Page 46 - 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

Transmitter Receiver
1 st
Modulator phase
Buffer
( ) Power reall. (a,w)

Parity Symbol Generator 2 nd
th
(k iteration) phase 1 st
phase
...
... ... ...
D
0 ( − 0 ) ... 0 ( − 1) 0 ( ) phase −1 ...
...
...
2
nd
... - + 1 st
... 0 ( − 1 ) 0 ( − 2) 0 ( − 1) D ... D Buffer 0 S phase Codeword
−1 ( − ) −1 ( − 2) −1 ( − 1) D ... D 0 ... De- - S + phase
nd
2
D ... D −1 mux −1 −1
Fig. 1 – DEF encoder structure. Each “ ” block represents a unit‑time delay. Blue blocks and signals denote new functionalities compared to prior
solutions.

approach could be used in the decoder to extend its input denotes the sub‑vector that contains the elements of b
so as to comprise delayed versions of received signals in a with indices in [ ∶ ]. Boldface upper case letters like
given time window. However, it can be shown that such a A denote matrices; , represents the element of A in the
th
th
generalization of the decoder does not bring any bene it row and column. Notation (v), where is a func‑
and therefore it will not be considered in the de inition of tion taking a scalar input, indicates the vector obtained by
DEF codes. The extended‑feedback encoder architecture applying to each element of v. Hadamard (i.e., element‑
is combined with different NN architectures of recurrent wise) product is denoted by ∘.
type, namely RNN, GRU and LSTM. The DEF code general‑
izes Deepcode [1] along several directions. Its major ben‑ 2. DEFINITION OF DEEP EXTENDED FEED‑
e its can be summarized as follows:
BACK CODE
• Improved error correction capability obtained The Deep Extended Feedback (DEF) code is the set of
by feedback extension. The DEF code generates codewords produced by the DEF encoder shown in Fig. 1.
parity symbols based on feedbacks in a longer time Blue blocks and signals in Fig. 1 denote the new func‑
window, thereby introducing long‑range dependen‑ tionalities of the DEF code compared to Deepcode [1], ex‑
cies between parity symbols. As the above long‑ tended feedback is shown by the unit‑time delay blocks la‑
range dependencies are a necessary ingredient of beled “ ” and their corresponding input/ouput signals;
all good error correcting codes, it is expected that QAM/PAM symbols are produced by the block labeled
feedback extension will bring performance improve‑ “Modulator”. DEF code and Deepcode operate according
ments.
to the same encoding procedure as described later on.
• Higher spectral ef iciency obtained by usage The novel DEF code features will be treated in dedicated
of QAM/PAM modulations. The DEF code uses subsections.
Quadrature Amplitude Modulation (QAM) with ar‑ The encoding procedure consists of two phases. In
bitrary order, thereby potentially achieving higher the irst phase, an ‑bit information message m =
spectral ef iciency. ( (0), … , ( −1)) is mapped to a sequence of real sym‑
bols x = ( (0), … , ( − 1)), hereafter called systematic
In this work, we initially focus on DEF codes’ performance symbols.
evaluation over channels with noiseless feedback, where The modulation sequence x is transmitted on the forward
the forward‑channel output observations are sent uncor‑ channel. The corresponding sequence ̄x observed by the
rupted to the encoder. receiver is given by
Notation: Lower case and upper case letters denote
scalar (real or complex) values. For any pair of positive ̄ x = x + n 0 (1)
integers and with < , [ ∶ ] denotes the sequence of
integers [ , + 1, … , ], sorted in increasing order. Bold‑ where n 0 represents Additive White Gaussian Noise
face lower case letters (e.g., b) denote vectors; unless oth‑ (AWGN) and other possible forward‑channel impair‑
erwise speci ied, all vectors are assumed to be column ments. In the performance evaluations of Section 4, n is
0
th
vectors. ( ) denotes the element of b; b( ∶ ), < , modeled as a sequence of white Gaussian noise samples.

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