论文标题
嘈杂的加法器多访问频道的签名代码
Signature Codes for a Noisy Adder Multiple Access Channel
论文作者
论文摘要
在这项工作中，我们考虑了$ Q $ - Y型$ k $和尺寸$ n $的$ q $ - 签名代码，用于嘈杂的加法器多访问频道。该模型中的签名代码具有以下属性，即任何子集的代码字可以根据从这些代码字的总和（超过整数）获得的任何向量进行唯一重建。我们表明存在一种算法来构造长度的签名代码$ k = \ frac {2n \ log {3}} {（1-2τ）\ left（\ log {n} +（q-1）\ log {\ log {\fracπ{2}}}}}}}}}}}}}}}}}}}} +\ Mathcal {o} \ left（\ frac {n} {\ log {n}（q +\ log {n}）} \ right）$能够在信道输出处校正$ 0 \ le fτ<τ<\ frac {q-1} {q-1} {2q} $ 0 \ 0 \ le freac frac {q-frac {q-frac {2q} $。此外，我们提出了具有多项式复杂性的签名代码字的明确构造是一个小的非负数。此外，我们证明了几个不存在的结果（相反边界），以$ q $ - arigar的签名代码实现误差校正。
In this work, we consider $q$-ary signature codes of length $k$ and size $n$ for a noisy adder multiple access channel. A signature code in this model has the property that any subset of codewords can be uniquely reconstructed based on any vector that is obtained from the sum (over integers) of these codewords. We show that there exists an algorithm to construct a signature code of length $k = \frac{2n\log{3}}{(1-2τ)\left(\log{n} + (q-1)\log{\fracπ{2}}\right)} +\mathcal{O}\left(\frac{n}{\log{n}(q+\log{n})}\right)$ capable of correcting $τk$ errors at the channel output, where $0\le τ< \frac{q-1}{2q}$. Furthermore, we present an explicit construction of signature codewords with polynomial complexity being able to correct up to $\left( \frac{q-1}{8q} - ε\right)k$ errors for a codeword length $k = \mathcal{O} \left ( \frac{n}{\log \log n} \right )$, where $ε$ is a small non-negative number. Moreover, we prove several non-existence results (converse bounds) for $q$-ary signature codes enabling error correction.
