We consider the point-to-point lossy coding for computing and channel coding problems with two-sided information. We first unify these problems by considering a new generalized problem. Then we develop graph-based characterizations and derive interesting reductions through explicit graph operations, which reduce the number of decision variables. After that, we design alternating optimization algorithms for the unified problems, so that numerical computations for both the source and channel problems are covered. With the help of extra root-finding techniques, proper multiplier update strategies are developed. Thus our algorithms can compute the problems for a given distortion or cost constraint and the convergence can be proved. Also, extra heuristic deflation techniques are introduced which largely reduce the computational time. Numerical results show the accuracy and efficiency of our algorithms.

翻译：我们考虑在双边信息条件下点对点有损编码计算与信道编码问题。首先通过引入新的广义问题统一这些任务，随后建立基于图的特征刻画，并利用显式图操作推导出能减少决策变量数量的有趣约简。在此基础上，为统一问题设计交替优化算法，从而覆盖信源与信道问题的数值计算。借助额外的求根技术，制定合适的乘子更新策略，使得算法能针对给定失真或代价约束进行计算，并证明其收敛性。同时引入启发式缩减技术，大幅缩短计算时间。数值结果表明了所提算法的准确性与高效性。