Optical intensity-modulated direct detection channels: signal space and lattice codes

Traditional approaches to constructing constellations for electrical channels cannot be applied directly to the optical intensity channel. This work presents a structured signal space model for optical intensity channels where the nonnegativity and average amplitude constraints are represented geometrically. Lattice codes satisfying channel constraints are defined and coding and shaping gain relative to a baseline are computed. An effective signal space dimension is defined to represent the precise impact of coding and shaping on bandwidth. Average optical power minimizing shaping regions are derived in some special cases. Example lattice codes are constructed and their performance on an idealized point-to-point wireless optical link is computed. Bandwidth-efficient schemes are shown to have promise for high data-rate applications, but require greater average optical power.     

Early detection and trellis splicing: reduced-complexity iterativedecoding

The bit-error rate (BER) performance of new iterative decoding algorithms (e,g,, turbodecoding) is achieved at the expense of a computationally burdensome decoding procedure. We present a method called early detection that can be used to reduce the computational complexity of a variety of iterative decoders. Using a confidence criterion, some information symbols, state variables, and codeword symbols are detected early on during decoding. In this way, the computational complexity of further processing is reduced with a controllable increase in the BER. We present an easily implemented instance of this algorithm, called trellis splicing, that can be used with turbodecoding. For a simulated system of this type, we obtain a reduction in the computational complexity of up to a factor of four, relative to a turbodecoder that obtains the same increase in the BER by performing fewer iterations     

Higher bit rates for dispersion-managed soliton communication systems via constrained coding

Constrained coding as a method to increase the data rate in dispersion-managed soliton (DMS) communication systems is proposed. This approach is well known and widely used in the context of magnetic and optical recording systems. This paper shows that it is also applicable to DMS systems due to certain similarities between the underlying physical channels. Since timing jitter is an important error-generating mechanism for solitons, a coding scheme specifically designed to combat pulse shifts is also presented, and its properties in the framework of a particular information-theoretic channel model are analyzed. A connection between the model used and the real physical channel is then established. Next, the coded system is compared with the original one from the channel capacity point of view with the help of numerical examples. Finally, the fact that the application of constrained coding may alleviate soliton pulse-to-pulse interaction is exploited. This, in turn, opens the door to the usage of higher-than-usual map strengths and ultimately leads to a significant increase of up to 50% in the bit rate.     

A more accurate one-dimensional analysis and design of irregular LDPC codes

We introduce a new one-dimensional (1-D) analysis of low-density parity-check (LDPC) codes on additive white Gaussian noise channels which is significantly more accurate than similar 1-D methods. Our method assumes a Gaussian distribution in message-passing decoding only for messages from variable nodes to check nodes. Compared to existing work, which makes a Gaussian assumption both for messages from check nodes and from variable nodes, our method offers a significantly more accurate estimate of convergence behavior and threshold of convergence. Similar to previous work, the problem of designing irregular LDPC codes reduces to a linear programming problem. However, our method allows irregular code design in a wider range of rates without any limit on the maximum variable-node degree. We use our method to design irregular LDPC codes with rates greater than 1/4 that perform within a few hundredths of a decibel from the Shannon limit. The designed codes perform almost as well as codes designed by density evolution.     

Feedback Quantization Strategies for Multiuser Diversity Systems

In a system utilizing multiuser diversity, regular feedback of channel-quality predictions to the base station is required for each user. Typically, the measure of channel quality must be quantized at each mobile station before it can be sent back. In this paper, we present two distributed scalar quantization schemes that optimize two different performance criteria: a) the minimization of the probability P _e of incorrectly identifying the user with the best channel quality and b) maximization of the resulting throughput R. For a typical Rayleigh-fading system with 30 users per sector, numerical optimization results show that the P_e and R realized by the uniform quantization strategy with 16 quantization levels for each user can be achieved by only three quantization levels using the two proposed strategies. A practical approximation of the proposed schemes is studied and is shown to provide near-optimal performance for both performance criteria as the number of quantization levels becomes large     

Tanner graphs for group block codes and lattices: construction andcomplexity

We develop a Tanner graph (TG) construction for an Abelian group block code L with arbitrary alphabets at different coordinates, an important application of which is the representation of the label code of a lattice. The construction is based on the modular linear constraints imposed on the code symbols by a set of generators for the dual code L*. As a necessary step toward the construction of a TG for L we devise an efficient algorithm for finding a generating set for L*. In the process, we develop a construction for lattices based on an arbitrary Abelian group block code, called generalized Construction A (GCA), and explore relationships among a group code, its GCA lattice, and their duals. We also study the problem of finding low-complexity TGs for Abelian group block codes and lattices; and derive tight lower bounds on the label-code complexity of lattices. It is shown that for many important lattices, the minimal label codes which achieve the lower bounds cannot be supported by cycle-free Tanner graphs     

Gallager codes for CDMA applications. II. Implementations, complexity, and system capacity

We focus our attention on Gallager codes with parameters compatible with the IS-95 cellular radio standard. We discuss low complexity software and hardware implementations of an iterative decoder for {N,-,3} Gallager codes. We estimate that by using Gallager codes, a factor of five improvement in the code-division multiple-access system capacity relative to an uncoded system can be achieved, equivalent to a factor of two improvement relative to state-of-the art orthogonal convolutional codes. Simulation results demonstrate the good performance of short-frame Gallager codes in the additive white Gaussian noise and certain fading channels.     

The helical window token ring

An access rule for token ring local-area networks called the helical-window token-ring protocol is introduced. It features the use of a window that limits the allowable messages a token-holding station can send. With the window, the operation of the protocol approaches that of a central single-server queuing system in the sense that messages are delivered in near first-come-first-served order on a network-wide basis. The introduction of the window also makes analysis of the networks tractable. Exact analytical formulas for the capacity and for the mean, variance, and moment-generating function of the message waiting time are derived. Numerical simulation is used to verify the results. Comparisons with continuous polling systems show that the imposition of the windowed access rule can lead to significant reductions in the delay variance (at the cost of increasing the mean system time) when the traffic is heavy and/or the message transmission time is large with respect to the walk time of the ring     

On factor graphs and the Fourier transform

We introduce the concept of convolutional factor graphs, which represent convolutional factorizations of multivariate functions, just as conventional (multiplicative) factor graphs represent multiplicative factorizations. Convolutional and multiplicative factor graphs arise as natural Fourier transform duals. In coding theory applications, algebraic duality of group codes is essentially an instance of Fourier transform duality. Convolutional factor graphs arise when a code is represented as a sum of subcodes, just as conventional multiplicative factor graphs arise when a code is represented as an intersection of supercodes. With auxiliary variables, convolutional factor graphs give rise to "syndrome realizations" of codes, just as multiplicative factor graphs with auxiliary variables give rise to "state realizations." We introduce normal and co-normal extensions of a multivariate function, which essentially allow a given function to be represented with either a multiplicative or a convolutional factorization, as is convenient. We use these function extensions to derive a number of duality relationships among the corresponding factor graphs, and use these relationships to obtain the duality properties of Forney graphs as a special case.