论文标题
关于Slepian-wolf编码的随机分布的更一般分布
On More General Distributions of Random Binning for Slepian-Wolf Encoding
论文作者
论文摘要
传统上，定义了Slepian-wolf（SW）代码的集合，以使每个源的每个$ n $ vector的每个bin在整个集合的均匀分布下随机绘制，$ \ {0,1，\ ldots，2^{nr_x}} nr_x} -1 \} -1 \} -1 \} -1 \} $ and $ \ \ {0,1,1,1,1,1,1,1，2^y} $ r_x $和$ r_y $是两个来源的编码率，分别是$ x $和$ y $。 In a few more recent works, where only one source, say, $X$, is compressed and the other one, $Y$, serves as side information available at the decoder, the scope is extended to variable-rate S-W (VRSW) codes, where the rate is allowed to depend on the type class of the source string, but still, the random-binning distribution is assumed uniform within the corresponding, type-dependent, bin index set. 在这项说明性工作中，我们从可靠性（根据误差指数术语定义）和压缩性能（从源编码指数的角度来衡量）的权衡的角度研究了随机构造分布的均匀性的作用。为此，我们研究了一系列更广泛的随机衬里分布，其中包括VRSW代码的集合作为一种特殊情况，但也相当大。我们首先表明，除了某些病理情况外，VRSW代码的较小合奏与较大的合奏一样，在误差指数与源编码指数之间的权衡方面也是如此。尽管有这一发现，但提出的更广泛的合奏会以两种方式激励。首先是，它在上述病理案例中胜过VRSW代码，其次是它允许鲁棒性：如果系统故障导致其中一个来源导致压缩位流的不可用，它仍然允许在某种可控的失真中重建另一个源。
Traditionally, ensembles of Slepian-Wolf (SW) codes are defined such that every bin of each $n$-vector of each source is randomly drawn under the uniform distribution across the sets $\{0,1,\ldots,2^{nR_X}-1\}$ and $\{0,1,\ldots,2^{nR_Y}-1\}$, where $R_X$ and $R_Y$ are the coding rates of the two sources, $X$ and $Y$, respectively. In a few more recent works, where only one source, say, $X$, is compressed and the other one, $Y$, serves as side information available at the decoder, the scope is extended to variable-rate S-W (VRSW) codes, where the rate is allowed to depend on the type class of the source string, but still, the random-binning distribution is assumed uniform within the corresponding, type-dependent, bin index set. In this expository work, we investigate the role of the uniformity of the random binning distribution from the perspective of the trade-off between the reliability (defined in terms of the error exponent) and the compression performance (measured from the viewpoint of the source coding exponent). To this end, we study a much wider class of random-binning distributions, which includes the ensemble of VRSW codes as a special case, but it also goes considerably beyond. We first show that, with the exception of some pathological cases, the smaller ensemble, of VRSW codes, is as good as the larger ensemble in terms the trade-off between the error exponent and the source coding exponent. Notwithstanding this finding, the wider class of ensembles proposed is motivated in two ways. The first is that it outperforms VRSW codes in the above-mentioned pathological cases, and the second is that it allows robustness: in the event of a system failure that causes unavailability of the compressed bit-stream from one of the sources, it still allows reconstruction of the other source within some controllable distortion.
