Costas N. Georghiades

Compression of binary sources with side information at the decoder using LDPC codes

We show how low-density parity-check (LDPC) codes can be used to compress close to the Slepian-Wolf limit for correlated binary sources. Focusing on the asymmetric case of compression of an equiprobable memoryless binary source with side information at the decoder, the approach is based on viewing the correlation as a channel and applying the syndrome concept. The encoding and decoding procedures are explained in detail. The performance achieved is seen to be better than recently published results using turbo codes and very close to the Slepian-Wolf limit.

Sequence estimation in the presence of random parameters via the EM algorithm

The expectation-maximization (EM) algorithm was first introduced in the statistics literature as an iterative procedure that under some conditions produces maximum-likelihood (hit) parameter estimates. In this paper we investigate the application of the EM algorithm to sequence estimation in the presence of random disturbances and additive white Gaussian noise. As examples of the use of the EM algorithm, we look at the random-phase and fading channels, and show that a formulation of the sequence estimation problem based on the EM algorithm can provide a means of obtaining ML sequence estimates, a task that has been previously too complex to perform.

On the Index Coding Problem and Its Relation to Network Coding and Matroid Theory

The index coding problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks. An instance of the index coding problem includes a sender that holds a set of information messages X={x1,...,xk} and a set of receivers R. Each receiver (x,H) in R needs to obtain a message x X and has prior side information consisting of a subset H of X . The sender uses a noiseless communication channel to broadcast encoding of messages in X to all clients. The objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers. In this paper, we analyze the relation between the index coding problem, the more general network coding problem, and the problem of finding a linear representation of a matroid. In particular, we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem. Our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem. Specifically, we show that vector linear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions.

Two EM-type channel estimation algorithms for OFDM with transmitter diversity

Combining Orthogonal Frequency Division Multiplexing (OFDM) with transmitter diversity can be used for capacity improvement in high-rate wireless data communication systems. For coherent detection in such systems, channel state information (CSI) is required. In this paper we investigate a Space-Alternating Generalized Expectation-Maximization (SAGE) algorithm to iteratively estimate the channel impulse responses associated with multiple transmitters and the receiver. The performance of the estimator is compared with a previously proposed Expectation-Maximization (EM) based algorithm in terms of convergence rate.

Exploiting faster-than-Nyquist signaling

Faster-than-Nyquist signaling introduces intersymbol interference, but increases the bit rate while preserving the signaling bandwidth. For sinc pulses, it has been established that with a small increase in the signaling rate beyond the Nyquist rate, there is no reduction in the minimum Euclidean distance for binary signaling. We generalize these observations to the family of raised-cosine pulses. The structure of the error events that reduce the minimum distance is examined, and constrained coding ideas are suggested that theoretically allow even faster signaling. Then we propose ways of achieving these gains practically by designing appropriate constrained codes and through equalization and iterative joint equalization and decoding (turbo equalization).

On code design for the Slepian-Wolf problem and lossless multiterminal networks

A Slepian-Wolf coding scheme for compressing two uniform memoryless binary sources using a single channel code that can achieve arbitrary rate allocation among encoders was outlined in the work of Pradhan and Ramchandran. Inspired by this work, we address the problem of practical code design for general multiterminal lossless networks where multiple memoryless correlated binary sources are separately compressed and sent; each decoder receives a set of compressed sources and attempts to jointly reconstruct them. First, we propose a near-lossless practical code design for the Slepian-Wolf system with multiple sources. For two uniform sources, if the code approaches the capacity of the channel that models the correlation between the sources, then the system will approach the theoretical limit. Thus, the great advantage of this design method is its possibility to approach the theoretical limits with a single channel code for any rate allocation among the encoders. Based on Slepian-Wolf code constructions, we continue with providing practical designs for the general lossless multiterminal network which consists of an arbitrary number of encoders and decoders. Using irregular repeat-accumulate and turbo codes in our designs, we obtain the best results reported so far and almost reach the theoretical bounds.

Product accumulate codes: a class of codes with near-capacity performance and low decoding complexity

We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalars (1999) simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2.

The expectation-maximization algorithm for symbol unsynchronized sequence detection

The expectation-maximization (EM) algorithm for maximizing likelihood functions, combined with the Viterbi algorithm, is applied to the problem of sequence detection when symbol timing information is not present. Although the EM algorithm is noncausal, results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations, making it both of theoretical and of practical interest. A practical algorithm based on the EM algorithm is introduced. It reduces the computational burden and improves performance by making use of timing estimates in previous observation windows. >

Joint source-channel coding of binary sources with side information at the decoder using IRA codes

We use systematic irregular repeat accumulate (IRA) codes as source-channel codes for the transmission of an equiprobable memoryless binary source with side information at the decoder. A special case of this problem is joint source-channel coding for a nonequiprobable memoryless binary source. The theoretical limits of this problem are given by combining the Slepian-Wolf theorem, the source entropy in the special case, with the channel capacity. The approach is based on viewing the correlation between the binary source output and the side information as a separate channel or an enhancement of the original channel. The joint source-channel encoding, decoding and code design procedures are explained in detail. The simulated performance results are better than the recently published solutions using turbo codes and very close to the theoretical limit.

Iterative maximum-likelihood sequence estimation for space-time coded systems

In previous work on decoding space-time codes, it is either assumed that perfect channel state information (CSI) is present, or a channel estimate is obtained using pilot symbols and then used as if it were perfect to extract symbol estimates. In the latter case, a loss in performance is incurred, since the resulting overall receiver is not optimal. We look at maximum-likelihood (ML) sequence estimation for space-time coded systems without assuming CSI. The log-likelihood function is presented for both-quasi-static and nonstatic fading channels, and an expectation-maximization (EM)-based algorithm is introduced for producing ML data estimates, whose complexity is much smaller than a direct evaluation of the log-likelihood function. Simulation results indicate the EM-based algorithm achieves a performance close to that of a receiver which knows the channel perfectly.