Showing papers presented at "Information Theory Workshop in 2001"

Coding for relay channels with confidential messages

Abstract: We consider a relay channel where a relay helps the transmission of messages from one sender to one receiver. The relay is considered not only as a sender that helps the message transmission but as a wire-tapper who can obtain some knowledge about the transmitted messages. In this paper we study the coding problem of the relay channel under the situation that some of transmitted messages are confidential to the relay. A security of such confidential messages is measured by the conditional entropy. We derive an explicit inner bound of the capacity region characterized with the set of transmission rates for which messages are reliably transmitted and the security of confidential messages is larger than a prescribed level.

The advantages of non-binary turbo codes

Abstract: Non-binary turbo codes are built from recursive systematic convolutional (RSC) component codes with m inputs (m/spl ges/2). This construction offers better performance than classical binary turbo codes, especially at very low BER and high coding rate. Some examples with rate 2/3 are given on 8-state and 16-state duo-binary turbo code associated with QPSK and 8-PSK modulation.

Regular low-density parity-check codes from combinatorial designs

Abstract: Analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. We construct (3, /spl rho/)-regular codes whose Tanner graph is free of 4-cycles for any integer /spl rho/, and examine girth and minimum distance properties of several classes of LDPC codes obtained from combinatorial designs.

An upper bound on the capacity of channels with memory and constraint input

Abstract: A method for computing upper bounds on capacity for a class of time-invariant indecomposable finite state channels is presented. It extends a result for finite-input memoryless channels. Numerical results are provided for selected channels having memory and constraint (binary) input.

Dense multiple antenna systems

Abstract: We consider multiple antenna systems in which a large number of antennas occupy a given physical volume. In this regime the assumptions of the standard models of multiple antennas systems become questionable. We show that for such spatially dense multiple antenna systems one should expect the behavior of the capacity to be qualitatively different than what the standard multiple antenna models predict.

Capacities of time-varying multiple-access channels with side information

Abstract: Summary form only given. We address the capacity problem for a class of time-varying multiple-access channels (TVMAC), when the underlying channel state evolves in time according to a probability law which is known to the transmitters and the receiver. Additionally, the transmitters and the receiver have access to varying degrees of channel state information (CSI) concerning the condition of the channel. Discrete-time channels with finite input, output and state alphabets are considered first. The special case of a memoryless TVMAC, with the channel state process being a time-invariant, indecomposable, aperiodic Markov chain, shows a surprising anomaly in that imperfect transmitter CSI can cause the capacity under some distributions for the initial state to be strictly larger than that under a stationary distribution for the initial state. We also consider a time-varying multiple-access fading channel with additive Gaussian noise, when various amounts of CSI are provided to the transmitters and perfect CSI is available to the receiver, and the fades are assumed to be stationary and ergodic. Implications for transmitter power control are discussed.

Unequal error protection applied to JPEG image transmission using turbo codes

Abstract: An investigation of unequal error protection (UEP) methods applied to JPEG image transmission using turbo codes is presented. The JPEG image is partitioned into two groups, i.e., DC components and AC components according to their respective sensitivity to channel noise. The highly sensitive DC components are better protected with a lower coding rate, while the less sensitive AC components use a higher coding rate. Simulation results are given to demonstrate how the UEP schemes outperforms the equal error protection (EEP) scheme in terms of bit error rate (BER) and peak signal to noise ratio (PSNR).

Asymptotic analysis of widely linear MMSE multiuser detection-complex vs real modulation

Abstract: We give the asymptotic signal-to-interference ratio for the so-called widely linear minimum mean-squared error multiuser receiver for transmission of multiple users to a common receiver with DS-CDMA. Observing that widely linear multiuser detection virtually doubles the spreading factor, we show that transmission with real-valued channel symbols can lead to a higher spectral efficiency than with complex-valued channel symbols when each user employs its own complex-valued random spreading sequence.

