Optimal Rate Allocation for Superposition Coding in Quasi-Static Fading Channels

Coding with a single fixed rate may not achieve the maximum throughput of a compound channel if the transmitter only has access to channel state statistics. Superposition coding for broadcast channels can be employed to increase the throughput. We study the optimal rate allocation for finite level superposition coding to maximize the throughput. Results show 2-level superposition coding is adequate to achieve most of the throughput gain in a quasi-static Rayleigh fading channel. Introduction This paper investigates how to maximize data throughput in compound channels with probability distributions on channel states. The focus is the quasi-static fading channel, a typical channel model for high speed wireless data transmission. A common approach to communicate in a compound channel with channel state information only available to the receiver (CSIR) is to guarantee a transmission rate for good channel states and suffer outage for bad channels. Care may be used to select a data rate to maximize the throughput. However, such throughput is not the maximum possible. To achieve a higher throughput, it is desirable that some data can be received correctly for certain bad channel states and an additional amount of data can be received for good channel states. Channel coding for such purpose will require unequal error protection (UEP) for different information bits and can be implemented using superposition coding scheme for degraded broadcast channels [ 11. To employ superposition coding, the channel states are first partitioned into sets. Each set is allocated an information rate (or equivalently power), which is achievable if the channel state realization falls in the set. Maximizing the throughput is a joint optimization of rate allocation and channel state partition. The asymptotical case for a quasi-static fading channel has been studied in [a] by partitioning the channel states into infinite many sets. In practice, only finite level superposition coding is possible. Therefore, we study the optimization in the case of finite partitioning of channel states. Optimal Rate Allocation and Results The system we consider is a general quasi-static model consisting of a single transmitter and a single receiver with channel states partitioned into M sets with descending quality. A transmission rate R, is achievable when the channel state H falls in j t h set with probability p,. Subject to average transmission power constraint, we want to find the optimal rate allocation vector 2 = [ R I . . . R M ] ~ to maximize the throughput