Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> Decision feedback equalization is presently of interest as a technique for reducing intersymbol interference in high-rate PAM data communications systems. The basic principle is to cancel out intersymbol interference arising from previously decided data symbols at the receiver, leaving remaining intersymbol interference components to be handled by linear equalization. In this work we consider the application of decision feedback equalization to quadrature-amplitude modulation (QAM) transmission, in which two independent information streams modulate quadrature carriers. Extending Salz's treatment in a companion paper of decision feedback for a baseband channel, we derive the form of the optimum receiver filters via a matrix Wiener-Hopf analysis. We obtain explicit analytical expressions for minimum mean-square error and optimum transmitting filters. The optimization is subject to a constraint on the transmitted signal power and assumes no prior decision errors. The class of QAM transmitter and receiver structures treated here is actually much larger than the class usually considered for QAM systems. However, our results for decision feedback equalization show that, for nonexcess bandwidth systems, optimum performance is achievable without taking advantage of the most general structure. If the transmitter is required to have the conventional QAM structure, study of the time continuous system that gives rise to the sampled data system considered here demonstrates that under quite general assumptions a nonexcess bandwidth system is optimum. Finally, the explicit description of the optimum transmitting matrix filter follows from an information-theoretic “water-pouring” algorithm in conjunction with the determination of the form of the points of maxima of a determinant extremal problem. <s> BIB001 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> We present some information-theoretic considerations used to determine upper bounds on the information rates that can be reliably transmitted over a two-ray propagation path mobile radio channel model, operating in a time division multiplex access (TDMA) regime, under given decoding delay constraints. The sense in which reliability is measured is addressed, and in the interesting eases where the decoding delay constraint plays a significant role, the maximal achievable rate (capacity), is specified in terms of capacity versus outage. In this case, no coding capacity in the strict Shannon sense exists. Simple schemes for time and space diversity are examined, and their potential benefits are illuminated from an information-theoretic stand point. In our presentation, we chose to specialize to the TDMA protocol for the sake of clarity and convenience. Our main arguments and results extend directly to certain variants of other multiple access protocols such as code division multiple access (CDMA) and frequency division multiple access (FDMA), provided that no fast feedback from the receiver to the transmitter is available. > <s> BIB002 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> A simple model is examined for a slow-fading channel operated under both average input power and decoding delay constraints. In this model, applicable in particular to frequency-hopping and slowly time-varying communication channels, the fading level is assumed constant over intervals of K symbols. The exponential behavior of the average message error probability, as well as outage probabilities, are investigated. The capacity vs. cut-off rate issue is addressed, and the relative efficacy of various diversity methods and interleaving schemes is discussed. <s> BIB003 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> This paper presents a new family of convolutional codes, nicknamed turbo-codes, built from a particular concatenation of two recursive systematic codes, linked together by nonuniform interleaving. Decoding calls on iterative processing in which each component decoder takes advantage of the work of the other at the previous step, with the aid of the original concept of extrinsic information. For sufficiently large interleaving sizes, the correcting performance of turbo-codes, investigated by simulation, appears to be close to the theoretical limit predicted by Shannon. <s> BIB004 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> The authors compute the capacity of bit-interleaved coded modulation (BICM) in the case of ideal interleaving. They show that for most signal sets with Gray labelling, this turns out to be almost equal to the capacity of the signal sets themselves. This implies that BICM can achieve the same coding gain as TCM. <s> BIB005 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design. <s> BIB006 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> A simple iterative decoding technique using hard-decision feedback is presented for bit-interleaved coded modulation (BICM). With an 8-state, rate-2/3 convolutional code, and 8-PSK modulation, the improvement over the conventional BICM scheme exceeds 1 dB for a fully-interleaved Rayleigh flat-fading