New low-complexity turbo-like codes

Abstract: We discuss the design of new low-complexity turbo-like codes based on a multiple parallel concatenation of 4-state and 2-state constituent codes. The new code designs take advantage of the big-numerator/little-denominator principle along with specially designed interleavers to outperform previously designed turbo codes over the entire range of signal-to-noise ratios. Puncturing at the encoder is used to produce low-complexity codes with excellent performance at code rates of 1/2 and 1/3. The multiple parallel concatenation and puncturing results in turbo-like encoders which are either partially systematic or completely nonsystematic. Comparisons with the proposed 8-state turbo coding standard and with other low-complexity alternative code designs are included.

Differential turbo space-time coding

Abstract: Serial concatenation of standard convolutional or block codes with differential space-time modulation is considered for flat fading multiple antenna channels. Extrinsic information transfer is used to predict thresholds for various outer codes. Using the differential structure of the inner code near coherent performance is obtained without the use of training symbols.

Using the mean reliability as a design and stopping criterion for turbo codes

Abstract: By means of the mean reliability (defined as the mean of the absolute values of log-likelihood ratios), a new design of parallel concatenated "turbo" codes is proposed. This criterion allows us to describe the behavior of the constituent decoders and, furthermore, to predict the behavior of the iterative decoder for large block lengths. The mean reliability can also be used as a stopping criterion.

The turbo principle in joint source channel decoding of variable length codes

Abstract: The turbo principle has been widely applied to various detection/decoding problems in recent years. Here we show how the general idea can be extended to a communication scheme where a variable length code is used for data compression followed by a channel code to protect the data against channel errors. Iterations are performed between the channel decoder and the decoder for the variable length source code. Since the exchange of extrinsic information is essential for the performance of turbo decoding schemes we describe how EXIT-charts can be applied to predict the performance of the iterative source-channel decoding approach.

Design of low-density parity-check codes for bandwidth efficient modulation

Abstract: We design low-density parity-check (LDPC) codes for bandwidth efficient modulation using a multilevel coding (MLC) technique. We develop a method to analyze the asymptotic performance of the LDPC codes using message-passing decoding at each level of the MLC scheme as the codeword length goes to infinity. Simulation of very large block size LDPC codes verifies the accuracy of the analytical results. We jointly optimize the code rates and code parameters of the LDPC codes at each level of the MLC scheme, and the asymptotic performance of the optimized irregular LDPC codes is very close to the channel capacity of the additive white Gaussian noise (AWGN) channel.

Iterative multiuser joint detection and parameter estimation: a factor-graph approach

Abstract: We examine a multiple-access AWGN channel with synchronous DS-CDMA in which the channel amplitude and noise variance parameters are unknown a priori. We derive an iterative joint multiuser decoder and parameter estimator based on soft interference cancellation and on soft decision-driven least-squares estimation. Our derivation is obtained by applying the sum-product algorithm to the factor graph of the joint a posteriori probability measure of the information bits and of the unknown channel parameters.

Analog decoding and beyond

Abstract: In 1998, Hagenauer and Loeliger et al. independently proposed to decode error correcting codes by analog electronic networks. In contrast to previous work on analog Viterbi decoders, the work both by Hagenauer and by Loeliger et al. was inspired by turbo-style decoding of codes described by graphs. Large gains, in terms of speed or power consumption, over digital implementations were envisaged. Since 1998, much effort has been spent towards turning these ideas into working chips. While only decoders of "toy" codes have so far been successfully manufactured, extensive simulations of such circuits have not revealed any fundamental problems. Some progress has also been made in analyzing the effects of transistor mismatch. While much remains to be learned, the author feels confident that analog decoders will eventually find their way into applications. The present paper, rather than reporting on circuit details, offers some thoughts on "the bigger picture"- the underlying principles, motivations, and possible directions of future research.

Analog decoding of product codes

Abstract: A design approach is presented for soft-decision decoding of block product codes ("block turbo codes") using analog computation with MOS devices. Application of analog decoding to large code sizes is also considered with the introduction of serial analog interfaces and pipeline schedules.

