Mutual Information Of Channel Research Articles

A Deterministic Algorithm for the Capacity of Finite-State Channels

We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concave in a parameter taking values in a compact convex subset of some Euclidean space, our first algorithm proves to achieve polynomial accuracy in polynomial time and, moreover, for some special families of finite-state channels our algorithm can achieve exponential accuracy in polynomial time under some technical conditions. For the case that the channel mutual information rate may not be strongly concave, our second algorithm proves to be at least locally convergent.

Optimization of linear MIMO precoding assuming MMSE-based turbo equalization

In this paper, we focus on the optimization of a linear multiple-input multiple-output (MIMO) precoder assuming an outer forward error correction code and an iterative minimum mean square error (MMSE)-based interference cancellation (turbo equalization) at the receiver side. Given perfect channel state information at both sides of the communication, we propose a novel precoder that is specifically designed to use with turbo equalization. In contrast to the conventional precoders that maximize the mutual information (MI) between finite alphabet input and the corresponding output over the precoded MIMO channel, the proposed precoder aims to maximize the MI between the finite alphabet input and the corresponding output of the equalizer. The precoder is targeted for applications that require low complexity, where forward error correction (FEC) codes with low-complex encoding and decoding structures are used. Simulation results show the error-rate performance gain of the resulting precoder compared to two other reference precoders presented in the literature, which are derived from the maximization of the precoded MIMO channel MI.

Complexity Reduction for the Optimization of Linear Precoders over Random MIMO Channels

Precoder optimization with full channel state information for finite alphabet signals over multiple-input multiple-output random channels is investigated in this paper. The precoder is represented by a product of power allocation matrix and constellation-forming matrix. There was an optimal algorithm introduced in the literature to globally maximize the channel mutual information by iteratively optimizing these two matrices. However, the computational complexity of the optimal algorithm is painfully high, especially when it is used with the high-order modulation and the high-data stream number. In this paper, we propose a novel sub-optimal low-complexity precoding algorithm and compare it with the optimal one. The new algorithm proceeds in two steps. First, the constellation-forming matrix is fixed in order to maximize the minimum Euclidean distance between the received symbols, which ensures high channel mutual information. Then, given the constellation-forming matrix, an iterative algorithm searches for the power allocation matrix that maximizes the channel mutual information. Since optimizing only one matrix instead of two, the new algorithm not only achieves a lower computational complexity but also avoids the use of initial values, which must be carefully selected for each channel and signal-to-noise ratio for fast convergence. Another advantage of the new algorithm is that the resulting precoder has a fixed form of received constellation thanks to the fixed constellation-forming matrix. This allows us to optimize the symbol mapping on the received constellation. Simulation results show that the proposed low-complexity precoder achieves error-rate performance that is close to performance of the optimal one when the conventional mapping is used. In addition, the new precoder used with optimized mapping at received constellation shows significant error-rate performance improvement.

On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.

Enhanced Precision Through Multiple Reads for LDPC Decoding in Flash Memories

Multiple reads of the same Flash memory cell with distinct word-line voltages provide enhanced precision for LDPC decoding. In this paper, the word-line voltages are optimized by maximizing the mutual information (MI) of the quantized channel. The enhanced precision from a few additional reads allows frame error rate (FER) performance to approach that of full-precision soft information and enables an LDPC code to significantly outperform a BCH code. A constant-ratio constraint provides a significant simplification in the optimization with no noticeable loss in performance. For a well-designed LDPC code, the quantization that maximizes the mutual information also minimizes the FER in our simulations. However, for an example LDPC code with a high error floor caused by small absorbing sets, the MMI quantization does not provide the lowest frame error rate. The best quantization in this case introduces more erasures than would be optimal for the channel MI in order to mitigate the absorbing sets of the poorly designed code. The paper also identifies a trade-off in LDPC code design when decoding is performed with multiple precision levels; the best code at one level of precision will typically not be the best code at a different level of precision.

Constellation Design for Memoryless Phase Noise Channels

In this paper, we optimize the constellation sets to be used in communication systems affected by phase noise. The main objective is to find the constellation which maximizes the channel mutual information under given power constraints. For any given constellation, the average mutual information (AMI) and the pragmatic average mutual information (PAMI) of the channel are calculated approximately, assuming that both the additive noise and phase noise are memoryless. Then, a simulated annealing algorithm is used to optimize the constellation. When the objective function is the PAMI, the proposed algorithm jointly optimizes the constellation and the binary labeling. We focus on constellations with 8, 16, 64 and 256 signals. The performances of the optimized constellations are compared with conventional constellations showing considerable gains in all system scenarios. In particular, it is shown that the optimized constellations are much more robust with respect to the changes in the phase noise characteristics than the phase shift keying (PSK) modulation and quadrature amplitude modulation (QAM).

