Issue link: https://read.uberflip.com/i/1464683
LoRaWAN ® Fragmented Data Block Transport Specification TS004-2.0.0 ©2022 LoRa Alliance ® Page 24 of 32 The authors reserve the right to change specifications without notice. The coded fragments P M N are constructed by performing a bit-by-bit XOR operation between 636 different subsets of the uncoded fragments. The XOR operator is noted '+', the AND 637 operator is noted '.'. 638 639 Each coded fragment is defined as: 640 P M N = ( 1 ) . 1 + ( 2 ) . 2 + . . . + ( ). 641 642 Where ( ) is a function of M,N and i, and whose value is either 0 or 1. 643 • 0. 1 is a binary word of the same length as the fragment 1 with all bits = 0. 644 • 1. 1 is equal to 1 . 645 The binary vector ( , ) = [ (1), (2), . . . , ( )] of M bits is a function of M and N and 646 is given by a function matrix_line(M,N) . 647 648 It is sufficient to know that this function generates either: 649 • If N<=M, a vector of length M with a single 1 at position N, all other bits = 0. 650 • If N>M, a parity check vector containing statistically as many zeros as ones in a 651 pseudo-random order. 652 The parity check matrix, as defined by Gallager in his 1963 thesis, is an MxN matrix 653 containing the on column i and line N. 654 The following picture illustrates an example of such a matrix generated by the proposed 655 function for M=26 and with a coding ratio CR=1/2; this matrix has 26/CR = 52 lines. It allows 656 the creation of 52 coded fragments from the 26 original uncoded fragments. 657