On the fading number of multi-antenna systems

Abstract: It has recently been shown that at high signal-to-noise ratios (SNR) the capacity of multi-antenna systems over flat fading channels (without receiver or transmitter side-information) typically grows only double-logarithmically in the SNR. Here we further refine the analysis and study the "fading number" /spl chi/, which we define as the limit of the difference between channel capacity and log(1+log(1+SNR)). It is suggested that at high SNR, i.e., at rates that significantly exceed the fading number, a capacity increase of one bit per channel use requires the squaring of the SNR, or equivalently, the doubling of the SNR as expressed in decibels. In this loose sense, the fading number can be viewed as the channel limiting rate for power-efficient communication. Note, however, that the fading number may be negative. While the use of multiple antennas does not typically change the double-logarithmic asymptotic dependence of channel capacity on the SNR, multiple antennas do typically increase the fading number, albeit at times (e.g., in the Rayleigh fading case) only in an additive way that grows only logarithmically with the number of antennas.

Impact of multiple access on uplink scheduling

Abstract: We consider uplink scheduling for bursty traffic. We characterize the achievable rate region for Gaussian multiple access in terms of minimum required powers, with a constraint on average transmission delay for all users. We show that delay and rate constrained, power minimizing schemes perform scheduling accompanied with power control. Further, for the class of randomized stationary schedulers, it is shown that the achievable region is a convex polytope. We highlight that power requirements of a user can be reduced by either allowing additional delay (time scheduling gain) or increasing the power of another user (multiuser power exchange). Results are presented for two user additive white Gaussian noise channel and can be extended to finite state fading channels.

Information capacity of a multipath mobile communication channel with large number of receiving antennas

Abstract: The expression for stationary channel information capacity of a mobile communication channel with a large number of receiving antennas in the presence of multipath signal propagation is shown. It has been shown that the capacity is approaching information capacity of the orthogonal Gaussian channel with no interference. The system with adaptive linear MMSE receivers and adaptive interference cancellation is presented as a possible low computational complexity solution achieving the theoretical capacity.

A random matrix model for the antenna array channel with decaying power delay profile

Abstract: The random matrix model for multipath propagation on the antenna array channel is generalised to decaying power delay profiles. Results are given in terms of Stieltjes transforms of the eigenvalue distributions of the channel's space-time covariance matrix.

Random CDMA in the multiple cell uplink environment: the effect of fading on various receivers

Abstract: A simple multi-cell Rayleigh fading uplink communication model is suggested and analyzed for optimally coded randomly spread DS-CDMA with multiuser detection. The model adheres to Wyner's (1994) infinite linear cell-array setting, according to which only adjacent-cell interference is present, and characterized by a single parameter 0/spl les//spl alpha//spl les/1. The discussion is confined to asymptotic analysis where both the number of users per cell and the processing gain go to infinity, while their ratio goes to some finite constant. The spectral efficiency of various multiuser detection strategies is evaluated assuming single cell-site processing, and equal transmit powers for all users in all cells. Comparative results demonstrate how performance is affected by the introduction of inter-cell interference (with and without fading), and what is the penalty associated with the randomly spread coded DS-CDMA strategy.

Joint decoding of serially concatenated coded CDMA: iterative schedule study

Abstract: Joint iterative decoding of forward error control (FEC) encoded code-division multiple-access (CDMA) systems is studied. Serially concatenated convolutional codes are used as FEC codes. We apply iterative decoding to this system and study the effect of component decoders and different decoding partition schemes via a variance transfer analysis. It is shown that distinct partition schemes result in similar pinch off SNRs.

MMSE analysis of certain large isometric random precoded systems

Abstract: Linear precoding consists in multiplying by a N/spl times/K matrix a K-dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. We analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using new tools, borrowed from the so-called free probability theory, it can be shown that the signal to interference plus noise ratio at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N/spl rarr/+/spl infin/ and K/N/spl rarr//spl alpha//spl les/1. These asymptotic results are used to optimally balance the redundancy introduced between linear precoding and classical convolutional coding, while preserving a simple MMSE equalization scheme at the receiver.