Cross-Layer Framework for Multiuser Real Time H.264/AVC Video Encoding and Transmission over Block Fading MIMO Channels Using Outage Probability

We present a framework for cross-layer optimized real time multiuser encoding of video using a single layer H.264/AVC and transmission over MIMO wireless channels. In the proposed cross-layer adaptation, the channel of every user is characterized by the probability density function of its channel mutual information and the performance of the H.264/AVC encoder is modeled by a rate distortion model that takes into account the channel errors. These models are used during the resource allocation of the available slots in a TDMA MIMO communication system with capacity achieving channel codes. This framework allows for adaptation to the statistics of the wireless channel and to the available resources in the system and utilization of the multiuser diversity of the transmitted video sequences. We show the effectiveness of the proposed framework for video transmission over Rayleigh MIMO block fading channels, when channel distribution information is available at the transmitter.

Constellation Optimization in the Presence of Strong Phase Noise

In this paper, we address the problem of optimizing signal constellations for strong phase noise. The problem is investigated by considering three optimization formulations, which provide an analytical framework for constellation design. In the first formulation, we seek to design constellations that minimize the symbol error probability (SEP) for an approximate ML detector in the presence of phase noise. In the second formulation, we optimize constellations in terms of mutual information (MI) for the effective discrete channel consisting of phase noise, additive white Gaussian noise, and the approximate ML detector. To this end, we derive the MI of this discrete channel. Finally, we optimize constellations in terms of the MI for the phase noise channel. We give two analytical characterizations of the MI of this channel, which are shown to be accurate for a wide range of signal-to-noise ratios and phase noise variances. For each formulation, we present a detailed analysis of the optimal constellations and their performance in the presence of strong phase noise. We show that the optimal constellations significantly outperform conventional constellations and those proposed in the literature in terms of SEP, error floors, and MI.

Low Density Parity Check Codes with Non-Equiprobable Symbols

In this letter, we analyze how to decode LDPC codes with non-equiprobable binary symbols. For such symbols, we need to modify the conventional Tanner graph, because the message passing from check nodes to information bits and to parity check bits are diverse. In other words, in conventional Tanner graph, the message passing along two directions are identical, while in our case, the message along the forward direction and backward direction are different. A method to optimize signaling constellation which maximizes the channel mutual information is presented as well. In the numerical section, symbols with prior probabilities (0.3,0.7) could gain 0.72 dB in performance if we replace equal space constellation with optimal constellation. Several cases of short LDPC codes (N, K =1024, 512) are explored and gain almost 0.4 dB. The simulation shows that additional gain of only 0.2 dB could be attainable, if optimal source coding is achievable.

Performance of Mutual Information Inference Methods Under Unknown Interference

In this paper, the problem of fast point-to-point multiple-input-multiple-output channel mutual information estimation is addressed, in the situation where the receiver undergoes unknown colored interference, whereas the channel with the transmitter is perfectly known. The considered scenario assumes that the estimation is based on a few channel use observations during a short sensing period. Using large dimensional random matrix theory, an estimator referred to as G-estimator is derived. This estimator is proved to be consistent as the number of antennas and observations grow large and its asymptotic performance is analyzed. In particular, the G-estimator satisfies a central limit theorem with asymptotic Gaussian fluctuations. Simulations are provided which strongly support the theoretical results, even for small system dimensions.

