Patching Based Extra Short Packet Forward Error Control Coding for Ultra-Reliable Low Latency Communications (URLLC) in 5G

Abstract

Extra short packets are common in the 5G Internet which provides low latency, ultra-reliable services for applications such as autonomous driving, remote surgery, industry automation, to name just a few. The multitude number of low cost devices cannot afford to run high power forward error control coding algorithms, such as Turbo codes, LDPC codes, Polar codes, and so on, to meet the stringent requirements of ultra-reliability and extremely low latency. In this paper, we propose using patching as the basis for forward error control coding of extra short packets, where replicas of a packet along with its checksum are transmitted adaptively. At the receiver, we propose using dynamic formation of a full packet based on the theory of Finite Projective Plane. The newly formed packet is then checked for being non-faulty. The approach of patching with dynamic formation of a full packet is systematic and well suitable for extra short packets. Despite the fact that the proposed coding scheme provides lower coding rate for a fixed packet error rate in comparison to the Polar codes and LDPC codes, the main advantages lie in its flexibility and simplicity of processing ideal for asymmetric configuration with low power receiving devices providing ultra-reliable low latency communications.

Appendix

We list the sets for FPP of $N$ points, where $N$ = 7,13, and 21, respectively as follows.

1.1 ${\varvec{N}} = 7$

The sets for a FPP of 7 points are as follows. (1, 2, 3), (1, 4, 5), (1, 6, 7), (2, 4, 6), (2, 5, 7), (3, 5, 6), and (3, 4, 7); The sets that share a common point from 1 to 7 are as follow. $C_{1} = \left( {1,2,3} \right)$, $C_{2} = \left( {1,4,5} \right)$, $C_{3} = \left( {1,6,7} \right)$, $C_{4}$ = (2,4,7), $C_{5} = \left( {2,5,6} \right)$, $C_{6} = \left( {3,4,6} \right)$, and $C_{7} = \left( {3,5,7} \right)$, where $C_{i}$ contains the set numbers that share the common point “i.”

1.2 ${\varvec{N}} = 13$

A FPP of 13 points includes the following 13 sets of points: (1, 2, 3, 4), (1, 5, 6, 7), (1, 8, 9, 10), (1, 11, 12, 13), (2, 5, 8, 11), (2, 6, 9, 12), (2, 7, 10, 13), (3, 5, 10, 12), (3, 6, 8, 13), (3, 7, 9, 11), (4, 5, 9, 13), (4, 6, 10, 11), and (4, 7, 8, 12). The sets that share a common point, from 1 to 13 are as follows.

$C_{1} = \left( {1,2,3,4} \right)$, $C_{2} = \left( {1,5,6,7} \right)$, $C_{3} = \left( {1,8,9,10} \right)$, $C_{4} = \left( {1,11,12,13} \right)$,

$C_{5} = \left( {2,5,8,11} \right)$, $C_{6} = \left( {2,6,9,12} \right)$, $C_{7} = \left( {2,7,10,13} \right)$, $C_{8} = \left( {3,5,9,13} \right)$,

$C_{9} = \left( {3,6,10,11} \right)$, $C_{10} = \left( {3,7,8,12} \right)$, $C_{11} = \left( {4,6,10,12} \right)$, $C_{12} = \left( {4,6,8,13} \right)$,

$C_{13} = \left( {4,7,9,11} \right)$.

1.3 ${\varvec{N}} = 21$

A FPP of 21 points includes the following 21 sets: (1, 2, 3, 4, 5), (1, 6, 7, 8, 9), (1, 10, 11, 12, 13), (1, 14, 15, 16, 17), (1, 18, 19, 20, 21), (2, 6, 10, 14, 18), (2, 7, 11, 15, 19), (2, 8, 12, 16, 20), (2, 9, 13, 17, 21), (3, 6, 11, 16, 21), (3, 7, 10, 17, 20), (3, 8, 13, 14, 19), (3, 9, 12, 15, 18), (4, 6, 12, 17, 19), (4, 7, 13, 16, 18), (4, 8, 10, 15, 21), (4, 9, 11, 14, 20), (5, 6, 13, 15, 20), (5, 7, 12, 14, 21), (5, 8, 11, 17, 18), and (5, 9, 10, 16, 19). The sets of points that share a common point from point 1 to point 21, are as follows.

$C_{1} = \left( {1,2,3,4,5} \right)$, $C_{2} = \left( {1,6,7,8,9} \right)$ $C_{3} = \left( {1,10,11,12,13} \right),$ $C_{4} = \left( {1,14,15,16,17} \right)$, $C_{5} = \left( {1,18,19,20,21} \right)$, $C_{6} = \left( {2,6,10,14,18} \right)$, $C_{7} = \left( {2,7,11,15,19} \right)$,

$C_{8} = \left( {2,8,12,16,20} \right)$, $C_{9} = \left( {2,9,13,17,21} \right)$, $C_{10} = \left( {3,6,11,16,21} \right)$,

$C_{11} = \left( {3,7,10,17,20} \right)$, $C_{12} = \left( {3,8,13,14,19} \right)$, $C_{13} = \left( {3,9,12,15,18} \right)$,

$C_{14} = \left( {4,6,12,17,19} \right)$, $C_{15} = \left( {4,7,13,16,18} \right)$, $C_{16} = \left( {4,8,10,15,21} \right)$,

$C_{17} = \left( {4,9,11,14,20} \right)$, $C_{18} = \left( {5,6,13,15,20} \right)$, $C_{19} = \left( {5,7,12,14,21} \right)$,

$C_{20} = \left( {5,8,11,17,18} \right)$, $C_{21} = \left( {5,9,10,16,19} \right)$.