TW202316811A - Communications system using polar codes and decoding method thereof - Google Patents

Communications system using polar codes and decoding method thereof Download PDF

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TW202316811A
TW202316811A TW110138061A TW110138061A TW202316811A TW 202316811 A TW202316811 A TW 202316811A TW 110138061 A TW110138061 A TW 110138061A TW 110138061 A TW110138061 A TW 110138061A TW 202316811 A TW202316811 A TW 202316811A
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decoding
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polar code
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TWI783727B (en
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陳彥銘
胡宸瑋
黃柏綸
李志鵬
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國立中山大學
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Abstract

A communications system includes a transmitter and a receiver. The transmitter is configured to transmit a polar code signal. The receiver is configured to receive the polar code signal and perform a list decoding process on the polar code signal by utilizing a decoding method with variable-to-check (V2C) dynamic scheduling.

Description

使用極化碼之通訊系統及其解碼方法Communication system using polar code and its decoding method

本揭示是有關於用於通訊系統之解碼方法，且特別是有關於對極化碼訊號進行解碼的通訊系統及其解碼方法。The present disclosure relates to a decoding method for a communication system, and in particular to a communication system for decoding a polar code signal and a decoding method thereof.

極化碼（polar code）已被證實當其碼長無限長時在二進位離散無記憶通道（binary discrete memoryless channel）中可達到香農極限（Shannon Limit）。然而，在現實的通訊系統下，均以有限碼長的碼字進行編解碼及傳輸。如何在此限制下設計極化碼的解法方式，以達到高系統吞吐量，同時具有高解碼效能及低運算複雜度，已為相關領域的從業者致力的目標之一。Polar codes have been proven to reach the Shannon Limit in a binary discrete memoryless channel when the code length is infinite. However, under the actual communication system, code words with finite code length are used for encoding, decoding and transmission. How to design a polar code solution under this limitation to achieve high system throughput while having high decoding performance and low computational complexity has become one of the goals that practitioners in related fields are committed to.

本揭示內容之一態樣為一種使用極化碼之通訊系統，其包含發送端和接收端，其中發送端配置為發送極化碼（polar code）訊號，而接收端配置為接收極化碼訊號，並使用V2C（variable-to-check）動態排程（dynamic scheduling）解碼法對極化碼訊號進行列表解碼（list decoding）。One aspect of the present disclosure is a communication system using polar codes, which includes a transmitter and a receiver, wherein the transmitter is configured to transmit polar code signals, and the receiver is configured to receive polar code signals , and use the V2C (variable-to-check) dynamic scheduling decoding method to perform list decoding on the polar code signal.

依據一或多個實施例，極化碼訊號包含循環冗餘校驗（cyclic redundant check）資訊，且解碼端更配置為判別對極化碼訊號的循環冗餘校驗是否成功。According to one or more embodiments, the polar code signal includes cyclic redundancy check (cyclic redundancy check) information, and the decoder is further configured to determine whether the cyclic redundancy check on the polar code signal is successful.

依據一或多個實施例，解碼端應用排程多樣性（schedule diversity）至V2C動態排程解碼法以對極化碼訊號進行列表解碼。According to one or more embodiments, the decoder applies schedule diversity to the V2C dynamic scheduling decoding method to perform list decoding on the polar coded signal.

依據一或多個實施例，在使用解碼順序進行迭代解碼而失敗時，解碼端隨機打亂解碼順序進而產生新的解碼順序以接續進行迭代解碼。According to one or more embodiments, when the iterative decoding using the decoding order fails, the decoding end randomly disrupts the decoding order to generate a new decoding order for subsequent iterative decoding.

依據一或多個實施例，解碼端應用位元翻轉（bit flip）至V2C動態排程解碼法以對該極化碼訊號進行列表解碼。According to one or more embodiments, the decoding end applies bit flip to V2C dynamic scheduling decoding method to perform list decoding on the polar code signal.

本揭示內容之另一態樣為一種通訊方法，其包含接收極化碼訊號以及使用V2C動態排程解碼法對極化碼訊號進行列表解碼。Another aspect of the disclosure is a communication method, which includes receiving a polar code signal and performing list decoding on the polar code signal by using a V2C dynamic scheduling decoding method.

以下仔細討論本揭示的實施例。然而，可以理解的是，實施例提供許多可應用的概念，其可實施於各式各樣的特定內容中。所討論之特定實施例僅供說明，並非用以限定本揭示之範圍。Embodiments of the present disclosure are discussed in detail below. It should be appreciated, however, that the embodiments provide many applicable concepts that can be implemented in a wide variety of specific contexts. The specific embodiments discussed are illustrative only and do not limit the scope of the disclosure.

在本文中所使用的用語僅是為了描述特定實施例，非用以限制申請專利範圍。除非另有限制，否則單數形式的「一」或「該」用語也可用來表示複數形式。The terms used herein are only used to describe specific embodiments, and are not intended to limit the scope of patent applications. Unless otherwise limited, the terms "a" or "the" in the singular may also be used in the plural.

圖1為本發明實施例之通訊系統100的示意圖。通訊系統100包含發送端110、接收端120和無線通道130，其中發送端110和接收端120經由無線通道130通訊連接。發送端110和接收端120分別用於發送和接收訊號，而通道。在一些實施例中，發送端110和接收端120也可分別用於接收和發送訊號。進一步地，在通訊系統100中的通訊設備（例如發送端110、接收端120和/或其他通訊設備）可作為訊號傳輸端、訊號接收端或為訊號傳輸/接收端。此外，在通訊系統100中的通訊設備（例如發送端110、接收端120和/或其他通訊設備）可具有多種不同的實施方式，其包含但不限於例如用戶設備（user equipment；UE）、行動站（mobile station；MS）、筆記型電腦、行動電話等行動裝置和基站（base station；BS）、演進式基地台（evolved NodeB；eNB）、次世代基地台（next generation NodeB；gNB）、次世代演進式基地台（next generation evolved NodeB；ng-eNB）、計算機設備、伺服器設備、工作站等固定裝置，且可在移動環境下和/或在固定環境下與遠端實體進行無線通訊。通訊系統100支援的通訊技術包含但不限於第五代新無線電（fifth generation new radio；5G NR）、進階長期演進技術（Long-term Evolution Advanced；LTE-A）、進階升級版長期演進技術（Long-term Evolution Advanced Pro；LTE-A Pro）、無線區域網路（wireless local area network；WLAN）通訊技術和/或其他相似的無線通訊技術。FIG. 1 is a schematic diagram of a communication system 100 according to an embodiment of the present invention. The communication system 100 includes a transmitter 110 , a receiver 120 and a wireless channel 130 , wherein the transmitter 110 and the receiver 120 are connected via the wireless channel 130 . The sending end 110 and the receiving end 120 are respectively used for sending and receiving signals, and channels. In some embodiments, the sending end 110 and the receiving end 120 can also be used for receiving and sending signals respectively. Further, the communication devices (such as the transmitter 110 , the receiver 120 and/or other communication devices) in the communication system 100 can serve as a signal transmission terminal, a signal reception terminal or a signal transmission/reception terminal. In addition, the communication devices (such as the sending end 110, the receiving end 120 and/or other communication devices) in the communication system 100 may have various implementations, including but not limited to user equipment (user equipment; UE), mobile Mobile station (mobile station; MS), notebook computer, mobile phone and other mobile devices and base station (base station; BS), evolved base station (evolved NodeB; eNB), next generation base station (next generation NodeB; gNB), secondary Next generation evolved base station (next generation evolved NodeB; ng-eNB), computer equipment, server equipment, workstations and other fixed devices, and can perform wireless communication with remote entities in a mobile environment and/or in a fixed environment. The communication technologies supported by the communication system 100 include but are not limited to fifth generation new radio (5G NR), Long-term Evolution Advanced (LTE-A), and advanced long-term evolution technology (Long-term Evolution Advanced Pro; LTE-A Pro), wireless local area network (wireless local area network; WLAN) communication technology and/or other similar wireless communication technologies.

發送端110採用的編碼方式為極化碼編碼，其透過並行系統建碼，將資訊位元向量對映至特定碼字，以產生極化碼訊號，並將極化發訊號經由無線通道130發送至接收端120。接收端120接收該極化碼訊號後，使用動態排程（dynamic scheduling）解碼法對極化碼訊號進行列表解碼（list decoding），以從極化碼訊號解碼出資訊位元。The encoding method adopted by the transmitting end 110 is polar code encoding, which maps the information bit vector to a specific code word through parallel system code building to generate a polar code signal, and sends the polar signal through the wireless channel 130 to the receiver 120. After receiving the polar code signal, the receiver 120 uses a dynamic scheduling decoding method to perform list decoding on the polar code signal to decode information bits from the polar code signal.