Optimal Power Allocation for $(N,K)$-Limited Access Channels

In this paper, we consider a system that consists of N independent parallel channels, where the receiver starts to decode the information being transmitted when it has access to at least K of them. We refer to this system as the (N,K)-limited access channel. No prior knowledge for the distribution about which transmissions will be received is assumed. In addition, both the channel inputs and channel disturbances can be arbitrary, except that the mutual information function for each channel is assumed strictly concave with respect to the input power. Hence, the channel capacity below which the code rate is guaranteed to be attainable by a sequence of codes with vanishing error can be determined by the minimum mutual information among any K out of N channels. We then investigate the power allocation that maximizes this minimum mutual information subject to a total power constraint. As a result, the optimal solution can be determined via a systematic algorithmic procedure by performing at most K single-power-sum-constrained maximizations. Based on this result, the closed-form formula of the optimal power allocation for an (N,K) -limited access channel with channel inputs and additive noises, respectively, scaled from two independent and identically distributed random vectors of length N is subsequently established, and is shown to be well interpreted by a two-phase water-filling principle. Specifically, in the first noise-power redistribution phase, the least N-K noise powers (equivalently, second moments) are first poured (as noise water) into a tank consisting of K interconnected unit-width vessels with solid base heights, respectively, equal to the remaining K largest noise powers. Afterward, those W vessels either with noise water inside or with solid base height equal to the new water surface level are subdivided into N-K+W vessels of rectangular shape with the same heights (as the water surface level) and widths in proportion to their noise powers. In the second signal-power allocation phase, the heights of vessel bases will be first either lifted or lowered according to the total signal power and channel mutual information functions, followed by the usual signal-power water-filling scheme. The two-phase water-filling interpretation then hints that the degree of “noisiness” for a general (possibly, nonadditive and non-Gaussian) limited access channel might be identified by composing the derivative of the mutual information function with its inverse.

On the relationship between the multi-antenna secrecy communications and cognitive radio communications

This paper studies the achievable rates of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channel with multiple single-/multi-antenna eavesdroppers. By assuming Gaussian input, the maximum achievable secrecy rate is obtained with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The maximum secrecy rate computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by existing methods. To handle this difficulty, this paper explores a new relationship between the secrecy channel and the recently developed cognitive radio (CR) channel, in which the secondary user transmits over the same spectrum simultaneously with multiple primary users, subject to the received interference power constraints at the primary users, or the so-called "interference temperature (IT)" constraints. By constructing an auxiliary multi-antenna CR channel that has the same channel responses as the secrecy channel, this paper shows that the optimal transmit covariance to achieve the maximum secrecy rate is the same as that to achieve the CR spectrum sharing capacity with properly selected IT constraints. Thereby, finding the optimal complex transmit covariance matrix for the secrecy channel becomes equivalent to searching over a set of real IT constraints in the auxiliary CR channel. Based on this relationship, efficient algorithms are proposed to solve the non-convex secrecy rate maximization problem by transforming it into a sequence of convex CR spectrum sharing capacity computation problems, under various setups of the secrecy channel.

On the Mutual Information Distribution of MIMO Rician Fading Channels

In a fading environment, the statistical distribution of the mutual information of a multiple-input multiple-output (MIMO) system depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant and the trace of a Wishart matrix. Based on the obtained distributions, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the mutual information of a MIMO system in Rician fading environments. The bounds obtained on the CCDF of mutual information provide further insights into the channel mutual information, and show the effects of the system parameters on the mutual information distribution explicitly. In addition, results for the Rayleigh channels are obtained as a special case.

Communication with causal CSI and controlled information outage

In this letter, a Rayleigh block-fading (BF) channel, subject to an information outage probability constraint, is considered. The transmitter is assumed to have causal knowledge of the channel state information (CSI), which is exploited to intelligently allocate the power over the blocks (and hence vary the channel mutual information) to minimize the average transmitted power per block for satisfying the outage probability constraint for a given target code-rate. We first show that the optimal solution to this problem can be obtained by solving the reverse problem of minimizing the outage probability for a range of long-term power constraints through repeated uses of dynamic programming (DP), which is nevertheless prohibitively complex. Then, we develop a suboptimal allocation algorithm which still uses DP to exploit the CSI causality but at a much reduced complexity. A performance lower-bound is further derived, which permits us to see that the proposed algorithm is near-optimal, especially in the small outage probability regime. A scheme called equal-outage-probability per block (EOPPB) which compromises the performance further for reducing the complexity is also devised. To compare the methods, we evaluate both analytically and numerically their complexities and performance. The results are finally generalized to multiple-input multiple-output (MIMO) BF channels.

The Universal Operation of LDPC Codes Over Scalar Fading Channels

Root and Varaiya proved the existence of a code that can communicate reliably over any linear Gaussian channel for which the channel mutual information level exceeds the transmitted rate. This paper provides several examples of scalar (single-input single-output) fading channels and shows that on these channels the performance of low-density parity-check (LDPC) codes lies in close proximity to the performance limits identified by Root and Varaiya. Specifically, we consider periodic fading channels and partial-band jamming (PBJ) channels. A special case of periodic fading is the variation of signal-to-noise ratio across orthogonal frequency division modulation subchannels. The robustness of LDPC codes to periodic fading and PBJ across parameterizations of these different channels is demonstrated through the consistency of the required mutual information to provide a specified bit error rate. For the periodic fading case, the Gaussian approximation to density evolution has been adapted such that asymptotic threshold measures can be compared to simulated code performance in various periodic fading scenarios