Weak variable-length Slepian-Wolf coding with linked encoders for mixed sources

Abstract: Slepian and Wolf (see IEEE Trans. Inform. Theory, vol.19, p.471-80, July 1973) first considered the data compression of correlated sources called the SW system, where two sequences emitted from correlated sources are separately encoded to codewords, and sent to a single decoder which has to output original sequence pairs. Recently, Oohama (see IEEE Trans. Inform. Theory, vol.42, p.837-47, May 1996) has extended the SW system and investigated a more general case where there are some mutual linkages between two encoders of the SW system. In this paper, we investigate variable-length coding which allows asymptotically vanishing probability of error for the system considered by Oohama. We clarify the admissible rate region for mixed sources characterized by two ergodic sources, and show that this region is strictly wider than that for fixed-length codes.

Performance of iterative multiuser decision-feedback receivers

Abstract: We compare the performance of iterative multi-user successive and parallel decision feedback detectors (DFDs) for code-division multiple access (CDMA). An adaptive successive-DFD (S-DFD) is first presented, which requires only a training sequence and associated timing to estimate all filter coefficients. Simulation results show that with limited training, the adaptive S-DFD performs significantly better than the adaptive parallel-DFD (P-DFD). A large system analysis of error rate for non-adaptive iterative DFDs is also presented, and shows that the S-DFD converges with fewer iterations than the P-DFD.

On the design of bit-interleaved turbo-coded modulation

Abstract: Bit-interleaved turbo-coded modulations (BITCM) have been shown to achieve bit error rate performance very close to the capacity limit over both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels. So far, most studies have been done on BITCM systems designed using rectangular QAM signal sets. In this paper, we address the problem of finding some constellations that would be more suitable than rectangular QAM for designing power efficient BITCM. When the parameter M is in the form M=2/sup 2p/ where p is an integer, we show that rectangular QAM constellations are surprisingly the most attractive signal sets for the design of power-efficient BITCM schemes over AWGN channels. This is not necessarily true with Rayleigh fading channels.

On the spectral efficiency of CDMA with multiple antennas

Abstract: We consider the impact of transmit diversity on the capacity of synchronous, randomly-spread code-division multiple-access, in the presence of frequency-flat fading. For large user populations, we characterize the spectral efficiency (capacity per chip) of two systems that use different spreading sequences on each antenna: a theoretically optimal system in which each transmit antenna is fed by independent data streams, and a code sequence diversity scheme that transmits the same data on each antenna.

Methods and limits of iterative multiuser decoding

Abstract: Previous work has identified iterative multiuser decoding techniques that are often only limited by theoretical channel capacity. These investigations usually dealt with the case where user waveforms are decorrelated to some degree. Investigations with identical waveforms indicate that the theoretical capacity limits are not always achieved. Performance has a threshold-like behaviour, as one might expect with a capacity limit, but the threshold is, in some cases, above the theoretical capacity for the channel under investigation. In this paper, an explanation for this behaviour is proposed.

Robust space-time codes for time-selective fading

Abstract: We consider the design of robust codes that exploit both space and time diversity, using bit-interleaved coded modulation. Under quasi-static fading conditions, codes constructed in this way achieve full diversity and perform close to the best space-time trellis codes of comparable complexity. Under fast-fading conditions, these same codes achieve higher diversity than previously known codes of the same complexity.

Product accumulate codes: properties and performance

Abstract: A new class of codes, named product accumulate codes, which are the concatenation of an outer product code and an inner rate-1 differential encoder (or accumulator) is proposed. We show that these codes can perform within a few tenths of a dB from the Shannon limit for rates/spl ges/1/2. For practical block lengths, these codes provide similar performance to turbo codes but with significantly lower decoding complexity.