在並行系統建碼上，首先根據資訊位元向量中的資訊位元和凍結位元（frozen bits）生成訊息矩陣E。在訊息矩陣E中，對應凍結位元位置的行的元素全為0，而對應資訊位元位置的行在對應資訊位元次序的列的元素為1，其餘元素則為0。舉例而言，若資訊位元向量

Figure 02_image001
的長度為8（
Figure 02_image003
=8），其中
Figure 02_image005
、
Figure 02_image007
、
Figure 02_image009
、
Figure 02_image011
為資訊位元，而
Figure 02_image013
、
Figure 02_image015
、
Figure 02_image017
、
Figure 02_image019
為凍結位元，則生成的訊息矩陣
Figure 02_image021
如式(1)所示：
Figure 02_image023
且其對應的反轉置換（bit-reversal permutation matrix）矩陣
Figure 02_image025
如式(2)所示：
Figure 02_image027
In the code building of the parallel system, the message matrix E is first generated according to the information bits and frozen bits in the information bit vector. In the message matrix E, the elements in the row corresponding to the frozen bit position are all 0, and the elements in the row corresponding to the information bit position in the column corresponding to the information bit order are 1, and the rest of the elements are 0. For example, if the information bit vector
Figure 02_image001
has a length of 8 (
Figure 02_image003
=8), where
Figure 02_image005
,
Figure 02_image007
,
Figure 02_image009
,
Figure 02_image011
is the information bit, and
Figure 02_image013
,
Figure 02_image015
,
Figure 02_image017
,
Figure 02_image019
For frozen bits, the resulting message matrix
Figure 02_image021
As shown in formula (1):
Figure 02_image023
And its corresponding bit-reversal permutation matrix
Figure 02_image025
As shown in formula (2):
Figure 02_image027

對資訊位元向量

Figure 02_image029
。進行編碼運算後得到的非反轉極化碼
Figure 02_image031
和反轉極化碼
Figure 02_image033
分別以式(3)和式(4)表示：
Figure 02_image035
Figure 02_image037
其中
Figure 02_image039
為階數，
Figure 02_image041
為基礎矩陣
Figure 02_image043
等於
Figure 02_image045
的第
Figure 02_image039
階克羅內內積（Kronecker product），
Figure 02_image047
，
Figure 02_image025
為反轉置換矩陣。
Figure 02_image049
和
Figure 02_image051
均等於單位矩陣（identity matrix）且尺寸相同，故無論是將反轉極化碼
Figure 02_image031
乘上矩陣
Figure 02_image053
，或是將反轉極化碼
Figure 02_image033
乘上矩陣
Figure 02_image055
，均可得到資訊位元向量
Figure 02_image057
。 bit vector
Figure 02_image029
. The non-inverted polar code obtained after encoding operation
Figure 02_image031
and reverse polarity code
Figure 02_image033
Respectively represented by formula (3) and formula (4):
Figure 02_image035
Figure 02_image037
in
Figure 02_image039
is the order,
Figure 02_image041
is the fundamental matrix
Figure 02_image043
equal
Figure 02_image045
First
Figure 02_image039
order Kronecker product (Kronecker product),
Figure 02_image047
,
Figure 02_image025
is the inverse permutation matrix.
Figure 02_image049
and
Figure 02_image051
are equal to the identity matrix (identity matrix) and have the same size, so whether it is to reverse the polar code
Figure 02_image031
multiply the matrix
Figure 02_image053
, or reverse the polar code
Figure 02_image033
multiply the matrix
Figure 02_image055
, both can get the information bit vector
Figure 02_image057
.

圖2為極化碼生成因子示意圖。在圖2中，每一邊線代表攜帶0或1的位元訊號，且每一節點代表對收到的位元訊號進行二進制加法運算和/或送出位元訊號至下一階節點，其中最左側節點對應資訊位元向量，而對應最右側節點的位元

Figure 02_image059
至
Figure 02_image061
為極化碼位元。 Fig. 2 is a schematic diagram of polar code generation factors. In Figure 2, each edge represents a bit signal carrying 0 or 1, and each node represents a binary addition operation on the received bit signal and/or sends a bit signal to the next-level node, where the leftmost The node corresponds to the information bit vector, and the bit corresponding to the rightmost node
Figure 02_image059
to
Figure 02_image061
is the polar code bit.

在極化碼解碼端，可使用置信傳播（belief propagation；LBP）解碼方式對收到的極化碼訊號進行解碼。基於置信傳播解碼的因子圖具有

Figure 02_image063
個基本運算塊和
Figure 02_image065
個節點，其中
Figure 02_image003
為碼字長度，而
Figure 02_image067
代表階數。圖3示出碼字長度
Figure 02_image003
為8的置信傳播解碼因子圖，其具有12個基本運算塊和32個節點。每一基本運算塊的示意圖如圖4所示，且其依據式(5)至式(8)進行運算：
Figure 02_image069
Figure 02_image071
Figure 02_image073
Figure 02_image075
其中
Figure 02_image077
、
Figure 02_image079
分別代表位元序號和階數序號，
Figure 02_image081
和
Figure 02_image083
分別代表因子圖中右側至左側訊息和左側至右側訊息，且函式
Figure 02_image085
表示如下：
Figure 02_image087
。函式
Figure 02_image085
近似為
Figure 02_image089
，其中
Figure 02_image091
為偏移係數。 At the polar code decoding end, a belief propagation (LBP) decoding method may be used to decode the received polar code signal. The factor graph based on belief propagation decoding has
Figure 02_image063
basic arithmetic blocks and
Figure 02_image065
nodes, where
Figure 02_image003
is the codeword length, and
Figure 02_image067
represents the order. Figure 3 shows the codeword length
Figure 02_image003
Belief propagation decoding factor graph of 8, which has 12 basic operation blocks and 32 nodes. The schematic diagram of each basic operation block is shown in Figure 4, and it operates according to formula (5) to formula (8):
Figure 02_image069
Figure 02_image071
Figure 02_image073
Figure 02_image075
in
Figure 02_image077
,
Figure 02_image079
represent the bit sequence number and the order sequence number respectively,
Figure 02_image081
and
Figure 02_image083
represent the right-to-left message and left-to-right message in the factor graph, respectively, and the function
Figure 02_image085
Expressed as follows:
Figure 02_image087
. function
Figure 02_image085
approximately
Figure 02_image089
,in
Figure 02_image091
is the offset coefficient.

在進行置信傳播解碼時，可先利用式(9)及式(10)分別對所有的訊息進行初始化：

Figure 02_image093
Figure 02_image095
接著再利用式(5)-(8)及函式
Figure 02_image085
近似為
Figure 02_image089
的特性，由因子圖的右側至左側計算出所有的
Figure 02_image081
，且到達最左側後，再由因子圖的左側至右側計算出所有的
Figure 02_image097
，而完成一次迭代運算。 When performing belief propagation decoding, all information can be initialized by using formula (9) and formula (10):
Figure 02_image093
Figure 02_image095
Then use equations (5)-(8) and the function
Figure 02_image085
approximately
Figure 02_image089
The properties of the factor graph are calculated from the right side to the left side of all
Figure 02_image081
, and after reaching the far left, calculate all the
Figure 02_image097
, and complete an iterative operation.

為了具有較佳的解碼效能，置信傳播解碼的最大迭代次數通常會設定較高。然而，若未設定提早停止迭代的條件，則即使已成功解碼出一個合法碼字，只要迭代次數未達到上限值，置信傳播解碼的迭代運算就會繼續進行，導致運算複雜度過高，甚至在後續迭代運算無法解碼出合法碼字。為避免上述情形發生，可加上早期終止迭代運算的條件。首先，產生極化碼生成矩陣

Figure 02_image099
，其中
Figure 02_image101
為尺寸
Figure 02_image103
的反轉置換矩陣，且接著將生成矩陣
Figure 02_image105
中包含凍結位元（frozen bits）的列移除，而產生新的生成矩陣
Figure 02_image107
，其中
Figure 02_image109
為碼字中的資訊位元個數，之後再藉由高斯消去法（Gaussian elimination），將生成矩陣
Figure 02_image107
轉換為系統矩陣
Figure 02_image111
，其中
Figure 02_image113
為單位矩陣，並得到奇偶校驗（parity check）矩陣
Figure 02_image115
。最後，將碼字
Figure 02_image117
乘上奇偶校驗矩陣
Figure 02_image119
，以得到徵狀值。若徵狀值為零向量，則判別碼字
Figure 02_image117
為合法碼字，並終止迭代運算，且資訊位元向量
Figure 02_image121
可依據等式
Figure 02_image123
計算而得，反之則在迭代次數未達到上限值下進行下一次迭代運算。當迭代次數到達上限值，或是滿足奇偶校驗等式時，則決定資訊位元向量
Figure 02_image121
中每個位元
Figure 02_image125
的位元值為
Figure 02_image127
，其中
Figure 02_image129
為有號數運算（signed operation），且
Figure 02_image131
和
Figure 02_image133
分別代表最近一次迭代操作的
Figure 02_image135
和
Figure 02_image137
。 In order to have better decoding performance, the maximum number of iterations of belief propagation decoding is usually set higher. However, if no conditions are set to stop iterations early, even if a legal codeword has been successfully decoded, as long as the number of iterations does not reach the upper limit, the iterative operation of belief propagation decoding will continue, resulting in high computational complexity, even Legal codewords cannot be decoded in subsequent iterative operations. In order to avoid the above situation, a condition for early termination of the iterative operation can be added. First, generate the polar code generation matrix
Figure 02_image099
,in
Figure 02_image101
for size
Figure 02_image103
The inverse permutation matrix of , and will then generate the matrix
Figure 02_image105
Columns containing frozen bits (frozen bits) are removed, and a new generator matrix is generated
Figure 02_image107
,in
Figure 02_image109
is the number of information bits in the codeword, and then the Gaussian elimination method (Gaussian elimination) will generate the matrix
Figure 02_image107
Convert to system matrix
Figure 02_image111
,in
Figure 02_image113
Is the identity matrix, and get the parity check (parity check) matrix
Figure 02_image115
. Finally, the code word
Figure 02_image117
Multiply the parity check matrix
Figure 02_image119
, to get the symptom value. If the symptom value is a zero vector, the discriminative codeword
Figure 02_image117
is a legal codeword, and terminates the iterative operation, and the information bit vector
Figure 02_image121
According to the equation
Figure 02_image123
Otherwise, the next iteration will be performed when the number of iterations does not reach the upper limit. When the number of iterations reaches the upper limit, or when the parity check equation is satisfied, the information bit vector is determined
Figure 02_image121
in each bit
Figure 02_image125
The bit value of
Figure 02_image127
,in
Figure 02_image129
is a signed operation, and
Figure 02_image131
and
Figure 02_image133
represent the latest iterative operation
Figure 02_image135
and
Figure 02_image137
.