channel and exceeds 1.5 dB for a channel with additive white Gaussian noise. This robust performance makes BICM with iterative decoding suitable for both types of channels. <s> BIB007 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "water-pouring" in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading. <s> BIB008 </s> Coding for the Fading Channel: a Survey <s> Speech vs. data: The delay issue <s> A new iterative decoding (ID) scheme is suggested for bit-interleaved coded modulation (BICM). The bit-metric generation at the demodulator is optimised with the soft-output feedback from the convolutional decoder. Computer simulation results indicate that BICM-ID, with a few iterations, significantly outperforms conventional trellis coded modulation and is therefore another promising technique to achieve large coding gain without bandwidth expansion. <s> BIB009
A relevant factor in the choice of a coding scheme is the decoding delay that one may allow. For example, recently proposed, extremely powerful codes (the "Turbo Codes" of BIB004 ) suffer from a considerable decoding delay, and hence their applicability is restricted. Consider, for example, real-time speech transmission. Here, a strict decoding delay is imposed (e.g., 100 ms, at most BIB002 ). In this case, the transmission of a code word may span only a few TDMA channel bursts, over which the channel fading is strongly correlated. Thus, a code word experiences only a few significant fading values, which makes the assumption of a memoryless channel, normally achieved by ideal or very long interleaving, no longer valid. On the contrary, with data traffic a large interleaving delay is tolerable, so that very effective coding techniques are available. For example, as we shall see, convolutional codes, bit interleaving, and high-level modulation (such as 8PSK or 16QAM) can be used. These techniques are generally referred to as Bit-Interleaved Coded Modulation (BICM) and have been extensively studied in BIB006 BIB005 BIB006 (Combination of BICM with the "turbo" idea has even been recently proposed, with very promising results. See  BIB009  BIB007 ). Capacity calculations show that with large interleaving BICM performs as well as optimal coding over more complicated alphabets, and its complexity is much lower, so that the performance-complexity trade-off of BICM is very attractive. Moreover, capacity calculations BIB008 show that constant-power constant-rate transmission performs very close to optimal transmission schemes where power and rate are adapted dynamically to the channel conditions via a perfect feedback link. Then, with large interleaving and powerful coding, there is no need for implementing such complicated adaptive techniques and feedback links. 2.1.1. Modeling the delay constraints. The delay constraints can be easily taken into account when designing a coding scheme if a "block-fading" channel model is used. In this model, the fading process is about constant for a number of symbol intervals. On such a channel, a single code word may be transmitted after being split into several blocks, each suffering from a different attenuation, thus realizing an effective way of achieving diversity. The "block-fading" channel model, introduced in BIB003 BIB002 , is motivated by the fact that, in many mobile radio situations, the channel coherence time is much longer than one symbol interval, and hence several transmitted symbols are affected by the same fading value. Use of this channel model allows one to introduce a delay constraint for transmission, which is realistic whenever infinite-depth interleaving is not a reasonable assumption. This model assumes that a code word of length n = M N spans M blocks of length N (a group of M blocks will be referred to as a frame.) The value of the fading in each block is constant. M turns out to be a measure of the interleaving delay of the system. In fact, M = 1 corresponds to N = n, i.e., to no interleaving, while M = n corresponds to N = 1, and hence to ideal interleaving. Thus, the results for different values of M illustrate the downside of nonideal interleaving. It should also be observed that the coding scheme implied by this channel model generalizes standard diversity techniques. In fact, the latter can be seen as a special case of coding for a block-fading channel on which repetition codes are used. With no delay constraint, a code word can span an arbitrarily large number M of fading blocks. If this is the case then capacity, as derived in BIB008 , is a good performance indicator. This applies, for example, to variable-rate systems (e.g., wireless data networks). On the other hand, most of today's mobile radio systems carry real-time speech (cellular telephony), for which constant-rate, constrained-delay transmission should be considered. In the latter case, that is, when each code word must be transmitted and decoded within a frame of M 1 blocks, information outage rate, rather than capacity, is the appropriate performance limit indicator. We shall not delve in this issue any further here, and the interested reader is referred to BIB001 BIB002 .