We prove that the Variational distance (and its positive multiples) is the only f-divergence that satisfies both the identity of indiscernibles and the triangle inequality. Therefore it is the unique f-divergence which serves as a metric. This point is interpreted as a fundamental confliction of the convexity for f(x) with the metric properties for its associated f-divergence. Therefore, we relax the convexity of f(x) and replace it with other constraints to create new metrics.

With the application of optical add-drop multiplexers, wavelength assignment has become an important issue in SONET/WDM design. Among wavelength assignment methods, circle construction is of great importance. In this paper, we propose a novel matrix based circle construction algorithm for all-to-all uniform traffic in a bidirectional SONET/WDM ring.

Partial transmit sequence (PTS) is a well known technique used to reduce the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) signal. However, it has relatively high complexity due to the computation of multiple inverse fast Fourier transforms (IFFTs). To reduce this complexity, we use intermediate signals within a decimation in frequency (DIF) radix IFFT and propose a new PTS subblocking technique which requires the computation of only partial IFFTs. Performance results are presented which show a PAPR reduction similar to that with other techniques such as original PTS (O-PTS). Further, we show that complexity reduction can be achieved with either low or high radix IFFT algorithms.

In this paper, we study the capacity and performance of nonorthogonal pulse position modulation (NPPM) for Ultra-Wideband (UWB) communication systems over both AWGN and IEEE802.15.3a channels. The channel capacity of NPPM is determined for a time-hopping multiple access UWB communication system. The error probability and performance bounds are derived for a multiuser environment. It is shown that with proper selection of the pulse waveform and modulation index, NPPM can achieve a higher capacity than orthogonal PPM, and also provide better performance than orthogonal PPM with the same throughput.

In this letter, it is shown that a MAP detector can be employed with differential pulse-position modulation (L-DPPM) in an indoor optical wireless system. The MAP detector error performance is evaluated and compared with that of a hard-decision detector and MLSD over an intersymbol interference channel. It is shown that a MAP detector provides superb performance even in a dispersive channel with high DT.

In this paper, the capacity and error probability of orthogonal space-time block codes (STBCs) are presented for PAM/PSK/QAM modulation in correlated flat fading channels. We consider an equivalent scalar AWGN (additive white Gaussian noise) channel with a channel gain proportional to the Frobenius norm of the matrix channel. A unified approach to the error probability analysis for correlated Rayleigh and Rician fading channels is presented. Closed form error probability expressions are derived for Rayleigh fading channels. We also determine the capacity and probability of error for a multiuser direct sequence code division multiple access (DS-CDMA) system employing a STBC over correlated fading channels.

In 2008, the authors and Makwakwa demonstrated a close link between variable-length T-codes and cyclic equivalence classes, which introduces a limit on the the number of codewords of a particular length that a T-code can have. This paper presents a collection of new results on the codeword length distribution of T-codes based on this link. In particular, the average and average weighted codeword lengths are investigated for systematic T-codes. Several results are presented on subsets of T-code codewords for which the aforementioned limit is reached, and asymptotic expressions are derived for the variance and the coefficient of variation of codeword length distributions.

In this paper, the average symbol error probability (SEP) performance of decode-and-forward (DF) relaying mobile-to-mobile (M2M) systems with transmit antenna selection (TAS) over N-Nakagami fading channels is investigated. The moment generating function (MGF) method is used to derive exact SEP expressions, and the analysis is verified via simulation. The optimal power allocation problem is investigated. Performance results are presented which show that the fading coefficient, number of cascaded components, relative geometrical gain, number of antennas, and power allocation parameter have a significant effect on the SEP.

Tone reservation (TR) has been proposed for peak to average power reduction (PAPR) in real-baseband multicarrier systems [1]. In this technique, the peak reduction signal is computed by optimization via linear programming (LP). As shown in [1], the computational complexity of the LP optimization is largely determined by the complexity of the inverse fast Fourier transform (IFFT) algorithm. In this paper, we use submatrices of the inverse fast Fourier transform (IFFT) to reduce the number of constraints in the LP-based optimization. We show that a significant complexity reduction can be achieved compared to the conventional TR algorithm, with similar PAPR reduction.

The performance of an orthogonal frequency division multiplexing (OFDM) system is degraded if the peak-to-average power ratio (PAPR) is high. In general, in order to obtain optimal PAPR reduction using the partial transmitted sequence (PTS) technique, an exhaustive search of the possible subblocks and rotation factors must be done. As the number of subblocks and rotation factors increases, PAPR reduction improves, but the computational load becomes impractical. In order to reduce the complexity while still improving the OFDM system performance, a new method using a genetic algorithm (GA) is proposed to find a set of rotation factors that reduces both the PAPR and the computational load. A comparison is made between the proposed method and previously developed techniques such as exhaustive and gradient descent PTS methods. The superiority of the proposed method is demonstrated as a reduction in computational load compared with exhaustive PTS and the gradient method, and an improvement in performance compared with the iterative and gradient methods.

Consider the source coding problem of finding the optimal code, in the sense of average redundancy, for the class of monotone sources with n symbols. The solution of this problem, known as the M code, is the Huffman code for the average distribution of the monotone sources. In this paper, we evaluate the average redundancy of the M code (on the class of monotone sources), and compare it with that of the Huffman code. It is demonstrated that for large n, although the M code is a fixed code (i.e., the codewords are independent of the symbol probabilities) for all monotone sources, its average redundancy is very close to that of the Huffman code. Moreover, it is shown that when n is large, the M code is a near-optimal code not only in the sense of average redundancy, but also the redundancy of almost all monotone sources. In particular, the redundancy of the M code converges in probability to its average value (0.029). As a result, the maximum redundancy of the M code, which can be as large as log n -log ln n, rarely occurs.

This letter considers the problem of detecting an offset quadrature phase shift keying (O-QPSK) modulated signal in colored Gaussian noise. The generalized likelihood ratio test (GLRT) is employed for detection. By deriving the GLRT, it is shown that the assumption of colored Gaussian noise results in a more complicated problem than with the white noise assumption that was previously examined in the literature. An efficient solution for the detection maximization problem is proposed, based on which the GLRT is implemented. Performance results are presented to illustrate the detector performance.