置信傳播解碼因子圖可變更為包含著校驗節點（check node；CN）及變數節點（variable node；VN）之二向圖（bipartite graph）。舉例而言，對圖5之用於(8,4)極化碼（

Figure 02_image003
=8、
Figure 02_image109
=4）的置信傳播解碼因子圖變更後的二向圖而言，如圖5所示，其包含32個變數節點、24個校驗節點和60個兩端分別連接變數節點和校驗節點的邊線（edge）。然而，節點和邊線個數過多將伴隨著校驗矩陣參雜過多小循環的問題，導致降低置信傳播解碼的性能，故有必要進一步對二向圖進行簡化。 The belief propagation decoding factor graph can be changed into a bipartite graph including a check node (CN) and a variable node (VN). For example, for the (8,4) polar code of Fig. 5 (
Figure 02_image003
=8,
Figure 02_image109
=4) for the bidirectional graph after the change of the belief propagation decoding factor graph, as shown in Figure 5, it contains 32 variable nodes, 24 check nodes and 60 variable nodes and check nodes connected at both ends respectively edge. However, too many nodes and edges will be accompanied by the problem that the check matrix is mixed with too many small cycles, which will reduce the performance of belief propagation decoding, so it is necessary to further simplify the bidirectional graph.

二向圖中校驗節點（check node；CN）與變數節點（variable node；VN）計算資訊的方式分別以式(11)和式(12)定義如下：

Figure 02_image139
Figure 02_image141
其中
Figure 02_image143
、
Figure 02_image145
分別為從節點
Figure 02_image147
至節點
Figure 02_image149
之資訊和從節點
Figure 02_image151
至節點
Figure 02_image153
之資訊，
Figure 02_image155
、
Figure 02_image157
為與節點
Figure 02_image147
相連的所有節點和與節點
Figure 02_image149
相連的所有節點，
Figure 02_image159
為除了節點
Figure 02_image149
以外與節點
Figure 02_image147
相連的所有節點，
Figure 02_image161
為除了節點
Figure 02_image147
以外與節點
Figure 02_image149
相連的所有節點，而
Figure 02_image163
為節點
Figure 02_image147
的先驗資訊。如圖5所示，變數節點又分為通道變數節點（channel variable node）、隱藏變數節點（hidden variable node）和凍結變數節點（frozen variable node），其中通道變數節點為接收通道LLR 的變數節點，也就是置信傳播解碼因子圖最右側的變數節點，隱藏變數節點為不具任何通道資訊（先驗資訊）的變數節點，而凍結變數節點為置信傳播解碼因子圖最左側的變數節點中對應凍結位元的變數節點。舉例而言，若資訊位元向量
Figure 02_image165
中的位元
Figure 02_image013
、
Figure 02_image015
、
Figure 02_image017
、
Figure 02_image019
為凍結位元，則變數節點中的隱藏變數節點、凍結變數節點和通道變數節點即如圖5所示。 The method of calculating information of check node (check node; CN) and variable node (variable node; VN) in the bidirectional graph is defined by formula (11) and formula (12) respectively as follows:
Figure 02_image139
Figure 02_image141
in
Figure 02_image143
,
Figure 02_image145
slave node
Figure 02_image147
to node
Figure 02_image149
information and slave nodes
Figure 02_image151
to node
Figure 02_image153
of information,
Figure 02_image155
,
Figure 02_image157
for and node
Figure 02_image147
All nodes connected to and with nodes
Figure 02_image149
all connected nodes,
Figure 02_image159
for except the node
Figure 02_image149
other than node
Figure 02_image147
all connected nodes,
Figure 02_image161
for except the node
Figure 02_image147
other than node
Figure 02_image149
all connected nodes, and
Figure 02_image163
for node
Figure 02_image147
prior information. As shown in Figure 5, variable nodes are further divided into channel variable nodes (channel variable node), hidden variable nodes (hidden variable node) and frozen variable nodes (frozen variable node), where the channel variable node is the variable node of the receiving channel LLR, That is, the variable node on the far right of the belief propagation decoding factor graph, the hidden variable node is a variable node without any channel information (prior information), and the frozen variable node is the corresponding frozen bit in the leftmost variable node of the belief propagation decoding factor graph variable node. For example, if the information bit vector
Figure 02_image165
bits in
Figure 02_image013
,
Figure 02_image015
,
Figure 02_image017
,
Figure 02_image019
If the bit is frozen, the hidden variable node, frozen variable node and channel variable node in the variable node are as shown in Figure 5.

極化碼二向圖可依下列數種場景下進行簡化處理。第一，由於凍結變數節點的先驗對數似然比（log-likelihood ratio；LLR）為無限大，其無助於資訊的更新，故可直接移除所有的凍結變數節點。The polar code bidirectional graph can be simplified in the following scenarios. First, because the prior log-likelihood ratio (log-likelihood ratio; LLR) of the frozen variable nodes is infinite, it is not conducive to updating information, so all frozen variable nodes can be removed directly.

第二，在刪除節點的過程中，會產生部分只有連結到1個變數節點的校驗節點（這些校驗節點又稱為1階校驗節點），且這些校驗節點通過校驗的唯一方式就是與其相連的變數節點個數為0，故其對數似然比為無限大，同樣無助於資訊的更新，因此可將這些校驗節點以及與其相連的變數節點移除。Second, in the process of deleting nodes, there will be some check nodes that are only connected to one variable node (these check nodes are also called first-order check nodes), and the only way for these check nodes to pass the check That is, the number of variable nodes connected to it is 0, so its logarithmic likelihood ratio is infinite, which is also not conducive to updating information. Therefore, these verification nodes and the variable nodes connected to them can be removed.

第三，當2階校驗節點連接的變數節點中，有一個變數節點為1階變數節點時，可移除此2階校驗節點。如圖6A所示，首先由1階通道變數節點v ch傳遞通道資訊

Figure 02_image167
至與其連接的2階校驗節點c 1，且接著此校驗節點c 1必傳遞通道資訊
Figure 02_image167
至另一個連接的變數節點，即隱藏變數節點v h。上述步驟與1階通道變數節點v ch直接傳遞通道資訊
Figure 02_image167
至隱藏變數節點v h的意義相同，故此2階校驗節點c 1不具實質作用且可移除，且隱藏變數節點v h可由1階通道變數節點v ch取代。 Third, when one of the variable nodes connected to the second-order check node is a first-order variable node, the second-order check node can be removed. As shown in Figure 6A, the channel information is first transmitted by the first-order channel variable node v ch
Figure 02_image167
To the second-level verification node c 1 connected to it, and then this verification node c 1 must transmit channel information
Figure 02_image167
to another connected variable node, namely the hidden variable node v h . The above steps and the first-order channel variable node v ch directly transmit channel information
Figure 02_image167
The meaning to the hidden variable node v h is the same, so the second-order check node c 1 has no real function and can be removed, and the hidden variable node v h can be replaced by the first-order channel variable node v ch .

第四，由於1階隱藏變數節點傳遞的通道資訊必為0，且由式(13)可知，與1階隱藏變數節點連接的校驗節點傳遞至其他連接的變數節點的通道資訊亦為0，其無助於資訊的更新，因此可將1階隱藏變數節點以及與其相連的校驗節點移除。以圖6B為例，由於1階隱藏變數節點v h1傳遞至校驗節點c 1的通道資訊為0，故校驗節點c 1傳遞至其他連接的變數節點v h2、v h3的通道資訊亦為0。在本例中，可將1階隱藏變數節點v h1和校驗節點c 1移除。

Figure 02_image169
Fourth, since the channel information transmitted by the first-order hidden variable node must be 0, and it can be seen from formula (13), the channel information transmitted by the check node connected to the first-order hidden variable node to other connected variable nodes is also 0, It does not help to update information, so the first-order hidden variable node and the check node connected to it can be removed. Taking Figure 6B as an example, since the channel information transmitted by the first-order hidden variable node v h1 to the check node c 1 is 0, the channel information transmitted by the check node c 1 to other connected variable nodes v h2 and v h3 is also 0. In this example, the first-order hidden variable node v h1 and the check node c 1 can be removed.
Figure 02_image169

第五，對於2階隱藏變數節點而言，其僅將由其中一個連接的校驗節點接收的通道資訊直接轉傳遞至另一個連接的校驗節點，且其先驗資訊為0。由式(14)可知，由於2階隱藏變數節點並無涉及資訊更新，故可將2階隱藏變數節點移除，且可將2階隱藏變數節點所連接的兩個校驗節點合併為單一校驗節點。在圖6C所示的例子中，由於通道資訊

Figure 02_image171
、
Figure 02_image173
相同，故可移除2階隱藏變數節點v h，且可合併校驗節點c 1、c 2為單一校驗節點。
Figure 02_image175
Fifth, for the second-order hidden variable node, it only directly transfers the channel information received by one of the connected check nodes to the other connected check node, and its prior information is 0. It can be seen from formula (14) that since the second-order hidden variable node does not involve information update, the second-order hidden variable node can be removed, and the two check nodes connected to the second-order hidden variable node can be combined into a single calibration node. test point. In the example shown in Figure 6C, since the channel information
Figure 02_image171
,
Figure 02_image173
The same, so the second-order hidden variable node v h can be removed, and the check nodes c 1 and c 2 can be combined into a single check node.
Figure 02_image175

第六，若是2階校驗節點連接的兩個變數節點均為隱藏變數節點，則此2階校驗節點僅作為轉送通道資訊且無涉及資訊更新，故可將2階隱藏變數節點移除，且可將這兩個隱藏變數節點合併為單一隱藏變數節點。以圖6D為例，由於校驗節點c 1連接的兩個變數節點均為隱藏變數節點且其先驗資訊均為0，故可移除校驗節點c 1，且可合併隱藏變數節點為單一隱藏變數節點。 Sixth, if the two variable nodes connected to the 2nd-level verification node are hidden variable nodes, then the 2nd-level verification node is only used as a transfer channel information and does not involve information update, so the 2nd-level hidden variable node can be removed. And these two hidden variable nodes can be merged into a single hidden variable node. Taking Figure 6D as an example, since the two variable nodes connected to the check node c 1 are both hidden variable nodes and their prior information is 0, the check node c 1 can be removed, and the hidden variable nodes can be merged into a single Hides variable nodes.

