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NR polar code VII - SCL (successful cancellation list coding)

2022-04-23 01:35:00 【Bai Xiaosheng of Ming Dynasty】

Preface

SC Is a greedy algorithm , Finally, only one is decoded , Although it can pass through SC Decoding reaches Shannon capacity . But in finite code length , Because of Murphy's law , Follow CRC Problem with collaboration , The improvement in performance is not so obvious .

SCL Can better follow CRC Collaboration , It generates a list , The list includes [1,2,4,8,16]msg.

adopt CRC After verification , Normally, the remaining one will pass the verification , Improved CRC Probability of successful verification . Although it increases the complexity , However, the communication performance is significantly improved , There is no mathematical proof of this , It's just an engineering practice .

Catalog ：

SC Decoding and Murphy's law
SCL（succesive cancellation list decoding）
DM(decision SC)& PM
M = 4 Example

One SC decoding and Murphy's law

in the light of k Messages bit:

Polar After decoding , Need to carry out CRC. because CRC Need all of bit All bits must be transmitted correctly ,99.9% It's no use being right , It still needs to be retransmitted .

SC Coding is based on probability , from u_1 To u_N The probability of correct transmission is higher and higher .

n The probability of correct transmission of all codes is p= p_1*p_2*p_3*...p_n

Then the probability of at least one error is err=1-p.

for instance ：

（N=10,K=400） The encoding length is 1024, Information bit Count by 400

At least one probability of error 0.3449(BEC channel ）

40% Probability has to be retransmitted , Of course K Set less , Can improve CRC Success , However, it will lead to low utilization of time slot resources .

This is also modem The question of universality , Need an overall assessment , Scene is complicated , Often one problem is solved , More complicated problems will be caused by . For example, as mentioned earlier OFDM, Inside GI,CP How to calculate , If you don't do well, your performance will be worse .

SC Put it forward , Many years later, someone proposed to use SCL solve ,List decoding It has a very long history , It's not new . But the combination of the two found that the practical effect is better .

Two SCL（succesive cancellation list decoding）

3.1 brief introduction

Until now, we have been based on binary tree method to elaborate polar, Bilken University, Turkey Erdal　Arikan professor

The original work discusses its core idea based on information theory and matrix . This method is also called SSCL,SSC(simplified SCL)

A simplified version of SCL, The functions and principles are the same , It's just that the methods and perspectives are different .

SCL There is no strict mathematical proof that it must be effective , It can be understood through computer risk theory ,

The original SC decoding , Finally, only the most probable result is decoded msg.

adopt SCL Can give [1,2,4,16] Kind of msg list , after CRC After normal, there will be one left , For other cases, it can be based on PM Choose the penalty factor and the smallest .

3.2 Program flow

First step ： add CRC

This is what the physical layer does , Follow Polar irrelevant .

To send a TB, Assumed length is A individual bits, after CRC after , To become a

The length is K bits Information about

Actually need to send msg by k bits

The second step Polar

Unreliable channel transmission N-K A freeze bit, Fixed for 0

Transmit on a reliable channel K individual bit

The third step Output codeword

Now output a codeword Is the actual value

Step four ： BPSK AWGN Post transmission

Step five ： The receiving party checks the received data SC List Decoder

$\begin{bmatrix} msg1\\ msg2 \\ msg3 \\ msg4 \end{bmatrix}$

SC decoder after , Will only output a maximum probability msg

list Decoder Will be output [4,8,16] individual msg. Every msg All are

A predicted value of the original transmission data

Step six ： CRC

Received by the physical layer msg List Conduct estimate.

There are three normal situations ：

1： Only one passed CRC check , Retain

2： One doesn't pass CRC check , Retransmission

3： More than one pass , adopt PM Strategy , Choose a penalty factor and the smallest .

In the actual scene, the 3 Kind of , Rarely encounter a probability of less than one in a million （ Follow CRC It depends on the length ）

3、 ... and DM(decision SC)& PM

The original SC programme , Decoding i individual bit when , be based on L(u) Only one result will be given , Or 0, Or 1.

SCL programme ,

For news bit:

Decoding i individual bit When , At the same time give 2 results .

If $L(u_i)\geq 0$ :

$\hat{u_i}=0$ , $DM_i=0$ ,DM Decision penalty factor . Now for 0

$\hat{u_i}=1,DM_i=|L(u_i)|$ , Because at the moment with belief Make the opposite decision , So belief The absolute value of is used as the penalty factor