Abstract -Zehavi 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 [2] . 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. Keywordsing, fading channels. Coded modulation, bit interleav- Ever since 1982, when Ungerboeck published his landmark paper on trellis-coded modulation [l], it has been generally accepted that modulation and coding should be combined in a single entity for improved performance. Of late, the increasing interest for mobile-radio channels has led to the consideration of coded modulation for fading channels. Thus, at first blush it seemed quite natural to apply the same "Ungerboeck's paradigm" of keeping coding combined with modulation even in a situation (the Rayleigh fading channel) where the code performance depends strongly, rather than on the minimum Euclidean distance of the code, on its minimum Hamming distance (the "code diversity" ) . A notable departure from Ungerboeck's paradigm was followed by Zehavi [23, who recognized that the code diversity could be further improved by making it equal to the smallest number of distinct bits (rather than channel symbols) along any error event. This is achieved by bit-wise interleaving the encoder output and by using an appropriate soft-decision bit metric as an input to the Viterbi decoder. Many further results along this line were recently reported (see references in [4]). This paper elaborates on Zehavi's idea. Our goal is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation (BICM) and to provide a general information-theoretical framework for this concept. This analysis also yields tools for evaluating the performance of BICM (with bounds to error probabilities tighter than those previously known) as well as guidelines for its design. We consider a vector channel characterized by a family of transition probability density functions (pdf) parametrized by a complex-valued vector 8 representing the channel state (e denotes the complex field). We assume that 6 is a stationary finite-memory process independent of the channel input x. In general, BICM can be obtained by concatenating an encoder for a binary code C, with an N-dimensional memoryless modulator over a signal set X 5 c of size 1x1 = 2", through a bit interleaver and a oneto-one binary labeling map p : (0, l}m + X . The code sequence c is first interleaved by T . Next, the interleaved sequence n(c) is broken into subsequences of m bits each, which are mapped onto signals in X . Finally, the resulting signal sequence g is transmitted over the vector channel. The bit interleaver can be seen as a one-to-one correspondence r : k -+ (k', i), where k denotes the time ordering of the coded bits Ck, k' denotes the time ordering of the signals Xk' transmitted over the vector channel, and i indicates the position of the bit ck in the label of Xk'. In the following we assume ideal (i.e., infinite-depth) bitinterleaving. Let ti(x) denote the i-th bit of the label of x, and X i the subset of all the signals x E X whose label has the value b E {0,1} in position i (i.e., such that ti(x) = b.) Let 6 denote the complement of b and X i the complement set of X i . Finally, let y the channel output resulting from the transmission of x. The conditional pdf of y , given @(x) = 6 E ( 0 , l ) and 0 , assuming independent and uniformly distributed "bits" b, is Pe(Y I X) (2) The above pdf is the conditional pdf of an equivalent channel model for BICM consisting of a set of m parallel independent and memoryless binary input channels connected to the encoder output by a random switch, which models ideal interleaving.
To achieve this goal, the coded bits in the first block and the last block should be assigned to the labeling bit positions x b REF l and x b 2 l , respectively.
Bit-interleaved coded modulation
Proceedings of ICC'97 - International Conference on Communications
Proceedings of ICC'97 - International Conference on Communications
Computer Science