經由上述簡化處理，可在不顯著降低位元錯誤率表現下，有效縮減奇偶校驗矩陣（由校驗節點與變數節點的關係構成）的尺寸，進而降低系統解碼的複雜度。以(8,4)極化碼為例，奇偶校驗矩陣的尺寸可由24×32縮減至5×9。Through the above simplification process, the size of the parity check matrix (consisting of the relationship between check nodes and variable nodes) can be effectively reduced without significantly reducing the performance of the bit error rate, thereby reducing the complexity of system decoding. Taking the (8,4) polar code as an example, the size of the parity check matrix can be reduced from 24×32 to 5×9.

解碼排程為變數節點與校驗節點在解碼期間的訊息傳遞次序，其包含靜態排程和動態排程等方式。靜態排程主要分為平行排程（parallel scheduling）和串行排程（serial scheduling），其中平行排程為在每次迭代時，所有的校驗節點利用前次迭代資訊及式(12)更新資訊並傳遞資訊至其連接的變數節點，且所有的變數節點利用前次迭代資訊及式(11)更新資訊並傳遞資訊至其連接的校驗節點，泛洪（flooding）排程即為平行排程的其中一種，而串行排程為先決定更新順序，接著再依據此更新順序進行資訊更新，故又稱為標準順序排程（standard sequential scheduling；SSS）。分層置信傳播（layered belief propagation；LBP）解碼法（下稱LBP解碼法）即為串行排程的其中一種。The decoding schedule is the sequence of message transmission between variable nodes and check nodes during decoding, which includes static scheduling and dynamic scheduling. Static scheduling is mainly divided into parallel scheduling (parallel scheduling) and serial scheduling (serial scheduling), in which parallel scheduling is that in each iteration, all check nodes are updated using the previous iteration information and formula (12) information and transmit the information to the variable nodes connected to it, and all the variable nodes use the previous iteration information and formula (11) to update the information and transmit the information to the check nodes connected to it, the flooding schedule is parallel scheduling One of the schedules, and the serial scheduling is to determine the update order first, and then update the information according to the update order, so it is also called standard sequential scheduling (SSS). A layered belief propagation (layered belief propagation; LBP) decoding method (hereinafter referred to as the LBP decoding method) is one of serial scheduling.

相較於靜態排程解碼，動態排程解碼不僅可進一步加快收斂速度，且可擁有較佳的效能。以下列舉動態排程解碼法，包含殘差置信傳播（residual belief propagation）解碼法（下稱RBP解碼法）、節點導向殘差置信傳播（node-wise residual belief propagation）解碼法（下稱NWRBP解碼法）、基於殘差衰減之殘差置信傳播（residual decaying based residual belief propagation）解碼法（下稱RDRBP解碼法）、基於殘差衰減之節點導向殘差置信傳播（residual decaying based node-wise residual belief propagation）解碼法（下稱RDNWRBP解碼法）和V2C（variable-to-check）動態排程解碼法等。然而，其他異於上述列舉內容的動態排程解碼法亦可應用於本發明。Compared with statically scheduled decoding, dynamically scheduled decoding can not only further speed up the convergence speed, but also have better performance. The following lists dynamic scheduling decoding methods, including residual belief propagation (residual belief propagation) decoding method (hereinafter referred to as RBP decoding method), node-wise residual belief propagation (node-wise residual belief propagation) decoding method (hereinafter referred to as NWRBP decoding method) ), residual decay based residual belief propagation (residual decaying based residual belief propagation) decoding method (hereinafter referred to as RDRBP decoding method), residual decay based node-wise residual belief propagation (residual decaying based node-wise residual belief propagation) ) decoding method (hereinafter referred to as RDNWRBP decoding method) and V2C (variable-to-check) dynamic scheduling decoding method, etc. However, other dynamic scheduling decoding methods other than those listed above can also be applied to the present invention.

殘差置信傳播解碼法是基於局部最優演算法的貪婪演算法（Greedy Algorithm），即每次選擇更新順序時，都是在所有位置選擇出具有最大殘差的位置進行更新。資訊在位置k的殘差定義為

Figure 02_image177
，其中
Figure 02_image179
和
Figure 02_image181
分別為在位置
Figure 02_image109
的當前更新資訊和前次更新資訊。殘差置信傳播解碼法用於極化碼二向圖（Tanner graph）上，可先初始化所有資訊
Figure 02_image183
為0及初始化資訊
Figure 02_image143
為
Figure 02_image163
，並計算出所有資訊
Figure 02_image183
的殘差及產生資訊佇列Q，接著由校驗節點端為始，選擇出具有最大殘差的邊線（edge），即選擇最大的
Figure 02_image185
，且連接此邊緣的初始校驗節點利用式(8)更新資訊及傳遞更新後的資訊至連接此邊緣的變數節點
Figure 02_image187
，並將選擇出的邊線的殘差設定為0及重排序資訊佇列Q。接著，變數節點
Figure 02_image187
利用式(11)更新資訊及傳遞更新後的資訊分別至除了初始校驗節點以外其他與變數節點
Figure 02_image187
連接的所有校驗節點
Figure 02_image189
的更新資訊。對於每一校驗節點
Figure 02_image189
而言，可利用式(12)預先計算至除了變數節點
Figure 02_image187
以外其他與校驗節點
Figure 02_image189
連接的所有變數節點
Figure 02_image191
的更新資訊，並據以重排序資訊佇列Q。上述由校驗節點端為始選擇出具有最大殘差的邊線至最後重排序資訊佇列Q的步驟為一次完整的迭代且可重複進行，直到迭代次數到達預定值，或是解碼結果滿足奇偶校驗等式。 The residual belief propagation decoding method is a greedy algorithm based on a local optimal algorithm (Greedy Algorithm), that is, each time the update order is selected, the position with the largest residual error is selected for update at all positions. The residual of information at position k is defined as
Figure 02_image177
,in
Figure 02_image179
and
Figure 02_image181
respectively in position
Figure 02_image109
Current and previous update information for . The residual belief propagation decoding method is used on the polar code bidirectional graph (Tanner graph), and all information can be initialized first
Figure 02_image183
0 and initialization information
Figure 02_image143
for
Figure 02_image163
, and calculate all the information
Figure 02_image183
The residual and generate information queue Q, then start from the check node end, select the edge with the largest residual, that is, choose the largest
Figure 02_image185
, and the initial check node connected to this edge uses formula (8) to update information and transmit the updated information to the variable node connected to this edge
Figure 02_image187
, and set the residual of the selected edge to 0 and reorder the information queue Q. Next, the variable node
Figure 02_image187
Utilize formula (11) to update the information and transmit the updated information to other and variable nodes except the initial check node
Figure 02_image187
All checkpoints connected
Figure 02_image189
update information for . For each checkpoint
Figure 02_image189
In terms of, formula (12) can be used to pre-compute to except the variable node
Figure 02_image187
check node
Figure 02_image189
All variable nodes connected
Figure 02_image191
, and reorder the message queue Q accordingly. The above-mentioned steps from selecting the edge with the largest residual error to the final reordering information queue Q from the check node end is a complete iteration and can be repeated until the number of iterations reaches the predetermined value, or the decoding result satisfies the parity check. test equation.

NWRBP解碼法與殘差置信傳播解碼法的差別在於，在選擇出具有最大殘差的邊線後，連接此邊緣的初始校驗節點利用式(12)更新資訊及傳遞更新後的資訊至連接此初始校驗節點的所有變數節點

Figure 02_image187
，並將連接此初始校驗節點的所有邊線的殘差設定為0及重排序資訊佇列Q。每一變數節點
Figure 02_image187
進行的步驟相似於前述殘差置信傳播解碼法所述之變數節點
Figure 02_image187
進行的步驟，故不再重複說明。 The difference between the NWRBP decoding method and the residual belief propagation decoding method is that after the edge with the largest residual is selected, the initial check node connected to this edge updates information using formula (12) and transmits the updated information to the initial All variable nodes of the check node
Figure 02_image187
, and set the residuals of all edges connected to this initial check node to 0 and reorder the information queue Q. Each variable node
Figure 02_image187
The steps to be performed are similar to the variable nodes described in the aforementioned residual belief propagation decoding method
Figure 02_image187
steps, so the description will not be repeated.

