Approaching V-BLAST Capacity With Adaptive Modulation and LDPC Encoding

This paper presents a practical implementation of the vertical Bell Laboratories layered space-time (V-BLAST) type system, in which the multiple-input multiple-output (MIMO) open-loop capacity can be approached with conventional scalar coding, using adaptive modulation with appropriate channel codes, e.g., low-density parity-check (LDPC) codes and optimum successive detection (OSD). The density evolution (DE) technique is employed to determine the maximal achievable rate of an LDPC code for each transmit antenna for a given channel realization at a given SNR. Numerical results show that the average sum rate of the adaptively modulated LDPC-encoded system is quite close to the V-BLAST capacity with both rate and power adaptations. Considering the performing degradation caused by error propagation due to the imperfect feedback and relatively long decoding delay in the OSD, we use parallel interference cancellation (PIC) followed by minimum mean square error (MMSE) filtering in the bit error rate (BER) performance simulation. Simulation results show that a target BER of 10-5 can be achieved by the optimally designed LDPC codes. To simplify the code design, we replace the LDPC codes optimally designed for each channel realization with rate-compatible punctured LDPC codes, at the cost of a slight sum rate loss. If the fading process is nonergodic, the outage capacity corresponding to a given outage probability is used to measure the channel performance. As an example, we design the LDPC codes for an adaptively modulated 2 × 2 V-BLAST system to approach its outage capacity for a given outage probability.      

Matched information rate codes for Partial response channels

In this paper, we design capacity-approaching codes for partial response channels. The codes are constructed as concatenations of inner trellis codes and outer low-density parity- check (LDPC) codes. Unlike previous constructions of trellis codes for partial response channels, we disregard any algebraic properties (e.g., the minimum distance or the run-length limit) in our design of the trellis code. Our design is purely probabilistic in that we construct the inner trellis code to mimic the transition probabilities of a Markov process that achieves a high (capacity-approaching) information rate. Hence, we name it a matched information rate (MIR) design. We provide a set of five design rules for constructions of capacity-approaching MIR inner trellis codes. We optimize the outer LDPC code using density evolution tools specially modified to fit the superchannel consisting of the inner MIR trellis code concatenated with the partial response channel. Using this strategy, we design degree sequences of irregular LDPC codes whose noise tolerance thresholds are only fractions of a decibel away from the capacity. Examples of code constructions are shown for channels both with and without spectral nulls.     

Design and analysis of simple irregular LDPC codes with finite‐lengths and their application in CDMA systems

In this paper, we design and optimize simple irregular low‐density parity‐check (LDPC) codes for finite‐length applications where the asymptotic noise threshold of the channel cannot play as a dominant optimization factor. Our design procedure is based on some observations resulted from analytical study of these codes. Although we present our design procedure for some specified rates but it can generally be used for any rate. Specifically, we design a simple irregular LDPC code for IS‐95 and compare its performance with the other reported codes 1 - 3 for this application. Our results show a 3.7‐fold increase in the capacity at bit error rate (BER) equal to 10⁻⁵ compared to the low‐rate orthogonal convolutional codes and 1.2 times increase compared to a high performance LDPC code of Reference 3 . Copyright © 2004 John Wiley & Sons, Ltd.     

Maximal diversity algebraic space-time codes with low peak-to-mean power ratio

The design requirements for space-time coding typically involves achieving the goals of good performance, high rates, and low decoding complexity. In this paper, we introduce a further constraint on space-time code design in that the code should also lead to low values of the peak-to-mean envelope power ratio (PMEPR) for each antenna. Towards that end, we propose a new class of space-time codes called the "low PMEPR space-time" (LPST) codes. The LPST codes are obtained using the properties of certain cyclotomic number fields. The LPST codes achieve a performance identical to that of the threaded algebraic space-time (TAST) codes but at a much smaller PMEPR. With M antennas and a rate of one symbol per channel use, the LPST codes lead to a decrease in PMEPR by at least a factor of M relative to a Hadamard spread version of the TAST code. For rates beyond one symbol per channel use and up to a guaranteed amount, the LPST codes have provably smaller PMEPR than the corresponding TAST codes. Additionally, with the concept of punctured LPST codes proposed in this paper, significant performance improvement is obtained over the full diversity TAST schemes of comparable complexity. Numerical examples are provided to illustrate the advantage of the proposed codes in terms of PMEPR reduction and performance improvement for very high rate wireless communications.     