Universal space-time codes from demultiplexed trellis codes

In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents two-dimensional trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes, found by exhaustive search, guarantee consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or, in some cases, superior, frame-error rate and bit-error rate performance under quasi-static Rayleigh fading, as compared with trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh-fading scenario

Universal Space–Time Codes From Demultiplexed Trellis Codes

In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents 2-D trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes are found by an exhaustive search that guarantees consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or in some cases, superior frame-error rate and bit-error rate performance under quasi-static Rayleigh fading to trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh fading scenario.

Reliable channel regions for good binary codes transmitted over parallel channels

We study the average error probability performance of binary linear code ensembles when each codeword is divided into J subcodewords with each being transmitted over one of J parallel channels. This model is widely accepted for a number of important practical channels and signaling schemes including block-fading channels, incremental redundancy retransmission schemes, and multicarrier communication techniques for frequency-selective channels. Our focus is on ensembles of good codes whose performance in a single channel model is characterized by a threshold behavior, e.g., turbo and low-density parity-check (LDPC) codes. For a given good code ensemble, we investigate reliable channel regions which ensure reliable communications over parallel channels under maximum-likelihood (ML) decoding. To construct reliable regions, we study a modifed 1961 Gallager bound for parallel channels. By allowing codeword bits to be randomly assigned to each component channel, the average parallel-channel Gallager bound is simplified to be a function of code weight enumerators and channel assignment rates. Special cases of this bound, average union-Bhattacharyya (UB), Shulman-Feder (SF), simplified-sphere (SS), and modified Shulman-Feder (MSF) parallel-channel bounds, allow for describing reliable channel regions using simple functions of channel and code spectrum parameters. Parameters describing the channel are the average parallel-channel Bhattacharyya noise parameter, the average channel mutual information, and parallel Gaussian channel signal-to-noise ratios (SNRs). Code parameters include the union-Bhattacharyya noise threshold and the weight spectrum distance to the random binary code ensemble. Reliable channel regions of repeat-accumulate (RA) codes for parallel binary erasure channels (BECs) and of turbo codes for parallel additive white Gaussian noise (AWGN) channels are numerically computed and compared with simulation results based on iterative decoding. In addition, an examp

On the effect of receiver estimation error upon channel mutual information

Our goal in this paper is to study the effect of the receiver structure upon the achievable data rates. We consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output (MIMO) wireless channel. To encompass a number of transmission schemes, we study this problem utilizing affine precoding, which is a unified model of linearly precoded data symbols with superimposed training. We focus on Bayesian receivers that estimate both the unknown fading coefficients and the data symbols. The receiver may adopt either of the following strategies to retrieve the data symbols: strategy (i) the receiver obtains joint Bayesian channel and symbol estimates, strategy, (ii) the receiver obtains a Bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols. For both strategies, we provide lower bounds on the mutual information between the data symbols and their corresponding estimates, and we relate these bounds to the symbol Cramer-Rao bound (CRB) matrices. In contrast to strategy (ii), for strategy (i) the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error. For strategy (ii) we show that asymptotically (as the size of the transmission block grows) there is no loss of information after the maximum a posteriori (MAP) estimate of Gaussian symbols. We also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint.

Multiple-Antenna Channel Hardening and Its Implications for Rate Feedback and Scheduling

Wireless data traffic is expected to grow over the next few years and the technologies that will provide data services are still being debated. One possibility is to use multiple antennas at base stations and terminals to get very high spectral efficiencies in rich scattering environments. Such multiple-input/multiple-output (MIMO) channels can then be used in conjunction with scheduling and rate-feedback algorithms to further increase channel throughput. This paper provides an analysis of the expected gains due to scheduling and bits needed for rate feedback. Our analysis requires an accurate approximation of the distribution of the MIMO channel mutual information. Because the exact distribution of the mutual information in a Rayleigh-fading environment is difficult to analyze, we prove a central limit theorem for MIMO channels with a large number of antennas. While the growth in average mutual information (capacity) of a MIMO channel with the number of antennas is well understood, it turns out that the variance of the mutual information can grow very slowly or even shrink as the number of antennas grows. We discuss implications of this "channel-hardening" result for data and voice services, scheduling, and rate feedback. We also briefly discuss the implications when shadow fading effects are included.