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Polar |MK| Decoder parameters

--dec-type, -D

Type:text
Allowed values:SC SCL ASCL CHASE ML
Default:SC
Examples:--dec-type SCL

|factory::Decoder::p+type,D|

Description of the allowed values:

Value Description
SC Select the original |SC| algorithm from :cite:`Arikan2009`.
SCL Select the |SCL| algorithm from :cite:`Tal2011`, also support the improved |CA|-|SCL| algorithm.
ASCL Select the |A-SCL| algorithm from :cite:`Li2012`, only the |PA-SCL| variant is available.
CHASE See the common :ref:`dec-common-dec-type` parameter.
ML See the common :ref:`dec-common-dec-type` parameter.

At this time, the SC, SCL and ASCL decoders support only a subset of polar kernels listed below.

T2_{Arikan} =
\begin{bmatrix}
   1 & 0 \\
   1 & 1
\end{bmatrix}.

T2_{Arikan} is the original 2 \times 2 kernel proposed by Arikan :cite:`Arikan2009`. This matrix is invertible and can be used for systematic encoding/decoding schemes.

T3_{Huawei1} =
\begin{bmatrix}
   1 & 1 & 1 \\
   1 & 0 & 1 \\
   0 & 1 & 1
\end{bmatrix}.

T3_{Huawei1} is a 3 \times 3 kernel proposed in :cite:`Gabry2017`. This matrix is not invertible and cannot be used for systematic encoding/decoding schemes.

T3_{Huawei2} =
\begin{bmatrix}
   1 & 0 & 0 \\
   1 & 1 & 0 \\
   1 & 0 & 1
\end{bmatrix}.

T3_{Huawei2} is a 3 \times 3 kernel proposed in :cite:`Bioglio2018c`. This matrix is invertible and can be used for systematic encoding/decoding schemes.

T4_{Huawei} =
\begin{bmatrix}
   1 & 0 & 0 & 0 \\
   1 & 1 & 0 & 0 \\
   1 & 0 & 1 & 0 \\
   1 & 1 & 1 & 1
\end{bmatrix}.

T4_{Huawei} is a 4 \times 4 kernel proposed in :cite:`Bioglio2018c`. This matrix is invertible and can be used for systematic encoding/decoding schemes.

T5_{Huawei} =
\begin{bmatrix}
   1 & 0 & 0 & 0 & 0 \\
   1 & 1 & 0 & 0 & 0 \\
   1 & 0 & 1 & 0 & 0 \\
   1 & 0 & 0 & 1 & 0 \\
   1 & 1 & 1 & 0 & 1
\end{bmatrix}.

T5_{Huawei} is a 5 \times 5 kernel proposed in :cite:`Bioglio2018c`. This matrix is invertible and can be used for systematic encoding/decoding schemes.

--dec-implem

Type:text
Allowed values:NAIVE
Default:NAIVE
Examples:--dec-implem NAIVE

|factory::Decoder::p+implem|

Description of the allowed values:

Value Description
NAIVE Select the naive implementation which is typically slow.

--dec-lists, -L

Type:integer
Default:8
Examples:--dec-lists 1

|factory::Decoder_polar_MK::p+lists,L|

--dec-node-type

Type:text
Allowed values:MS SPA
Default:MS
Examples:--dec-node-type SPA

|factory::Decoder_polar_MK::p+node-type|

Description of the allowed values:

Value Description
MS L_a \boxplus L_b \simeq \text{sign}(L_a).\text{sign}(L_b).\min(|L_a|,|L_b|).
SPA L_a \boxplus L_b = 2\tanh^{-1}(\tanh(\frac{L_a}{2}).\tanh(\frac{L_b}{2})).

References

.. bibliography:: references_dec.bib