A Discretization Approach to Compute–Forward
A Discretization Approach to Compute–Forward
复制标题
前向计算的离散化方法
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
M. Gastpar
中科院分区：
文献类型：
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作者：
A. Pastore;S. Lim;Chen Feng;B. Nazer;M. Gastpar
我们提出了一种新的统一框架的计算前向可实现的速率区域同时解码的多个线性码字组合。该框架涵盖了广泛的离散和连续输入通道，以及有限域，整数和实数上的计算。由此产生的速率区域恢复了几个众所周知的可扩展性结果，并在某些情况下扩展了它们。该框架是建立在最近建立的可实现的速率区域的基础上的线性码和联合典型性解码。后者是从有限域上的整数计算，并通过离散化的方法，计算与整数系数和连续输入的实数。评估后者与高斯分布，我们得到了一个封闭形式的率区域，它概括了经典的计算转发率最初通过格码由Nazer和Gastpar。
We present a novel unified framework of compute-forward achievable rate regions for simultaneous decoding of multiple linear codeword combinations. This framework covers a wide class of discrete and continuous-input channels, and computation over finite fields, integers, and reals. The resulting rate regions recover several well-known achievability results, and in some cases extend them. The framework is built upon a recently established achievable rate region based on linear codes and joint typicality decoding. The latter is extended from finite fields to computation over the integers and, via a discretization approach, to computation over the reals with integer coefficients and continuous inputs. Evaluating the latter with Gaussian distributions, we obtain a closed-form rate region which generalizes the classic compute-forward rates originally derived by means of lattice codes by Nazer and Gastpar.