Eado Meron

Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss

We evaluate the advantage of using space-time coding in order to increase the tolerance of fiber-optic communications systems to polarization-dependent loss (PDL). Focusing on three particular codes, the Golden Code, the Silver Code (SC), and the Alamouti Code (AC), we calculate the amount of average PDL that can be tolerated for a given signal-to-noise ratio margin that is designed into the system. The SC is shown to be optimal in the case of low to moderate PDL, whereas, in the case of extreme PDL, the AC shows the best performance.

Finite-memory universal prediction of individual sequences

The problem of predicting the next outcome of an individual binary sequence under the constraint that the universal predictor has a finite memory, is explored. In this analysis, the finite-memory universal predictors are either deterministic or random time-invariant finite-state (FS) machines with K states (K-state machines). The paper provides bounds on the asymptotic achievable regret of these constrained universal predictors as a function of K, the number of their states, for long enough sequences. The specific results are as follows. When the universal predictors are deterministic machines, the comparison class consists of constant predictors, and prediction is with respect to the 0-1 loss function (Hamming distance), we get tight bounds indicating that the optimal asymptotic regret is 1/(2K). In that case of K-state deterministic universal predictors, the constant predictors comparison class, but prediction is with respect to the self-information (code length) and the square-error loss functions, we show an upper bound on the regret (coding redundancy) of O(K/sup -2/3/) and a lower bound of /spl Theta/(K/sup -4/5/). For these loss functions, if the predictor is allowed to be a random K-state machine, i.e., a machine with random state transitions, we get a lower bound of /spl Theta/(1/K) on the regret, with a matching upper bound of O(1/K) for the square-error loss, and an upper bound of O(logK/K) Throughout the paper for the self-information loss. In addition, we provide results for all these loss functions in the case where the comparison class consists of all predictors that are order-L Markov machines.

Capacity limitations in fiber-optic communication systems as a result of polarization-dependent loss

We characterize the effect of polarization dependent loss (PDL) on the information capacity of fiber-optic channels. The reduction in the outage capacity owing to the PDL is quantified as well as the signal-to-noise ratio margin that needs to be allocated for the PDL in order to avoid loss of capacity.

Optical implementation of a space–time-trellis code for enhancing the tolerance of systems to polarization-dependent loss

We propose a space-time coding scheme designed to increase the tolerance of fiber-optic communications systems to polarization-dependent loss (PDL). A notable increase in the tolerable amount of average link PDL is achieved without affecting the complexity of the overall optical communications link. Other advantages include seamless integration with the broadly deployed blind equalization modules relying on the constant modulus algorithm.

Delay and Redundancy in Lossless Source Coding

The penalty incurred by imposing a finite delay constraint in lossless source coding of a memoryless source is investigated. It is well known that for the so-called block-to-variable and variable-to-variable codes, the redundancy decays at best polynomially with the delay, where in this case the delay is identified with the source block length or maximal source phrase length, respectively. In stark contrast, it is shown that for sequential codes (e.g., a delay-limited arithmetic code) the redundancy can be made to decay exponentially with the delay constraint. The corresponding redundancy-delay exponent is shown to be at least as good as the Rényi entropy of order 2 of the source, but (for almost all sources) not better than a quantity depending on the minimal source symbol probability and the alphabet size.

Optimal finite state universal coding of individual sequences

The problem of assigning a probability to the next outcome of an individual binary sequence under the constraint that the universal predictor has a finite number of states, is explored. The two main loss functions that are considered are the square error loss and the self-information loss. Universal prediction w.r.t. the self-information loss can be combined with arithmetic encoding to construct a universal encoder, thus explores the universal coding problem. The performance of randomized time-invariant K-state universal predictors, and provide performance bounds in terms of the number of states K for long enough sequences is analyzed. In the case where the comparison class consists of constant predictors for the square error loss, the tight bounds indicating that the optimal asymptotic expected redundancy is O(1/K) is provided. An upper bound on the coding redundancy of O((log K)/K) and a lower bound of O(1/K) is shown for the self-information loss.

Increasing the PDL tolerance of systems by use of the Golden-code

We demonstrate a large improvement in the tolerance of coherent polarization-multiplexed systems to polarization-dependent loss (PDL), that is achieved by use of a space-time code known as the Golden-code.

Bounds on Redundancy in Constrained Delay Arithmetic Coding

We address the problem of a finite delay constraint in an arithmetic coding system. Due to the nature of the arithmetic coding process, source sequences causing arbitrarily large encoding or decoding delays exist. Therefore, to meet a finite delay constraint, it is necessary to intervene with the normal flow of the coding process, e.g., to insert fictitious symbols. This results in an inevitable coding rate redundancy. In this paper, we derive an upper bound on the achievable redundancy for a memoryless source. We show that this redundancy decays exponentially as a function of the delay constraint, and thus it is clearly superior to block to variable methods in that aspect. The redundancy-delay exponent is shown to be lower bounded by log(1/alpha), where alpha is the probability of the most likely source symbol. Our results are easily applied to practical problems such as the compression of English text

Beneficial use of spectral broadening resulting from the nonlinearity of the fiber-optic channel

We discuss the possibility of exploiting spectral broadening resulting from fiber nonlinearity for the transmission of information. The spectral broadening induced by nonlinearity combined with the appropriate waveform can turn quadrature amplitude modulation-like constellations into frequency-shift-keying constellations over a much larger dimension. Thus, the Kerr effect can be thought of as a large dimensional mapper/modulator. A simple single-span fiber-optic link implemented over dispersion shifted fiber is assumed for the demonstration of the principle. It is shown that for a particular constellation the achievable data rates in the presence of nonlinearity can be significantly higher than the capacity characterizing a linear channel with the same input bandwidth.

Multi-relay regeneration for long haul communications

A concatenated additive white gaussian noise (AWGN) relay channel is considered. The different relays are only allowed to carry out simple symbol manipulation (e.g. hard limiter, linear amplifier or any symbol-wise analog scheme). The decay of the overall capacity as a function of the number of concatenated relays is explored. Contrary to point-to-point channels, where using a refined constellation can only increase the capacity, we show that the larger the constellation the faster the capacity decays. Since the initial point-to-point capacity of refined constellations is larger and their decay is faster, there is a tradeoff that leads to an optimal constellation size which is a function of the SNR and the number of relays.