# 3.2.4.5.2. Polar MK Decoder parameters¶

## 3.2.4.5.2.1. --dec-type, -D¶

Type

text

Allowed values

SC SCL ASCL CHASE ML

Default

SC

Examples

--dec-type SCL

Select the decoder algorithm.

Description of the allowed values:

Value

Description

SC

Select the original SC algorithm from .

SCL

Select the SCL algorithm from , also support the improved CA-SCL algorithm.

ASCL

Select the A-SCL algorithm from , only the PA-SCL variant is available.

CHASE

See the common --dec-type, -D parameter.

ML

See the common --dec-type, -D parameter.

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

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

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

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

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

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

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

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

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

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

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

## 3.2.4.5.2.2. --dec-implem¶

Type

text

Allowed values

NAIVE

Default

NAIVE

Examples

--dec-implem NAIVE

Select the implementation of the decoder algorithm.

Description of the allowed values:

Value

Description

NAIVE

Select the naive implementation which is typically slow.

## 3.2.4.5.2.3. --dec-lists, -L¶

Type

integer

Default

8

Examples

--dec-lists 1

Set the number of lists to maintain in the SCL decoder.

## 3.2.4.5.2.4. --dec-node-type¶

Type

text

Allowed values

MS SPA

Default

MS

Examples

--dec-node-type SPA

Select the type of computations to make in the decoding functions.

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

$$L_a \boxplus L_b = 2\tanh^{-1}(\tanh(\frac{L_a}{2}).\tanh(\frac{L_b}{2}))$$.

## 3.2.4.5.2.5. References¶

Pmkd-Ari09

E. Arikan. Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Transactions on Information Theory (TIT), 55(7):3051–3073, July 2009. doi:10.1109/TIT.2009.2021379.

Pmkd-BL18(1,2,3)

V. Bioglio and I. Land. On the marginalization of polarizing kernels. In International Symposium on Turbo Codes and Iterative Information Processing (ISTC), 1–5. December 2018. doi:10.1109/ISTC.2018.8625378.

Pmkd-GBLB17

F. Gabry, V. Bioglio, I. Land, and J. Belfiore. Multi-kernel construction of polar codes. In International Conference on Communications (ICC), 761–765. IEEE, May 2017. doi:10.1109/ICCW.2017.7962750.

Pmkd-LST12

B. Li, H. Shen, and D. Tse. An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check. IEEE Communications Letters (COMML), 16(12):2044–2047, December 2012. doi:10.1109/LCOMM.2012.111612.121898.

Pmkd-TV11

I. Tal and A. Vardy. List decoding of polar codes. In International Symposium on Information Theory (ISIT), 1–5. IEEE, July 2011. doi:10.1109/ISIT.2011.6033904.