Coding for the Fading Channel: a Survey <s> Bit-interleaved coded modulation <s> 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. <s> BIB001 </s> Coding for the Fading Channel: a Survey <s> Bit-interleaved coded modulation <s> Since the early 1970s, for power-limited applications, the convolutional code constraint length K=7 and rate 1/2, optimum in the sense of maximum free distance and minimum number of bit errors caused by remerging paths at the free distance, has become the de facto standard for coded digital communication. This was reinforced when punctured versions of this code became the standard for rate 3/4 and 7/8 codes for moderately bandlimited channels. Methods are described for using the same K=7, rate 1/2 convolutional code with signal phase constellations of 8-PSK and 160PSK and quadrature amplitude constellations of 16-QASK, 64-QASK, and 256-QASK to achieve, respectively, 2 and 3, and 2, 4, and 6 b/s/Hz bandwidth efficiencies while providing power efficiency that in most cases is virtually equivalent to that of the best Ungerboeck codes for constraint length 7 or 64 states. This pragmatic approach to all coding applications permits the use of a single basic coder and decoder to achieve respectable coding (power) gains for bandwidth efficiencies from 1 b/s/Hz to 6 b/s/Hz. > <s> BIB002 </s> Coding for the Fading Channel: a Survey <s> Bit-interleaved coded modulation <s> A suboptimal trellis coding approach based on the concept of combining a good convolutional code and bit interleavers is presented. The aim is to improve the reliability of digital radio communication over a fading channel. It is shown that over a Rayleigh channel and for a fixed code complexity the proposed system is superior to the baseline system. Its performance is analyzed using the generalized R/sub o/ and the upper bound on the bit error rate. The results suggest that on a Rayleigh channel, the standard trellis codes may not be the correct approach for improving the reliability of the communication channel. The discussion is restricted to a rate 2/3 coded system with 8-PSK modulation. > <s> BIB003 </s> Coding for the Fading Channel: a Survey <s> Bit-interleaved coded modulation <s> Preface. 1. Fading Channel Modeling. 2. Digital Transmission over Fading Channels. 3. Convolutional Codes. 4. Bandwidth-Efficient Coded-Modulation Schemes. 5. Trellis-Coded Modulation Schemes for Fading Channels. 6. Reed-Solomon Codes. 7. RS-Coded MPSK Schemes for Fading Channels. 8. Differential Detection of Coded-Modulation Schemes on a Fading Channel. 9. Performance of Coded Modulation Schemes on Shadowed Rician Fading Channels. 10. Quadrature Pulse-Overlapping Modulation Techniques. Appendix A: Calculation of the Chernoff Factors for Rician and Rayleigh Fading Channels. Appendix B: Calculation of the Transition Probabilities for the MPSK Signal Set over a Rayleigh Fading Channel. Appendix C: Encoding and Decoding Techniques for RS Codes Using Fourier Transform. Appendix D: Derivation of the Probability of Correct Decision for Reliable and Unreliable MPSK Symbols. References. Index. <s> BIB004 </s> Coding for the Fading Channel: a Survey <s> Bit-interleaved coded modulation <s> Recent work on lattices matched to the Rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency. We present a new family of lattice constellations, based on complex algebraic number fields, which have good performance on Rayleigh fading channels. Some of these lattices also present a reasonable packing density and thus may be used at the same time over a Gaussian channel. Conversely, we show that particular versions of the best lattice packings (D/sub 4/, E/sub 6/, E/sub 8/, K/sub 12/, /spl Lambda//sub 16/, /spl Lambda//sub 24/), constructed from totally complex algebraic cyclotomic fields, present better performance over the Rayleigh fading channel. The practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links. Some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results. <s> BIB005 </s> Coding for the Fading Channel: a Survey <s> Bit-interleaved coded modulation <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> Bit-interleaved coded modulation <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> Bit-interleaved coded modulation <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> BIB008
Ever since 1982, when Ungerboeck published his landmark paper on trellis-coded modulation BIB001 , it has been generally accepted that modulation and coding should be combined in a single entity for improved performance. Several results followed this line of thought, as documented by a considerable body of work aptly summarized and referenced in BIB004 (see also  Chap. 10] ). Under the assumption that the symbols were interleaved with a depth exceeding the coherence time of the fading process, new codes were designed for the fading channel so as to maximize their diversity. This implied in particular that parallel transitions should be avoided in the code, and that any increase in diversity would be obtained by increasing the constraint length of the code. One should also observe that for non-Ungerboeck systems, i.e., those separating modulation and coding with binary modulation, Hamming distance is proportional to Euclidean distance, and hence a system optimized for the additive white Gaussian channel is also optimum for the Rayleigh fading channel. A notable departure from Ungerboeck's paradigm was the core of BIB002 . Schemes were designed in which coded modulation is generated by pairing an M -ary signal set with a binary convolutional code with the largest minimum free Hamming distance. Decoding was achieved by designing a metric aimed at keeping as their basic engine an off-the-shelf Viterbi decoder for the de facto standard, 64-state rate-1=2 convolutional code. This implied giving up the joint decoder/demodulator in favor of two separate entities. Based on the latter concept, Zehavi BIB003 first recognized that the code diversity, and hence the reliability of coded modulation over a Rayleigh fading channel, could be further improved. Zehavi's idea was to make the code diversity equal to the smallest number of distinct bits (rather than channel symbols) along any error event. This is achieved by bit-wise interleaving at the encoder output, and by using an appropriate soft-decision bit metric as an input to the Viterbi decoder. For different approaches to the problem of designing coded modulation schemes for the fading channels see BIB005 . One of Zehavi's findings, rather surprising a priori, was that on some channels there is a downside to combining demodulation and decoding. This prompted the investigation whose results are presented in a comprehensive fashion in BIB006 (see also  ). An advantage of this solution is its robustness, since changes in the physical channel affect the reception very little. Thus, it provides good performance with a fading channel as well as with an AWGN channel (and, consequently, with a Rice fading channel, which can be seen as intermediate between these two). Recently, a very promising combination of BICM with the concept of turbo-decoding  BIB008  BIB007 has been discussed and analyzed.