Efficient use of DS/CDMA signals for broadband communications over power lines

This paper investigates the use of direct‐sequence/code‐division multiple access (DS/CDMA) signals for broadband communications over power lines. Each user is assumed to utilize all available spreading codes for sending the information to the destination. The transmitter and the receiver are assumed to have perfect channel knowledge with the receiver employing a zero‐forcing multiuser detector. Based on channel knowledge we attempt to maximize the data throughput by suitable choice of the number of codes used and the power and the constellation size (bit‐load) assigned to the data modulating each spreading code. We employ Gold codes, in addition to special codes derived based on the channel knowledge for ISI minimization, termed ‘eigen codes’. In contrast to some earlier results concerning CDMA and OFDM, we show that DS/CDMA signals can be optimized to achieve an overall data throughput of approximately 80% of that achieved by OFDM systems. This result shows that DS/CDMA signaling can be a good candidate for broadband power line communications. Copyright © 2011 John Wiley & Sons, Ltd.     

Source-optimized irregular repeat accumulate codes with inherent unequal error protection capabilities and their application to scalable image transmission.

The common practice for achieving unequal error protection (UEP) in scalable multimedia communication systems is to design rate-compatible punctured channel codes before computing the UEP rate assignments. This paper proposes a new approach to designing powerful irregular repeat accumulate (IRA) codes that are optimized for the multimedia source and to exploiting the inherent irregularity in IRA codes for UEP. Using the end-to-end distortion due to the first error bit in channel decoding as the cost function, which is readily given by the operational distortion-rate function of embedded source codes, we incorporate this cost function into the channel code design process via density evolution and obtain IRA codes that minimize the average cost function instead of the usual probability of error. Because the resulting IRA codes have inherent UEP capabilities due to irregularity, the new IRA code design effectively integrates channel code optimization and UEP rate assignments, resulting in source-optimized channel coding or joint source-channel coding. We simulate our source-optimized IRA codes for transporting SPIHT-coded images over a binary symmetric channel with crossover probability p. When p = 0.03 and the channel code length is long (e.g., with one codeword for the whole 512 x 512 image), we are able to operate at only 9.38% away from the channel capacity with code length 132380 bits, achieving the best published results in terms of average peak signal-to-noise ratio (PSNR). Compared to conventional IRA code design (that minimizes the probability of error) with the same code rate, the performance gain in average PSNR from using our proposed source-optimized IRA code design is 0.8759 dB when p = 0.1 and the code length is 12800 bits. As predicted by Shannon's separation principle, we observe that this performance gain diminishes as the code length increases.     

Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space--Part I:180°

Convolutional channel coding with expanded signal space improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. Due to the phase ambiguity(ies) in the expanded signal space, it is desirable to design the code' to be transparent to signal element rotations. In this paper, design rules and procedures for 180° rotationally invariant codes are presented. In a companion paper, we extend these rules and procedures to codes which are transparent to 90, 180, and 270° signal element rotations. We illustrate these rules and procedures by designing simple codes that achieve coding gain of 3-4 dB. These are the codes of practical interest. Codes with higher coding gain can be obtained using the same rules and procedures. Both feedforward and feedback codes are considered.     