RDRBP解碼法與殘差置信傳播解碼法的差別在於，殘差的計算變更為

Figure 02_image193
，其中
Figure 02_image195
為介於0與1之間的衰減係數，而
Figure 02_image197
為校驗節點
Figure 02_image151
至變數節點
Figure 02_image153
之邊線在每次迭代的累計更新次數。如此一來，殘差將隨著
Figure 02_image197
增加而降低，使得在同一次的迭代運算中，通常不會再次選擇更新次數過多的邊線，進而緩解同一群邊線消耗大部分更新資源的貪婪問題。當
Figure 02_image197
的總和達到更新次數閾值時，重設所有的
Figure 02_image197
為0。其他步驟相似於前述殘差置信傳播解碼法所述之對應步驟，故不再重複說明。 The difference between the RDRBP decoding method and the residual belief propagation decoding method is that the calculation of the residual is changed to
Figure 02_image193
,in
Figure 02_image195
is an attenuation coefficient between 0 and 1, and
Figure 02_image197
check node
Figure 02_image151
to variable node
Figure 02_image153
The cumulative update times of the edge line in each iteration. In this way, the residual will follow
Figure 02_image197
Increase and decrease, so that in the same iterative operation, the edges with too many updates are usually not selected again, thereby alleviating the greedy problem that the same group of edges consumes most of the update resources. when
Figure 02_image197
When the sum of the updates reaches the threshold, reset all
Figure 02_image197
is 0. Other steps are similar to the corresponding steps described in the aforementioned residual belief propagation decoding method, so the description will not be repeated.

然而，對一個特定的接收訊號而言，不同解碼排程可能因陷阱集（trapping sets）而導致解碼結果相異。陷阱集為部分的錯誤變數節點經過數次迭代後依然未得到更正，且連接到偶數個錯誤變數節點的校驗節點會因二進位運算的關係而抵銷錯誤訊息，導致其誤判相鄰變數節點已滿足奇偶校驗而未進行更正，而連接到奇數個錯誤變數節點的校驗節點直到解碼排程結束仍不滿足奇偶校驗。However, for a specific received signal, different decoding schedules may cause different decoding results due to trapping sets. The error variable nodes that are part of the trap set have not been corrected after several iterations, and the check nodes connected to an even number of error variable nodes will offset the error message due to the relationship between binary operations, resulting in misjudgment of adjacent variable nodes The parity check has been satisfied without correction, and the check nodes connected to an odd number of error variable nodes have not satisfied the parity check until the end of the decoding schedule.

為解決因陷阱集的影響而導致錯誤率上升的問題，並增加解碼成功的可能性，可採用排程多樣性（schedule diversity），其搭配圖7所示之排程多樣性解碼方法200的流程圖示例說明如下。首先，進行步驟S202，記錄接收到的通道對數似然比（log-likelihood ratio；LLR），且初始化解碼順序參數i和迭代次序參數j均為1。接著，進行步驟S204，使用第i種排程順序進行第j次迭代解碼。之後，進行步驟S206，判別解碼是否滿足奇偶校驗等式。若是，則代表解碼成功，且接著進行步驟S208，輸出解碼結果；反之，則接著進行步驟S210，判別迭代次序參數j是否到達最大迭代次數。在步驟S210中，若判別出迭代次序參數j到達最大迭代次數，則接著進行步驟S212，判別解碼順序參數i是否到達最大排程多樣性次數；反之，則接著進行步驟S214，迭代次序參數j增加1，且接著回到步驟S204以進行下一次迭代。在步驟S212中，若判別出解碼順序參數i到達最大排程多樣性次數，則進行步驟S208，輸出解碼結果；反之，則接著進行步驟S216，捨棄解碼結果，解碼順序參數i增加1，初始化迭代次序參數j為1，接著藉由隨機打亂第(i-1)解碼順序以產生不同的第i解碼順序，且讀取先前記錄的通道對數似然比，並接著回到步驟S204，使用新的第i解碼順序進行迭代解碼。In order to solve the problem of increased error rate due to the influence of trap sets and increase the possibility of successful decoding, schedule diversity can be used, which is matched with the flow of the schedule diversity decoding method 200 shown in FIG. 7 The figure examples are explained below. Firstly, proceed to step S202, record the received channel log-likelihood ratio (log-likelihood ratio; LLR), and initialize the decoding order parameter i and the iteration order parameter j to be 1. Next, proceed to step S204, using the i-th scheduling order to perform j-th iterative decoding. Afterwards, step S206 is performed to determine whether the decoding satisfies the parity check equation. If yes, it means that the decoding is successful, and proceed to step S208 to output the decoding result; otherwise, proceed to step S210 to determine whether the iteration order parameter j reaches the maximum number of iterations. In step S210, if it is determined that the iteration order parameter j has reached the maximum number of iterations, proceed to step S212 to determine whether the decoding order parameter i has reached the maximum number of scheduling diversity; otherwise, proceed to step S214, and the iteration order parameter j increases 1, and then return to step S204 for the next iteration. In step S212, if it is judged that the decoding sequence parameter i reaches the maximum number of schedule diversity times, proceed to step S208 to output the decoding result; otherwise, proceed to step S216 to discard the decoding result, increase the decoding sequence parameter i by 1, and initialize the iteration The order parameter j is 1, and then by randomly disrupting the (i-1)th decoding order to generate a different i-th decoding order, and read the previously recorded channel log likelihood ratio, and then return to step S204, use the new The iterative decoding of the i-th decoding order.

依據上述排程解碼說明，在使用第一種排程順序進行迭代解碼而失敗的情形下（例如迭代次數到達上限值時，解碼結果仍未滿足奇偶校驗等式），放棄以第一種解碼順序進行排程解碼的解碼結果，並重新讀取事先記錄的通道對數似然比，且隨機打亂前次解碼順序進而產生新的解碼順序，且到解碼結果輸出時所產生的解碼排程互為相異，以產生解碼排程多樣性。在高訊噪比（signal-to-noise ratio；SNR）的環境下，僅需單個或少數解碼順序即可解碼成功，故其解碼複雜度未顯著增加。According to the above description of scheduled decoding, in the case of failure of iterative decoding using the first scheduling order (for example, when the number of iterations reaches the upper limit, the decoding result still does not satisfy the parity check equation), give up using the first The decoding result of the decoding sequence is scheduled and decoded, and the pre-recorded channel log likelihood ratio is re-read, and the previous decoding sequence is randomly disrupted to generate a new decoding sequence, and the decoding schedule generated when the decoding result is output are different from each other to generate decoding schedule diversity. In a high signal-to-noise ratio (SNR) environment, only a single or a few decoding sequences are required for successful decoding, so the decoding complexity does not increase significantly.

然而，若將上述排程解碼應用在簡化後的極化碼上，會大幅增加預算複雜度，從而導致整體解碼複雜度顯著增加。為了保有動態更新的收斂速度且具有較佳的收斂位置，同時避免顯著增加整體解碼複雜度，可採用不需預算的V2C（variable-to-check）動態排程解碼法，其原理為利用相同位置的當前 V2C 資訊相較於前次V2C資訊的資訊差值作為更新解碼順序的依據，其差值愈大愈有可能對所連接的校驗節點的下一步更新產生極大影響，故優先更新這些對應的校驗節點，且為了避免貪婪效應發生，每個更新過的校驗節點在同一次迭代中不再進行更新。舉例而言，若變數節點

Figure 02_image153
至校驗節點
Figure 02_image151
具有最大資訊差值，且校驗節點
Figure 02_image151
尚未進行更新，則選擇校驗節點
Figure 02_image151
更新並傳遞資訊至除了變數節點
Figure 02_image153
以外所有與校驗節點
Figure 02_image151
相連的變數節點；接著，接收到資訊的變數節點均進行更新，並傳遞資訊至所有與這些變數節點連接的校驗節點，且由對應的邊線具有最大差值的校驗節點進行與校驗節點
Figure 02_image151
相同的資訊更新與傳遞步驟，依此類推，直到所有校驗節點均完成更新。當所有校驗節點均完成更新時，若是迭代次數到達預定值，或是解碼結果滿足奇偶校驗等式，則結束V2C動態排程解碼法；反之，則進行下一次的迭代操作。此外，V2C動態排程解碼法也可中途停止迭代運算。 However, if the above-mentioned scheduled decoding is applied to the simplified polar code, the budget complexity will be greatly increased, resulting in a significant increase in the overall decoding complexity. In order to keep the convergence speed of dynamic update and have a better convergence position, and avoid significantly increasing the overall decoding complexity, the V2C (variable-to-check) dynamic scheduling decoding method without budget can be used. The principle is to use the same position The information difference between the current V2C information and the previous V2C information is used as the basis for updating the decoding order. The larger the difference, the more likely it will have a great impact on the next update of the connected check node. Therefore, priority is given to updating these corresponding check nodes, and in order to avoid the greedy effect, each updated check node will not be updated in the same iteration. For example, if the variable node
Figure 02_image153
to checkpoint
Figure 02_image151
has the largest information difference, and the check node
Figure 02_image151
If the update has not been performed, select the check node
Figure 02_image151
update and pass information to all but variable nodes
Figure 02_image153
All other check nodes
Figure 02_image151
The connected variable nodes; then, the variable nodes that receive the information are all updated, and the information is transmitted to all the check nodes connected to these variable nodes, and the check node with the largest difference in the corresponding edge is compared with the check node
Figure 02_image151
The same information update and transfer steps, and so on, until all verification nodes are updated. When all the check nodes are updated, if the number of iterations reaches a predetermined value, or the decoding result satisfies the parity check equation, the V2C dynamic scheduling decoding method is ended; otherwise, the next iteration operation is performed. In addition, the V2C dynamic scheduling decoding method can also stop the iterative operation midway.

