the asynchronism level grows as O(eN α), with a below the synchronization threshold, a constant that admits a simple expression depending on the channel. If α exceeds the synchronization threshold, any decoder, sequential or nonsequential, locates the sync pattern with an error that tends to one as N → ∞. Hence, a sequential decoder can locate a sync pattern as well as the (nonsequential) maximum-likelihood decoder that operates on the basis of output sequences of maximum length A + N - 1, but with far fewer observations. [ABSTRACT FROM AUTHOR]

Since the standard union bound for space-time codes may diverge in quasi-static fading channels, the limit-before-average (LBA) technique has been exploited to derive tight performance bounds. However, it suffers from the computational burden arising from a multidimensional integral. In this paper, efficient bounding techniques for space-time codes are developed in the framework of Gallager bounds. Two closed-form upper bounds, the ellipsoidal bound and the spherical bound, are proposed that come close to simulation results within a few tenths of a decibel. In addition, two novel methods of weight enumeration operating on a further reduced state diagram are presented, which, in conjunction with the bounding techniques, give a thorough treatment of performance bounds for space-time codes. [ABSTRACT FROM AUTHOR]

There exist two important design criteria for unitary space time codes. In the situation where the signal-to-noise ratio (SNR) is large the diversity product (DP) of a constellation should be as large as possible. It is less known that the diversity sum (DS) is a very important design criterion for codes working in a low SNR environment. So far, no general method to design good-performing constellations with large diversity for any number of transmit antennas and any transmission rate exists. In this correspondence, we propose constellations with suitable structures, which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. The presented design methods work for any dimensional constellation and for any transmission rate. [ABSTRACT FROM AUTHOR]

One approach to designing structured low-density parity-cheek (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in short cycles. This approach is especially effective if the parity-check matrix of a code is a matrix composed of blocks of circulant permutation matrices, as is the case for the class of codes known as array codes. We show how to shorten array codes by deleting certain columns of their parity-check matrices so as to increase their girth. The shortening approach is based on the observation that for array codes, and in fact for a slightly more general class of LDPC codes. the cycles in the corresponding Tanner graph are governed by certain homogeneous linear equations with integer coefficients. Consequently, we can selectively eliminate cycles from an array code by only retaining those columns from the parity-check matrix of the original code that are indexed by integer sequences that do not contain solutions to the equations governing those cycles. We provide Ramsey-theoretic estimates for the maximum number of columns that can be retained from the original parity-check matrix with the property that the sequence of their indices avoid solutions to various types of cycle-governing equations. This translates to estimates of the rate penalty incurred in shortening a code to eliminate cycles. Simulation results show that for the codes considered, shortening them to increase the girth can lead to significant gains in signal-to-noise ratio (SNR) in the case of communication over an additive white Gaussian noise (AWGN) channel. [ABSTRACT FROM AUTHOR]

A new lower bound for the distance of cyclic codes is proposed. This bound depends on the defining set of the code, like several other bounds. The proposed bound improves upon the Bose-Chaudhuri-Hocquehghen (BCH) bound and, for some codes, improves upon the Hartmann-Tzeng bound and the Roos bound as well. [ABSTRACT FROM AUTHOR]

A high-resolution time-to-digital converter (TDC) implemented in a general purpose field-programmable-gate-array (FPGA) is presented. Dedicated carry lines of an FPGA are used as delay cells to perform time interpolation within the system clock period and to realize the fine time measurement. Two Gray-code counters, working on in-phase and out-of-phase system clocks respectively, are designed to get the stable value of the coarse time measurement. The fine time code and the coarse time counter value, along with the channel identifier, are then written into a first-in first-out (FIFO) buffer. Tests have been done to verify the performance of the TDC. The resolution after calibration can reach 50 Ps. [ABSTRACT FROM AUTHOR]