A variable-length cross-packet hybrid automatic repeat request (VL-XP-HARQ) is proposed to boost the spectral efficiency (SE) and the energy efficiency (EE) of communications. The SE is firstly derived in terms of the outage probabilities, with which the SE is proved to be upper bounded by the ergodic capacity (EC). Moreover, to facilitate the maximization of the SE, the asymptotic outage probability is obtained at high signal-to-noise ratio (SNR), with which the SE is maximized by properly choosing the number of new information bits while guaranteeing outage requirement. By applying Dinkelbach's transform, the fractional objective function is transformed into a subtraction form, which can be decomposed into multiple sub-problems through alternating optimization. By noticing that the asymptotic outage probability is a convex function, each sub-problem can be easily relaxed to a convex problem by adopting successive convex approximation (SCA). Besides, the EE of VL-XP-HARQ is also investigated. An upper bound of the EE is found and proved to be attainable. Furthermore, by aiming at maximizing the EE via power allocation while confining outage within a certain constraint, the methods to the maximization of SE are invoked to solve the similar fractional problem. Finally, numerical results are presented for verification.

翻译：为提升通信的频谱效率与能量效率，本文提出了一种变长跨包混合自动重传请求（VL-XP-HARQ）方案。首先，基于中断概率推导了频谱效率，并证明其上限为遍历容量。此外，为便于最大化频谱效率，在高信噪比条件下推导了渐近中断概率；通过合理选择新信息比特数并在满足中断需求的前提下实现频谱效率最大化。应用丁克尔巴赫变换后，将分数形式的目标函数转化为减法形式，并通过交替优化分解为多个子问题。注意到渐近中断概率为凸函数，可采用逐次凸近似方法将每个子问题松弛为凸优化问题。进一步研究了VL-XP-HARQ的能量效率，找到了其可达上界。在限定的中断约束条件下，通过功率分配最大化能量效率时，可借鉴前述频谱效率最大化的方法解决类似分数问题。最后，通过数值结果验证了所提方案。