Globally Constrained Power Control Across Multiple Channels in Wireless Data Networks

We investigate multi-channel transmission schemes for packetized wireless data networks. The transmitting unit transmits concurrently in several orthogonal channels (for example, distinct FDMA bands or CDMA codes) with randomly fluctuating interference and there is a global constraint on the total power transmitted across all channels at any time slot. Incoming packets to the transmitter are queued up in separate buffers, depending on the channel they are to be transmitted in. In each time slot, one packet can be transmitted in each channel from its corresponding queue. The issue is how much power to transmit in each channel, given the interference in it and the packet backlog, so as to optimize various power and delay costs associated with the system. We formulate the general problem taking a dynamic programming approach. Through structural decompositions of the problem, we design practical novel algorithms for allocating power to various channels under the global power constraint.     

Information Theoretic Foundations of Adaptive Coded Modulation

In wireless/mobile communications, terminals adapt their rate and transmit power or, more in general, their coding and modulation scheme, depending on the time-varying channel conditions. This paper presents, in a tutorial form, the information theoretic framework underlying such ldquoadaptive modulationrdquo techniques. First, we review fading channel models, channel state information assumptions, and related capacity results. Then, we treat the case of input power constraint, where the optimal input distribution is Gaussian. Finally, we address the case of discrete modulations. In order to treat the latter, we make use of the recently developed method of ldquomercury-waterfillingrdquo, based on the relationship between mutual information and minimum mean-square error (MMSE) estimation of the channel input from the channel output. While the traditional design of adaptive modulation schemes based on uncoded bit-error rate (BER) involves the optimization over a discrete set of signal constellations, when powerful (i.e., capacity approaching) coding schemes are used the corresponding adaptive coded modulation design becomes surprisingly simple. The regime of very powerful coding is justified by the use of modern coding schemes, such as turbo codes and low-density parity-check codes, able to perform close to channel capacity at very small BER.     

LDPC Codes for Flat Rayleigh Fading Channels with Channel Side Information

In this paper, we design capacity approaching lowdensity parity-check (LDPC) codes in the low signal-to-noise ratio (SNR) regime for flat Rayleigh fading channels with channel side information at transmitter and receiver. We use the structure advocated by Caire et al, which uses a single codebook with dynamic power allocation. The extrinsic information transfer (EXIT) function method is used to design the LDPC codes which approach the channel capacities.We also study the EXIT function properties of various demappers.     

Rate gains in block-coded modulation systems with interblock memory

This paper examines the performance gains achievable by adding interblock memory to, and altering the mapping of coded bits to symbols in, block-coded modulation systems. The channel noise considered is additive Gaussian, and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors. In the case of the additive white Gaussian noise channel, these goals translate into the design of block codes of a given weighted or `normalized' distance whose rate is as high as possible, and whose number of codewords at minimum normalized distance is low. The effect of designing codes for normalized distance rather than Hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest, and many such best codes are given     

Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space--Part II: Nonlinear Codes

This is the second paper on rotationally invariant convolutional channel coding with expanded signal space. Signal space with 90, 180, and 270° phase ambiguities is generally preferred to signal space with only 180° phase ambiguity. In this paper, design rules and procedures for 180° rotationally invariant convolutional codes in the previous paper are extended to rotationally invariant codes with expanded signal space having 90, 180, and 270° phase ambiguities. As in the previous paper, we illustrate these rules and procedures by designing simple codes with coding gain of 4 dB. Nonlinear convolutional codes result from these design rules and procedures. These simple nonlinear convolutional codes are being considered as international standards on voiceband modems at rate greater than or equal to 9.6 kbits/s. Codes with higher coding gain can be obtained using the same rules and procedures. Both feedforward and feedback codes are considered. In addition, a new class of codes described as "generalized feedback" is also considered.     

Binary transmission codes with higher order spectral zeros at zero frequency (Corresp.)

A method is presented for designing binary channel codes in such a way that both the power spectral density function and its low-order derivatives vanish at zero frequency. The performance of the new codes is compared with that of channel codes designed with a constraint on the unbalance Of the number of transmitted positive and negative pulses. Some remarks are made on the error-correcting capabilities of these codes.     

Pattern-Flipping Chase-Type Decoders with Error Pattern Extracting Viterbi Algorithm over Partial Response Channels

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.     

