We consider the problem of joint source–channel coding for transmitting $K$ samples of a complex Gaussian source over $T = bK$ uses of a block-fading multiple-input multiple-output (MIMO) channel with $M$ transmit and $N$ receive antennas. We consider the case when we are allowed to code over $L$ blocks. The channel gain is assumed to be constant over a block and channel gains for different blocks are assumed to be independent. The performance measure of interest is the rate of decay of the expected mean-squared error with the signal-to-noise ratio (SNR), called the distortion SNR exponent. We first show that using a broadcast strategy similar to that of Gunduz and Erkip, but with a different power and rate allocation policy, the optimal distortion SNR exponent can be achieved for $0 leq b ≪ (vert N-Mvert +1)/min (M,N)$ and for $b > MNL^{2}$. This is the first time the optimal exponent is characterized for $1/min (M,N) ≪ b ≪ (vert N-M vert + 1)/ min (M, N)$. Then, we propose a digital layered transmission scheme that uses both time layering and superposition. The new scheme is at least as good as currently known schemes for the entire range of bandwidth expansion factors $b$, whereas at least for some $M$, $N$, and $b$, it is strictly better than the currently known schemes.
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机译：我们考虑了联合源-信道编码问题，该问题用于在$ T = bK $上传输复杂高斯源的$ K $样本，使用块衰落多输入多输出（MIMO）信道以及$ M $传输和$ N $接收天线。我们考虑允许我们对$ L $块进行编码的情况。假设信道增益在一个块上是恒定的，并且不同块的信道增益被认为是独立的。感兴趣的性能度量是预期均方误差随信噪比（SNR）的衰减率，称为失真SNR指数。我们首先表明，使用类似于Gunduz和Erkip的广播策略，但采用不同的功率和速率分配策略，可以以$ 0 leq b≪（vert N-Mvert +1）/ min（ M，N）$和$ b> MNL ^ {2} $。这是第一次以$ 1 / min（M，N）≪ b≪（vert N-M vert + 1）/ min（M，N）$为特征来表征最佳指数。然后，我们提出了一种同时使用时间分层和叠加的数字分层传输方案。对于整个带宽扩展因子$ b $，新方案至少与目前已知的方案一样好，而至少对于某些$ M $， $ N $和$ b $，它严格来说是严格的。比目前已知的方案更好。
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