圖8為使用各種解碼法在訊噪比為3dB時的位元錯誤率收斂曲線圖。由圖8可知，與LBP解碼法相比，V2C動態排程解碼法的位元錯誤率收斂速度較快，且在位元錯誤率收斂的條件下，V2C動態排程解碼法的位元錯誤率明顯較RBP解碼法、NWRBP解碼法、RDRBP解碼法和RDNWRBP解碼法為低，且相近於LBP解碼法的位元錯誤率，顯示出其同時具備低複雜度與高可靠度等特性。FIG. 8 is a graph showing the convergence of bit error rates when the SNR is 3dB using various decoding methods. It can be seen from Figure 8 that, compared with the LBP decoding method, the bit error rate of the V2C dynamic scheduling decoding method converges faster, and under the condition of bit error rate convergence, the bit error rate of the V2C dynamic scheduling decoding method is obviously Compared with RBP decoding method, NWRBP decoding method, RDRBP decoding method and RDNWRBP decoding method, the bit error rate is lower, and the bit error rate is similar to that of LBP decoding method, showing that it has the characteristics of low complexity and high reliability at the same time.

圖9為使用各種解碼法在迭代上限次數為100下的位元錯誤率表現曲線圖，其中LBP代表排程多樣性上限次數為1的LBP解碼法（即未採用排程多樣性的LBP解碼法），Div=10、Div=50、Div=100分別代表排程多樣性上限次數為10、50、100且每次解碼排程使用固定解碼順序的LBP解碼法，Div=100(Rand)排程多樣性上限次數為100且每次解碼排程使用隨機解碼順序的LBP解碼法，而SCL8、SCL32分別代表列表長度為8、32的連續消除列表（successive cancellation list）解碼法（下稱SCL解碼法）。由圖9所示之模擬結果可知，在相同的排程多樣性次數下，每次解碼排程使用隨機解碼順序的LBP解碼法可具有較佳的位元錯誤率表現。此外，圖10示出使用各種傳播解碼法在迭代上限次數為 100下訊噪比所對應的更新次數。由圖10可知，在相同的排程多樣性次數下，每次解碼排程使用隨機解碼順序的LBP解碼法可具有較低的解碼複雜度。後續圖式說明中，LBP解碼法的每次解碼排程使用將以隨機解碼順序為例。Figure 9 is a performance curve of the bit error rate using various decoding methods when the upper limit of iterations is 100, where LBP represents the LBP decoding method with the upper limit of scheduling diversity being 1 (that is, the LBP decoding method without scheduling diversity ), Div=10, Div=50, and Div=100 respectively represent that the upper limit of scheduling diversity is 10, 50, and 100 and each decoding schedule uses the LBP decoding method with a fixed decoding order, Div=100 (Rand) scheduling The upper limit of diversity is 100 and each decoding schedule uses the LBP decoding method with random decoding order, while SCL8 and SCL32 represent the successive cancellation list (successive cancellation list) decoding method (hereinafter referred to as the SCL decoding method) with list lengths of 8 and 32, respectively. ). From the simulation results shown in FIG. 9 , it can be seen that under the same scheduling diversity times, the LBP decoding method using random decoding order for each decoding schedule can have a better bit error rate performance. In addition, Fig. 10 shows the number of updates corresponding to the signal-to-noise ratio when the upper limit of iterations is 100 using various propagation decoding methods. It can be seen from FIG. 10 that under the same scheduling diversity times, the LBP decoding method using random decoding order for each decoding schedule can have lower decoding complexity. In the subsequent illustrations, the use of each decoding schedule in the LBP decoding method will take a random decoding sequence as an example.

圖11為使用V2C動態排程解碼法在各種迭代上限次數和排程多樣性上限次數的組合下的位元錯誤率表現曲線圖，其中Iter=20、Iter=100分別代表迭代上限次數為20次和100次，且此V2C動態排程解碼法的排程多樣性解碼規則為，在所有未更新的校驗節點中，取出 5個具有前五大資訊差值的校驗節點，並在這些取出的校驗節點當中，隨機選取一個校驗節點進行更新，此選取方式仍維持同一次迭代操作中只更新一次特定校驗節點。由圖11可知，在訊雜比大於2.5dB的情形下，迭代上限次數為100次的V2C動態排程解碼法，其位元錯誤率隨訊雜比下降的幅度，低於迭代上限次數為20次且具有相同排程多樣性上限次數的V2C動態排程解碼法。進一步地，迭代上限次數為100次且排程多樣性上限次數為10的V2C動態排程解碼法在訊雜比為3dB時的位元錯誤率較迭代上限次數為20次且排程多樣性上限次數同樣為10的V2C動態排程解碼法在訊雜比同樣為3dB時的位元錯誤率高，迭代上限次數為100次且排程多樣性上限次數為100的V2C動態排程解碼法在訊雜比為3dB時的位元錯誤率較迭代上限次數為20次且排程多樣性上限次數同樣為100的V2C動態排程解碼法在訊雜比同樣為3dB時的位元錯誤率高。Figure 11 is a graph showing the performance curve of the bit error rate using the V2C dynamic scheduling decoding method under various combinations of the upper limit of iterations and the upper limit of scheduling diversity, where Iter=20 and Iter=100 respectively represent that the upper limit of iterations is 20 times and 100 times, and the scheduling diversity decoding rule of this V2C dynamic scheduling decoding method is, among all check nodes that have not been updated, take out 5 check nodes with the top five information differences, and among these taken out Among the check nodes, a check node is randomly selected for updating, and this selection method still maintains that only one specific check node is updated in the same iterative operation. It can be seen from Figure 11 that when the signal-to-noise ratio is greater than 2.5dB, the V2C dynamic scheduling decoding method with an upper limit of iterations of 100, the bit error rate decreases with the increase of the signal-to-noise ratio, which is lower than the upper limit of iterations of 20 V2C dynamic scheduling decoding method with the same scheduling diversity upper limit times. Furthermore, the bit error rate of the V2C dynamic scheduling decoding method with an upper limit of iterations of 100 and an upper limit of schedule diversity of 10 is higher than that of a V2C dynamic scheduling decoding method with an upper limit of iterations of 20 and an upper limit of schedule diversity. The V2C dynamic scheduling decoding method with the same frequency of 10 has a high bit error rate when the signal-to-noise ratio is also 3dB. The bit error rate when the noise ratio is 3dB is higher than that of the V2C dynamic scheduling decoding method whose upper limit of iterations is 20 and the upper limit of scheduling diversity is also 100 when the noise ratio is also 3dB.

由前述模擬結果可推知，因為每次解碼排程使用隨機解碼順序的V2C動態排程解碼法具有較快的收斂速度，故因解碼失敗而繼續大量的迭代操作，可能比提早放棄舊的解碼順序而採用新的解碼順序進行解碼還要可能解碼成錯誤碼字。From the above simulation results, it can be inferred that because the V2C dynamic scheduling decoding method with random decoding order for each decoding schedule has a faster convergence speed, it is possible to continue a large number of iterative operations due to decoding failures than to give up the old decoding order earlier. And adopting the new decoding order to decode may also decode into wrong codewords.

圖12為圖1之發送端110的示例方塊圖。發送端110包含循環冗餘校驗（cyclic redundancy check；CRC）編碼器112和極化碼編碼器114，其中循環冗餘校驗編碼器112用以依據生成多項式（generator polynomial）對資訊位元進行運算以得到校驗位元，且接著將校驗位元加在資訊位元的後方而形成循環冗餘校驗碼位元，而極化碼編碼器114接著對循環冗餘校驗碼位元進行系統建碼而產生極化碼位元。FIG. 12 is an example block diagram of the sending end 110 in FIG. 1 . The sending end 110 includes a cyclic redundancy check (cyclic redundancy check; CRC) encoder 112 and a polar code encoder 114, wherein the cyclic redundancy check encoder 112 is used to process information bits according to a generator polynomial (generator polynomial) operation to obtain parity bits, and then add the parity bits to the back of the information bits to form cyclic redundancy check code bits, and the polar code encoder 114 then performs cyclic redundancy check code bits Perform systematic coding to generate polarized code bits.

圖13為LBP解碼法與V2C動態排程解碼法在不同迭代上限與多樣性上限的組合變化和SCL解碼法均加上循環冗餘校驗後的位元錯誤率表現曲線圖，其中LBP div(∙)、V2C div(∙)分別代表LBP解碼法結合排程多樣性和V2C動態排程解碼法結合排程多樣性，I=20/100、D=10/100分別代表最大迭代次數為20/100和最大排程多樣性次數為10/100，而SCL8代表列表長度為8的SCL解碼法。與圖11之模擬結果相比可知，加上循環冗餘校驗後的各種解碼法可進一步提升位元錯誤率表現。進一步地，由圖13可發現，最大迭代次數為和最大排程多樣性次數均為100的LBP解碼法與V2C動態排程解碼法，在訊噪比為2.2dB以上時的位元錯誤率表現均優於列表長度為8的SCL解碼法。Fig. 13 is a graph showing the bit error rate performance curve of LBP decoding method and V2C dynamic scheduling decoding method at different iteration upper limit and diversity upper limit and SCL decoding method with cyclic redundancy check, wherein LBP div( ∙), V2C div(∙) represent LBP decoding method combined with scheduling diversity and V2C dynamic scheduling decoding method combined with scheduling diversity, I=20/100, D=10/100 represent the maximum number of iterations is 20/ 100 and the maximum scheduling diversity is 10/100, and SCL8 represents the SCL decoding method with a list length of 8. Compared with the simulation results in FIG. 11 , it can be known that various decoding methods with cyclic redundancy check can further improve the bit error rate performance. Further, it can be found from Figure 13 that the LBP decoding method and the V2C dynamic scheduling decoding method with the maximum number of iterations and the maximum number of scheduling diversity both being 100, the bit error rate performance when the signal-to-noise ratio is above 2.2dB Both are better than the SCL decoding method with a list length of 8.