Decode and forward polar coding for Half-duplex two-relay channels based on multilevel construction

Polar codes represent an emerging class of error-correcting codes with power to approach the capacity of the physically degraded relay channel and relevant coding schemes have been proposed in the literature. This paper aims to design new cooperative decode-and-forward (DF) polar coding schemes for half-duplex two-relay channel based on the Plotkin’s construction illustrating their performances gain. In these schemes, we consider the use of time-division process in transmission. The source node transmits its polar-coded information to both relays and the destination nodes during the first time slot. Each relay node receives the data from the source and processes it using the DF protocol. For the second transmission period, each relay first decodes the source signal then after reconstruction of the information reduction matrix based on the multilevel characteristics of polar codes, the extracted data at each relay are recoded using another polar code and transmitted to the destination. At destination node, the signals received from each relay and source nodes are processed by using multi-joint successive cancellation decoding for retrieving the original information bits. We demonstrate via simulation results that by carefully constructed polarisation matrix at each relay node, we can achieve the theoretical capacity in the half-duplex relay channel.     

Quasi‐regular rate‐compatible LDPC codes with a novel diagonal‐tailed encoding on noisy channels

It is well known that conventional rate‐compatible (RC) codes, such as Raptor codes, only perform well at long code lengths. However, we propose a class of RC codes with short code lengths in this paper. Particularly, we develop a computational approach to design online‐generated RC low‐density parity‐check (LDPC) codes available on noisy channels. We first propose a diagonal‐tailed encoding to generate Quasi‐regular low‐density generator matrix codes. Then, an optimal encoding profile for RC codes is achieved with a linear interpolation approach that is based on the fixed‐rate quasi‐regular LDPC codes. Finally, we evaluate the rateless and fixed‐rate performances of the proposed RC codes by extensive simulation results on various code rates with different modulations. Copyright © 2013 John Wiley & Sons, Ltd.     

The equivalence between slepian-wolf coding and channel coding under density evolution

We consider Slepian-Wolf code design based on low density parity-check (LDPC) coset codes. The density evolution formula for Slepian-Wolf coding is derived. An intimate connection between Slepian-Wolf coding and channel coding is then established. Specifically we show that, under density evolution, each Slepian-Wolf coding problem is equivalent to a channel coding problem for a binary-input output-symmetric channel.     

Tomlinson-Harashima Precoding for Broadcast Channels with Uncertainty

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.     

Channel coding with multilevel/phase signals

A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. This is achieved by channel coding with expanded sets of multilevel/phase signals in a manner which increases free Euclidean distance. Soft maximum--likelihood (ML) decoding using the Viterbi algorithm is assumed. Following a discussion of channel capacity, simple hand-designed trellis codes are presented for 8 phase-shift keying (PSK) and 16 quadrature amplitude-shift keying (QASK) modulation. These simple codes achieve coding gains in the order of 3-4 dB. It is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals, which we call "mapping by set partitioning." Based on a new distance measure between binary code sequences which efficiently lower-bounds the Euclidean distance between the corresponding channel signal sequences, a search procedure for more powerful codes is developed. Codes with coding gains up to 6 dB are obtained for a variety of multilevel/phase modulation schemes. Simulation results are presented and an example of carrier-phase tracking is discussed.     

The Code Design of the Space-time Trellis Codes with Dynamic Transmit Power Allocation

Space-time trellis codes (STTCs) have been shown to efficiently use transmit diversity to improve the error performance. In existing space-time trellis codes, the transmit power is equally distributed across all transmit antennas. However, this power allocation strategy is not optimum regarding the error performance. In this paper, we propose a design of space-time trellis codes with dynamic transmit power allocation (STTCs/DTPA), when partial channel state information (CSI) is available at the transmitter side. It is demonstrated that this new scheme can achieve a full diversity order and have much better error performance than the standard STTCs scheme, the existing STTCs/DTPA, and some other closed-loop transmit diversity schemes with partial CSI.