Coding for the wireless channel

• Authors: Ezio Biglieri
• Venue: The handbook of ad hoc wireless networks
• Year: 2003

We consider the design and the performance of coding schemes for a channel affected by fading and additive noise. Optimum coding schemes for this channel lead to the development of new criteria for code design, differing markedly from the Euclidean-distance criterion which is commonplace over the additive white Gaussian noise (AWGN) channel. In fact, for frequency flat, slow fading channels the code performance depends strongly, rather than on the minimum Euclidean distance of the code, on its minimum Hamming distance (the "code diversity"). If the channel model is not stationary, as happens for example in a mobile radio communication system, where it may fluctuate in time between the extremes of Rayleigh and AWGN, then a code designed to be optimal for a fixed channel model might perform poorly when the channel varies. Therefore, a code optimal for the Rayleigh fading channel may be actually suboptimal for a substantial fraction of the time, and rather than for an optimum solution one should look for a robust solution, i.e., one with performance that is not critically dependent on the environment. In these conditions, antenna diversity with maximum-gain combining may prove useful: in fact, under fairly general conditions, a channel affected by fading can be turned into an AWGN channel by increasing the number of diversity branches. Another robust solution is based on bit interleaving, which yields a large code diversity thanks to the choice of powerful error-control codes coupled with a bit interleaver and the use of a suitable bit metric. An important feature of bit-interleaved coded modulation is that it lends itself quite naturally to "pragmatic" designs, i.e., to coding schemes that keep as their basic engine an off-the-shelf decoder. Yet another solution is based on controlling the transmitted power so as to compensate for the attenuations due to fading. Adaptive techniques, allowing the coding/modulation scheme to be modified according to the channel conditions, are also examined. Finally, the effect of multiple transmit and receive antennas on the performance of a radio system is analyzed.