為解決因陷阱集的影響而導致錯誤率上升的問題，並增加解碼成功的可能性，可採用位元翻轉（Bit Flip），其搭配圖14所示之位元翻轉解碼方法300的流程圖示例說明如下。首先，進行步驟S302，記錄接收到的通道對數似然比（log-likelihood ratio；LLR），且初始化解碼翻轉位元位置參數k為1。接著，進行步驟S304，使用第k種翻轉位元位置（k=1為初始解碼）進行100次迭代解碼。之後，進行步驟S306，判別解碼是否滿足奇偶校驗等式。若是，則代表解碼成功，且接著進行步驟S308，輸出解碼結果；反之，則接著進行步驟S310，判別解碼翻轉位元位置參數k是否到達最大翻轉位元次數。在步驟S310中，若判別出解碼翻轉位元位置參數k到達最大翻轉位元次數，則進行步驟S308，輸出解碼結果；反之，則接著進行步驟S312，捨棄解碼結果，解碼翻轉位元參數k增加1，接著讀取先前記錄的通道對數似然比，並接著回到步驟S304，使用新的第k解碼翻轉位元位置進行迭代解碼。In order to solve the problem of increased error rate due to the influence of the trap set and increase the possibility of successful decoding, bit flip (Bit Flip) can be used, which is matched with the flow diagram of the bit flip decoding method 300 shown in FIG. 14 An example is as follows. First, proceed to step S302 , record the received channel log-likelihood ratio (log-likelihood ratio; LLR), and initialize the decoding flip bit position parameter k to 1. Next, proceed to step S304, and perform 100 iterations of decoding by using the kth flipped bit position (k=1 is initial decoding). Afterwards, step S306 is performed to determine whether the decoding satisfies the parity check equation. If yes, it means that the decoding is successful, and proceed to step S308 to output the decoding result; otherwise, proceed to step S310 to determine whether the decoding flip bit position parameter k has reached the maximum number of flip bits. In step S310, if it is judged that the decoding inversion bit position parameter k reaches the maximum number of inversion bits, then proceed to step S308 to output the decoding result; otherwise, proceed to step S312 to discard the decoding result, and the decoding inversion bit parameter k increases 1. Then read the log likelihood ratio of the previously recorded channel, and then return to step S304, and use the new k-th decoding flip bit position to perform iterative decoding.

圖15為使用V2C動態排程解碼法結合排程多樣性、使用LBP解碼法結合排程多樣性和使用列表長度L分別為8、16、32的循環冗餘校驗輔助連續消除列表（CRC aided successive cancellation list；CA-SCL）解碼法（下稱CA-SCL解碼法）結合排程多樣性在排程多樣性上限次數為3000且迭代上限次數為100的位元錯誤率表現曲線圖。由圖15可知，在訊噪比小於2dB時，V2C動態排程解碼法的位元錯誤率表現明顯優於和LBP解碼法和列表長度L為8和16的CA-SCL解碼法。此外，圖16示出使用V2C動態排程解碼法結合排程多樣性、使用LBP解碼法結合排程多樣性和使用列表長度L分別為8、16、32的CA-SCL解碼法結合排程多樣性在排程多樣性上限次數為3000且迭代上限次數為100的更新次數。由圖15和圖16可知，在訊噪比大於2dB下，雖然V2C動態排程解碼法與列表長度L為16的CA-SCL解碼法具有相近的位元錯誤率表現，但V2C動態排程解碼法會隨著訊噪比增加而進一步降低更新次數。因此，在綜合位元錯誤率表現和運算複雜度的考量上，V2C動態排程解碼法結合排程多樣性和迭代運算具有顯著優勢。Figure 15 shows the cyclic redundancy check assisted continuous elimination list (CRC aided Successive cancellation list; CA-SCL) decoding method (hereinafter referred to as CA-SCL decoding method) combined with scheduling diversity, the bit error rate performance curve when the upper limit of scheduling diversity is 3000 and the upper limit of iterations is 100. It can be seen from Figure 15 that when the signal-to-noise ratio is less than 2dB, the bit error rate performance of the V2C dynamic scheduling decoding method is significantly better than that of the LBP decoding method and the CA-SCL decoding method with the list length L being 8 and 16. In addition, Figure 16 shows the use of V2C dynamic scheduling decoding method combined with scheduling diversity, using LBP decoding method combined with scheduling diversity, and using CA-SCL decoding method with list length L of 8, 16, and 32 respectively. The maximum number of updates in scheduling diversity is 3000 and the maximum number of iterations is 100. From Figure 15 and Figure 16, it can be seen that when the signal-to-noise ratio is greater than 2dB, although the V2C dynamic scheduling decoding method and the CA-SCL decoding method with a list length L of 16 have similar bit error rate performance, the V2C dynamic scheduling decoding method The method further reduces the number of updates as the signal-to-noise ratio increases. Therefore, in terms of comprehensive bit error rate performance and computational complexity, the V2C dynamic scheduling decoding method combined with scheduling diversity and iterative operations has significant advantages.

圖17為使用V2C動態排程解碼法結合位元翻轉、使用LBP解碼法結合位元翻轉和使用列表長度L分別為8、16、32的CA-SCL解碼法結合位元翻轉在位元翻轉上限次數為3000且迭代上限次數為100的位元錯誤率表現曲線圖。由圖17可知，在訊噪比小於2dB時，V2C動態排程解碼法的位元錯誤率表現明顯優於和LBP解碼法和列表長度L為8和16的CA-SCL解碼法，且相近於列表長度L為32的CA-SCL解碼法。此外，圖18示出使用V2C動態排程解碼法結合位元翻轉、使用LBP解碼法結合位元翻轉和使用列表長度L分別為8、16、32的CA-SCL解碼法的訊噪比在位元翻轉上限次數為3000且迭代上限次數為100的更新次數。由圖18可知，在訊噪比約為2.2dB下，相較於列表長度L為16的CA-SCL解碼法，V2C動態排程解碼法具有較佳的位元錯誤率表現和運算複雜度。因此，在綜合位元錯誤率表現和運算複雜度的考量上，V2C動態排程解碼法結合位元翻轉和迭代運算亦具有顯著優勢。Figure 17 shows the upper limit of bit flipping using V2C dynamic scheduling decoding method combined with bit flipping, using LBP decoding method combined with bit flipping, and using CA-SCL decoding method with list length L of 8, 16, and 32 respectively. The performance curve of the bit error rate when the number of iterations is 3000 and the upper limit of iterations is 100. It can be seen from Figure 17 that when the signal-to-noise ratio is less than 2dB, the bit error rate performance of the V2C dynamic scheduling decoding method is significantly better than that of the LBP decoding method and the CA-SCL decoding method with a list length L of 8 and 16, and is similar to that of A CA-SCL decoding method with a list length L of 32. In addition, Fig. 18 shows the signal-to-noise ratios of using V2C dynamic scheduling decoding method combined with bit flipping, using LBP decoding method combined with bit flipping, and using CA-SCL decoding method with list length L of 8, 16, and 32 respectively. The number of updates with a meta flip cap of 3000 and an iteration cap of 100. It can be seen from Fig. 18 that when the signal-to-noise ratio is about 2.2dB, compared with the CA-SCL decoding method whose list length L is 16, the V2C dynamic scheduling decoding method has better bit error rate performance and computational complexity. Therefore, in terms of comprehensive bit error rate performance and computational complexity, the V2C dynamic scheduling decoding method combined with bit flipping and iterative operations also has significant advantages.

上述各實施例之極化碼解碼方法可藉由使用硬體（例如處理器或數位控制晶片）、軟體或兩者組合來實現。舉例而言，極化碼解碼方法可經編程而成為電腦程式產品，其可由處理器執行，且可儲存於處理器可存取的非暫態電腦可讀取媒體中。非暫態電腦可讀取媒體可以是唯讀記憶體、快閃記憶體、軟碟、硬碟、光碟、通用序列匯流排（USB）隨身碟、磁帶、可在網際網路上存取的資料庫、或其他對所述技術領域中具有通常知識者為顯而易見的電腦可讀取媒體。The polar code decoding methods of the above-mentioned embodiments can be realized by using hardware (such as a processor or a digital control chip), software or a combination of both. For example, the polar code decoding method can be programmed into a computer program product, which can be executed by a processor and stored in a non-transitory computer readable medium accessible by the processor. Non-transitory computer readable media can be read-only memory, flash memory, floppy disks, hard disks, compact disks, Universal Serial Bus (USB) flash drives, magnetic tape, databases accessible on the Internet , or other computer-readable media that would be obvious to those having ordinary knowledge in the technical field.

雖然本揭示內容已以實施方式揭露如上，然其並非用以限定本揭示內容，任何熟習此技藝者，在不脫離本揭示內容之精神和範圍內，當可做各種之更動與潤飾，因此本揭示內容之保護範圍當視後附之申請專利範圍所界定者為準。Although the content of this disclosure has been disclosed above in terms of implementation, it is not intended to limit the content of this disclosure. Anyone who is skilled in this art can make various changes and modifications without departing from the spirit and scope of this disclosure. Therefore, this The scope of protection of the disclosed content shall be subject to the definition of the appended patent application scope.

