Page 47 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 6 – Wireless communication systems in beyond 5G era

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 6

The receiver stores the observed signal ̄x locally and im‑ and of the symbols of the 2 nd parity symbol sequence p ,
1
mediately echoes it back to the transmitter through the … ( − 1) scales the amplitude of the th systematic
feedback channel. A corresponding sequence symbol ( − 1) and of the symbols of the th parity
symbol sequence p −1 . Power levels ( ) and ( ) are
̃ x = ̄x + g 0 (2) obtained by NN training. The following constraints pre‑
serve the codeword’s average power:
is obtained at the transmitter, where g represents ad‑
0
ditive white Gaussian noise and other possible feedback‑ −1
2
2
channel impairments. ∑ ( ) = 1, ∑ ( ) = 1. (8)
In the second phase, for each element ( ) of x, the en‑ =0 =0
coder computes a corresponding sequence of parity sym‑
bols
2.1 QAM/PAM modulator
p = ( (0), … , ( − 1)), = 0, … , − 1 (3) The DEF code modulator maps the ‑bit information mes‑

sage m = ( (0), … , ( − 1)) to a sequence of real sym‑
and transmits it through the forward channel. is the
number of parity symbols that the encoder generates per bols x = ( (0), … , ( − 1)), hereafter called systematic
symbols. Each pair of consecutive symbols ( (2 ), (2 +
systematic symbol. Thus, the total number of transmitted 1)), = 0, … , /2 − 1, orms a complex QAM symbol
symbols is (1 + ). The DEF code rate is de ined as the √ f
ratio of the message length over (1 + ), that is: ( ) = (2 ) + (2 + 1) −1, where ( ) is obtained by

mapping consecutive bits of m to 2 ‑QAM. The above
mapping produces = 2 / real systematic symbols at
DEF ≜ (1 + ) . (4) the modulator output.
Examples of QAM/PAM mapping of order = 2 and =
The receiver observes a set of corresponding parity sym‑ 4 are shown in Table 1 and Table 2.
bols sequences ̄ p , = 0, … , − 1. ̄ p can be written as

follows: 2.2 Extended feedback
̄ p = p + v , (5)

We call Parity Symbol Generator (PSG) the encoder block
where v = ( (0), … , ( − 1)) represents additive that computes the parity symbol sequences (see Fig. 1).

white Gaussian noise and other forward channel impair‑ Extended feedback consists of sending to the PSG a
ments. ̄ p is immediately echoed back to the transmitter sequence of forward‑channel output observations over

through the feedback channel so as to obtain longer time intervals compared to Deepcode [1].
̃ p = ̄ p + g , (6) Table 1 – Example of QAM/PAM mapping of order = 2.

where g represents additive white Gaussian noise and (2 ), (2 + 1) (2 ) (2 + 1)

other feedback channel impairments. 0, 0 1 1
The DEF codeword is de ined as z = 0, 1 1 ‑1
( (0), … , (( + 1) − 1)). The th codeword sym‑ 1, 0 ‑1 1
bol is de ined as follows: 1, 1 ‑1 ‑1
Table 2 – Example of QAM/PAM mapping of order = 4.
(0) ( ) ( ), 0 ≤ ≤ − 1
( ) = { (7)
( + 1) ( ) ( ), ≤ ≤( + 1) − 1 (4 ), (4 + 1), (4 + 2), (4 + 3) (2 ), (2 + 1)

= ( − ) mod , 0, 0, 0, 0 3, 3
0, 0, 0, 1 3, 1
= ⌊( − )/ ⌋ ,
0, 0, 1, 0 3, ‑3
where (0) and ( + 1), = 0, … , − 1, are codeword 0, 0, 1, 1 3, ‑1
power levels, ( ), = 0, … , −1, are symbol power lev‑ 0, 1, 0, 0 1, 3
th
els, ( ) is the systematic symbol, and ( ) is the th 0, 1, 0, 1 1, 1

th
symbol of the parity sequence (3). Codeword power 0, 1, 1, 0 ‑1, ‑3
levels reallocate the power among codeword symbols as 0, 1, 1, 1 ‑1, ‑1
follows: the systematic symbols are scaled by (0); the 1, 0, 0, 0 ‑3, 3
st
1 parity symbol of each parity sequence is scaled by 1, 0, 0, 1 ‑3, 1
(1), the 2 nd parity symbol of each parity sequence is 1, 0, 1, 0 ‑3, ‑3
scaled by (2), etc. Symbol power levels reallocate the 1, 0, 1, 1 ‑3, ‑1
power among codeword symbols as follows: (0) scales 1, 1, 0, 0 ‑1, 3
st
the amplitude of the 1 systematic symbol (0) and of 1, 1, 0, 1 ‑1, 1
st
the symbols of the 1 parity symbol sequence p , (1) 1, 1, 1, 0 ‑1, ‑3
0
scales the amplitude of the 2 nd systematic symbol (1) 1, 1, 1, 1 ‑1, ‑1
© International Telecommunication Union, 2021 35