Coding for the Fading Channel: a Survey <s> Introducing delay constraints: The block-fading channel <s> These Ecole polytechnique federale de Lausanne EPFL, n° 1672 (1997)Section de systemes de communication Reference doi:10.5075/epfl-thesis-1672Print copy in library catalog Record created on 2005-03-16, modified on 2016-08-08 <s> BIB001 </s> Coding for the Fading Channel: a Survey <s> Introducing delay constraints: The block-fading channel <s> This work considers the achievable diversity for coded systems appropriately characterized by a block-fading channel model. We are primarily interested in cases where the number of uncorrelated fading channel realizations (blocks) F, is small, so that ideal interleaving assumptions do not hold. This is usually the case in mobile radio systems which employ coded slow frequency-hopping such as the GSM system and its derivatives, We show that the diversity order is limited to a value less than or equal to F which depends on the code rate and the size of the signaling constellation. We report on the results of code searches for rate 1/n convolutional codes for simple AM constellations, which show the minimum complexity needed to achieve maximum diversity. We also present computer simulations of some codes in order to determine the effect of code complexity on the frame and bit error-rate performance. <s> BIB002 </s> Coding for the Fading Channel: a Survey <s> Introducing delay constraints: The block-fading channel <s> This paper considers coded diversity schemes on block fading Rayleigh channels. Based on random coding techniques we analyze the performance of binary block codes on such channels. New upper and lower bounds to the error probability are derived. The new upper bound, that is tighter than previously known results, reveals that the maximum diversity order achieved in a block fading channel with finite interleaving is dictated not only by the number of diversity channels L but also by the code rate R, and that the performance can be only marginally improved by increasing the block length of the code. Furthermore, it was found that low rate codes can effectively exploit the available diversity. For diversity order of L, codes of rate 1/L are in particular advantageous. The gains over conventional diversity schemes are shown to be significant (3-6 dB). Examples of systems that our model can be used for are the GSM or PCS1900, and the ATDMA proposal for UMTS. These systems employ slow frequency hopping TDMA. <s> BIB003 </s> Coding for the Fading Channel: a Survey <s> Introducing delay constraints: The block-fading channel <s> This paper considers coded diversity schemes over block-fading Rician channels using random coding techniques. Two random coding upper bounds on the error probability of block codes are derived: a new bound and a simpler but looser bound assuming binary input distribution. Also, a new lower bound for any block code is derived using the strong converse to channel coding theorem. The lower bound shows that the new random coding upper bound is quite tight. Furthermore, it is shown that the maximum achievable diversity order in a block-fading channel with finite interleaving depends not only on the number of subchannels L, but also on the code rate R and that the performance can only marginally be improved by increasing the block length of the code. The random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths N, demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes. <s> BIB004
The above analysis holds, mutatis mutandis, for the block-fading channel: it suffices in this case to interpret the variables x k as blocks of symbols, rather than symbols. In this situation, it should not come as a surprise (and can in fact be shown rigorously, see BIB001 BIB002 ) that the relevant criterion becomes the block-Hamming distance, i.e., the number of blocks in which two code words differ. An application of the Singleton Bound shows that the maximum block-Hamming distance achievable on an M -block fading channel is limited by where jSj is the size of the signal set S and R is the code rate, expressed in bits/symbol. Note that binary signal sets (jSj = 2) are not effective in this case, so that codes constructed over high-level alphabets should be considered BIB001 BIB002 . For a deeper analysis of the relationship between code diversity and code rate, see BIB003 BIB004 .