A mother polar code of length N = 2n is required for this purpose. When the code is too long (or too
short) for the specified code length E, it is punctured, shortened, or repeated until it is. Depending on
the channel, the minimum and maximum code lengths N for the uplink and downlink are 32 and 512,
1024, respectively. An additional cap is imposed by the minimum allowable coding rate of 1/8. Figure
6 depicts the various encoding methods planned for use in the 5G polar codes design. The bits of
information contained in vector a, denoted by the G code, will be conveyed using the payload of G
code bits. Depending on the parameters of the encoding scheme, the message could be split into two
parts, each of which would be encoded separately before being sent. For every AJ-bit segmented
vector, a polar code-word of length E will be generated. There is an associated L-bit CRC for each AJ-
bit vector. The resulting vector c is fed into an interleave, which requires K = AJ + L bits. To generate
a mother polar code of length N, we need to know the expected coding rate R, the expected codeword
length E, the relative bit channel reliability sequence, and the frozen set. While the remaining bits of
the N-bit u vector are held steady, the interleaved vector cJ and any parity-check bits are added to the
information set.
Using the generator matrix of the selected mother code, GN = G2n, we encode the vector u as d = u
GN. Sub-block interleaving is then used to divide the encoded d into 32 blocks of the same length.
Then, the circular buffer receives these blocks after they have been scrambled to produce y. For rate
matching, the N-bit vector y is modified in some way (puncturing, shortening, or repeating) to yield
the E-bit vector e. In the event that concatenation is necessary, the computed vector f is then ready to
be modulated and transmitted as g.
Having the parameters A and E in play makes it clear that there is a cap on the effectiveness of the
channel being used. While A 11 uses many different block codes, the uplink uses 12 A 1706. The
agreed upon codeword length range is 18 E 8192, even though G 16384 may cause the payload length
G to be longer. Segmentation could be used to do this, dividing the data bits into two polar codewords.
. For PDCCH in the downlink, the maximum value of A is 140, but in this case, if A is 11, the message
will be zero-padded until A = 12. Although E 8192 is employed for uplink, the presence of the CRC
lower limits E to 25. There is only one valid PBCH passcode that utilises the combination of A = 32
and E = 864. These flags are the Input Bits Interleaver Activation (IBIL) signal and the Channel
Interleaver Activation (CIA) (IIL). There are two kinds of PC helper bits, and NPC and nwm both
provide the total number of them.
Fig. 1. Yellow, red, and orange blocks are used in downlink, uplink, and both, respectively, in the 5G polar codes encoding chain.
3. DECODING CONSIDERATION
Even though the 3GPP does not provide any decoding instructions, the final code structure provides
some pointers on how to decode polar codes, which are commonly used in 5G. Figure 1 shows an
encoding sequence; flipping the sequence facilitates decoding. The received encoded symbols are then
padded and deinterleaved to the length of the mother polar code following a second block
segmentation and deinterleaving operation for the uplink. A rate-matching algorithm will be used to
determine the type of padding to be used, with punctuation requiring the addition of zeros, shortening
requiring the use of saturated symbols, and repetition calling for the merging of symbols. The
importance of properly handling the code's helper bits at this stage will be emphasised. After padding,
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