TY - JOUR
T1 - Joint Convexity of Error Probability in Blocklength and Transmit Power in the Finite Blocklength Regime
AU - Zhu, Yao
AU - Hu, Yulin
AU - Yuan, Xiaopeng
AU - Gursoy, M. Cenk
AU - Poor, H. Vincent
AU - Schmeink, Anke
N1 - Funding Information:
This work was supported in part by the China National Key Research and Development Program under Grant 2021YFB2900301, in part by the Federal Ministry of Education and Research (BMBF) Germany in the Program of "Souverän. Digital. Vernetzt. Joint Project 6G-RIC under Project 16KISK028, and in part by the U.S. National Science Foundation under Grant CNS-2128448.
Publisher Copyright:
© 2002-2012 IEEE.
PY - 2023/4/1
Y1 - 2023/4/1
N2 - To support ultra-reliable and low-latency services for mission-critical applications, transmissions are usually carried via short blocklength codes, i.e., in the so-called finite blocklength (FBL) regime. Different from the infinite blocklength regime where transmissions are assumed to be arbitrarily reliable at the Shannon's capacity, the reliability and capacity performances of an FBL transmission are impacted by the coding blocklength. The relationship among reliability, coding rate, blocklength and channel quality has recently been characterized in the literature, considering the FBL performance model. In this paper, we follow this model, and prove the joint convexity of the FBL error probability with respect to blocklength and transmit power within a region of interest, as a key enabler for designing systems to achieve globally optimal performance levels. Moreover, we apply the joint convexity to general use cases and efficiently solve the joint optimization problem in the setting with multiple users. We also extend the applicability of the proposed approach by proving that the joint convexity still holds in fading channels, as well as in relaying networks. Via simulations, we validate our analytical results and demonstrate the advantage of leveraging the joint convexity compared to other commonly-applied approaches.
AB - To support ultra-reliable and low-latency services for mission-critical applications, transmissions are usually carried via short blocklength codes, i.e., in the so-called finite blocklength (FBL) regime. Different from the infinite blocklength regime where transmissions are assumed to be arbitrarily reliable at the Shannon's capacity, the reliability and capacity performances of an FBL transmission are impacted by the coding blocklength. The relationship among reliability, coding rate, blocklength and channel quality has recently been characterized in the literature, considering the FBL performance model. In this paper, we follow this model, and prove the joint convexity of the FBL error probability with respect to blocklength and transmit power within a region of interest, as a key enabler for designing systems to achieve globally optimal performance levels. Moreover, we apply the joint convexity to general use cases and efficiently solve the joint optimization problem in the setting with multiple users. We also extend the applicability of the proposed approach by proving that the joint convexity still holds in fading channels, as well as in relaying networks. Via simulations, we validate our analytical results and demonstrate the advantage of leveraging the joint convexity compared to other commonly-applied approaches.
KW - Finite blocklength regime
KW - convexity
KW - error probability
KW - joint design
KW - resource allocation
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U2 - 10.1109/TWC.2022.3211454
DO - 10.1109/TWC.2022.3211454
M3 - Article
AN - SCOPUS:85139823532
SN - 1536-1276
VL - 22
SP - 2409
EP - 2423
JO - IEEE Transactions on Wireless Communications
JF - IEEE Transactions on Wireless Communications
IS - 4
ER -