100:通訊系統 110:發送端 112:循環冗餘校驗編碼器 114:極化碼編碼器 120:接收端 130:無線通道 200,300:方法 S202-S216,S302-S312:步驟 100: Communication system 110: sender 112: Cyclic redundancy check encoder 114: Polar code encoder 120: Receiver 130: wireless channel 200,300: method S202-S216, S302-S312: steps

為了更完整了解實施例及其優點，現參照結合所附圖式所做之下列描述，其中： [圖1]為本發明實施例之通訊系統的示意圖； [圖2]為極化碼生成因子示意圖； [圖3]示出碼字長度為8的置信傳播（belief propagation）解碼因子圖； [圖4]為[圖3]之置信傳播解碼因子圖每一基本運算塊的示意圖； [圖5]為用於(8,4)極化碼的置信傳播解碼因子圖變更後的二向圖（bipartite graph）； [圖6A]至[圖6D]為在各場景下對二向圖簡進行簡化處理的示例； [圖7]為本發明實施例之排程多樣性解碼方法的流程圖； [圖8]為使用各種解碼法在訊噪比為3dB時的位元錯誤率收斂曲線圖； [圖9]為使用各種傳播解碼法在迭代上限次數為100下的位元錯誤率表現曲線圖； [圖10]示出使用各種傳播解碼法在迭代上限次數為 100下訊噪比所對應的更新次數； [圖11]為使用V2C（variable-to-check）動態排程解碼法在各種迭代上限次數和排程多樣性上限次數的組合下的位元錯誤率表現曲線圖； [圖12]為[圖1]之編碼端的示例方塊圖； [圖13]為分層置信傳播（layered belief propagation；LBP）解碼法與V2C動態排程解碼法在不同迭代上限與多樣性上限的組合變化和連續消除列表（successive cancellation list）解碼法均加上循環冗餘校驗後的位元錯誤率表現曲線圖； [圖14]為極化碼加上位元擾動之排程多樣性解碼結合循環冗餘校驗方法的流程圖； [圖15]為使用V2C動態排程解碼法結合排程多樣性、使用分層置信傳播解碼法結合排程多樣性和使用循環冗餘校驗輔助連續消除列表解碼法結合排程多樣性的位元錯誤率表現曲線圖； [圖16]示出使用V2C動態排程解碼法結合排程多樣性、使用分層置信傳播解碼法結合排程多樣性和使用循環冗餘校驗輔助連續消除列表解碼法結合排程多樣性的更新次數； [圖17]為使用V2C動態排程解碼法結合位元翻轉、使用分層置信傳播解碼法結合位元翻轉和使用循環冗餘校驗輔助連續消除列表解碼法結合位元翻轉的位元錯誤率表現曲線圖；以及 [圖18]示出使用V2C動態排程解碼法結合位元翻轉、使用分層置信傳播解碼法結合位元翻轉和使用循環冗餘校驗輔助連續消除列表解碼法結合位元翻轉的更新次數。 For a more complete understanding of the embodiments and advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings, in which: [Fig. 1] is a schematic diagram of a communication system according to an embodiment of the present invention; [Fig. 2] is a schematic diagram of polar code generation factors; [Fig. 3] shows the decoding factor diagram of belief propagation (belief propagation) with a codeword length of 8; [Fig. 4] is a schematic diagram of each basic operation block of the belief propagation decoding factor graph of [Fig. 3]; [Figure 5] is the changed bipartite graph of the belief propagation decoding factor graph for (8,4) polar codes; [Figure 6A] to [Figure 6D] are examples of simplifying the bidirectional graph in each scenario; [ FIG. 7 ] is a flowchart of a scheduling diversity decoding method according to an embodiment of the present invention; [Fig. 8] is the bit error rate convergence curve when the signal-to-noise ratio is 3dB using various decoding methods; [Fig. 9] is a performance curve of bit error rate using various propagation decoding methods when the upper limit of iterations is 100; [Fig. 10] shows the number of updates corresponding to the signal-to-noise ratio when the upper limit of iterations is 100 using various propagation decoding methods; [Fig. 11] is a graph showing the performance curve of the bit error rate under various combinations of the upper limit of iterations and the upper limit of schedule diversity using the V2C (variable-to-check) dynamic scheduling decoding method; [Fig. 12] is an example block diagram of the encoding end of [Fig. 1]; [Figure 13] is the combined change of the layered belief propagation (LBP) decoding method and the V2C dynamic scheduling decoding method in different iteration upper bounds and diversity upper bounds and the continuous elimination list (successive cancellation list) decoding method. Performance curve of bit error rate after cyclic redundancy check; [ FIG. 14 ] is a flow chart of a polar code plus bit perturbation scheduling diversity decoding combined with a cyclic redundancy check method; [Figure 15] Bits for using V2C dynamic scheduling decoding method combined with scheduling diversity, using layered belief propagation decoding method combined with scheduling diversity, and using cyclic redundancy check-assisted continuous elimination list decoding method combined with scheduling diversity Meta error rate performance curve; [Fig. 16] shows the combination of scheduling diversity using V2C dynamic scheduling decoding method, combining scheduling diversity using layered belief propagation decoding method and combining scheduling diversity using cyclic redundancy check assisted consecutive elimination list decoding method number of updates; [Fig. 17] Bit error rate for using V2C dynamic scheduling decoding method combined with bit flipping, using layered belief propagation decoding method combined with bit flipping, and using cyclic redundancy check-assisted sequential elimination list decoding method combined with bit flipping Performance graphs; and [ FIG. 18 ] Shows the number of updates for decoding using V2C dynamic scheduling with bit flipping, using layered belief propagation decoding with bit flipping, and using cyclic redundancy check-assisted sequential elimination list decoding with bit flipping.

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100:通訊系統 100: Communication system

110:發送端 110: sender

120:接收端 120: Receiver

130:無線通道 130: wireless channel

Claims (10)

一種使用極化碼之通訊系統，包含： 一發送端，配置為發送一極化碼（polar code）訊號；以及 一接收端，配置為接收該極化碼訊號，並使用一V2C（variable-to-check）動態排程（dynamic scheduling）解碼法對該極化碼訊號進行列表解碼（list decoding）。 A communication system using polar codes, comprising: a transmitter configured to transmit a polar code signal; and A receiving end configured to receive the polar code signal, and use a V2C (variable-to-check) dynamic scheduling (dynamic scheduling) decoding method to perform list decoding on the polar code signal. 如請求項1所述之通訊系統，其中該極化碼訊號包含循環冗餘校驗（cyclic redundant check）資訊，且該解碼端更配置為判別對該極化碼訊號的循環冗餘校驗是否成功。The communication system as described in claim 1, wherein the polar code signal includes cyclic redundancy check (cyclic redundancy check) information, and the decoder is further configured to determine whether the cyclic redundancy check of the polar code signal is success. 如請求項1所述之通訊系統，其中該解碼端應用排程多樣性（schedule diversity）至該V2C動態排程解碼法以對該極化碼訊號進行列表解碼。The communication system as claimed in claim 1, wherein the decoding end applies schedule diversity to the V2C dynamic scheduling decoding method to perform list decoding on the polar code signal. 如請求項3所述之通訊系統，其中，在使用一解碼順序進行迭代解碼而失敗時，該解碼端隨機打亂該解碼順序進而產生新的解碼順序以接續進行迭代解碼。The communication system as claimed in claim 3, wherein when the iterative decoding using a decoding order fails, the decoding end randomly disrupts the decoding order to generate a new decoding order for subsequent iterative decoding. 如請求項1所述之通訊系統，其中該解碼端應用位元翻轉（bit flip）至該V2C動態排程解碼法以對該極化碼訊號進行列表解碼。The communication system as claimed in claim 1, wherein the decoding end applies bit flip (bit flip) to the V2C dynamic scheduling decoding method to perform list decoding on the polar code signal. 一種使用極化碼之通訊系統之解碼方法，包含： 接收一極化碼（polar code）訊號；以及 使用一V2C（variable-to-check）動態排程（dynamic scheduling）解碼法對該極化碼訊號進行列表解碼（list decoding）。 A decoding method for a communication system using polar codes, comprising: receiving a polar code signal; and A V2C (variable-to-check) dynamic scheduling decoding method is used to perform list decoding on the polar code signal. 如請求項6所述之解碼方法，更包含： 判別對包含循環冗餘校驗（cyclic redundant check）資訊之該極化碼訊號的循環冗餘校驗是否成功。 The decoding method described in claim 6 further includes: judging whether the cyclic redundancy check of the polar code signal including cyclic redundancy check (cyclic redundancy check) information is successful. 如請求項6所述之解碼方法，更包含： 應用排程多樣性（schedule diversity）至該V2C動態排程解碼法以對該極化碼訊號進行列表解碼。 The decoding method described in claim 6 further includes: Apply schedule diversity to the V2C dynamic scheduling decoding method to perform list decoding on the polar coded signal. 如請求項8所述之解碼方法，更包含： 在使用一解碼順序進行迭代解碼而失敗時，隨機打亂該解碼順序進而產生新的解碼順序以接續進行迭代解碼。 The decoding method described in Claim 8 further includes: When the iterative decoding using a decoding order fails, the decoding order is randomly disrupted to generate a new decoding order for subsequent iterative decoding. 如請求項6所述之解碼方法，更包含： 應用位元翻轉（bit flip）至該V2C動態排程解碼法以對該極化碼訊號進行列表解碼。 The decoding method described in claim 6 further includes: A bit flip is applied to the V2C dynamic scheduling decoding method to perform list decoding on the polar code signal.
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