Mn-fsc fast decoding algorithm for polar codes

Abstract

The application belongs to the field of channel coding, and particularly relates to a fast decoding algorithm of a polar code, namely MN (Major Node)-FSC algorithm; the method comprises the following steps: identifying special nodes of MN type which can be subjected to fast decoding at an encoding end, including but not limited to MN I, MN II, MN III and MN IV type nodes; after the identification is completed, corresponding fast decoding algorithms are used for decoding, and CRC checking is performed; if the CRC checking is passed, the decoding is considered to be successful, and if the CRC checking is failed, the decoding is considered to be unsuccessful. The minimum decoding unit of the traditional fast SC decoding is improved from 8 bits to 16 bits, that is, 16 bits can be decoded at least once, and the decoding tree can be greatly simplified. When 16 bits are taken as the minimum decoding unit, the four special nodes proposed in the application can decode more than 90% of the decoding nodes, and the remaining part can be decoded by using a traditional mode, so that the fast decoding scheme can effectively improve the decoding speed while ensuring the original block error rate.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of channel coding, and particularly relates to an improved algorithm based on FSC decoding algorithm in a polar code, namely MN (Major Node)-FSC. BACKGROUND

[0002] Polar codes are a class of error-correcting codes, which are theoretically proven to achieve the Shannon limit under binary-input discrete memoryless symmetric channels (BI-DMSC). Due to the good error correction performance and low complexity of the SC algorithm, polar codes are adopted in the latest 5G standard. However, the SC decoding algorithm has two main drawbacks. First, according to the polarization theory, the polar code under the SC decoding can only make the channel capacity tend to infinity under certain code length. Therefore, the SC decoding is insufficient in providing reasonable error correction performance for actual medium code length. Second, the sequential bit property of the SC decoding results in high decoding delay and low hardware implementation throughput, hindering its application in low-delay communication scenarios.

[0003] The first drawback mentioned above is mainly due to the suboptimality of the SC decoding relative to the maximum likelihood (ML) decoding. In order to partially compensate for this suboptimality, the list (SCL) decoding algorithm of the SC decoding is proposed in subsequent research. By maintaining a list of candidate codewords, the SCL decoding algorithm reduces the performance gap between SC and ML decoding at the cost of increased complexity. The second drawback is due to the sequential nature of the SC decoding. In order to solve this problem, many fast decoding schemes have been developed for polar codes, and the main idea behind these schemes is to directly decode at the intermediate nodes of the SC or SCL decoding tree instead of decoding from the first bit to the last bit. Since these intermediate node-based decoding schemes are highly dependent on the SC decoding, they inevitably inherit its sequential characteristics. Although true parallelism is unrealistic, intermediate node-based fast SC decoding schemes still have great advantages because they can achieve the same error correction performance as SC decoding, but with much lower decoding delay. The minimum node decoded by the existing fast decoding scheme is 8 bits, which is very limited for reducing decoding delay. Based on this problem, based on a large amount of statistical analysis, the minimum decoding node is improved to 16 bits in the present application, which can greatly simplify the decoding tree while maintaining the original block error rate and improve the decoding speed by 37.5% to 55% compared to the traditional SC decoding. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application proposes a MN-FSC fast decoding algorithm for polar codes, which comprises:

[0005] Step 1: First, polar coding and CRC code are used to transmit the codewords.

[0006] Step 2: Perform SC decoding. In the decoding process, different decoding algorithms are used to decode MN series nodes and traditional nodes.

[0007] During the decoding process, if the current decoding node is an MN series node, fast decoding is performed; if the decoding node is a traditional node, a traditional decoding algorithm is adopted. The intermediate values ​​that appear in the decoding algorithm have no actual physical meaning, and the decoding algorithm relies on these intermediate values ​​to estimate bits.

[0008] When decoding the MN series nodes, for the MNⅠ node, after obtaining all the estimated values, the binary tree is ascended according to the decoding principle of polar codes, and the obtained decoding estimates are... Compared with the previously obtained estimated value x i Perform modulo-2 addition, i.e., x i +x i+N / 2 The obtained value is used as the left node of node MNⅠ, and the decoding estimate is... As a right node, continuing to participate in the binary tree ascent yields the final decoding result; for MNⅡ nodes, the obtained decoding estimate will be... and With the median value and Performing a modulo-2 addition operation, i.e. and The obtained value is used as the left node of the MNⅡ node, and the decoding estimate. and As a right node, continuing to participate in the binary tree ascent yields the final decoding result; for node MNⅢ, the resulting decoding estimate will be... and The estimated value x is obtained by merging. i+N / 2 The obtained estimated value x i+N / 2 With the median value Performing a modulo-2 addition operation, i.e. The obtained value is used as the left node of MNⅢ, and the decoding estimate. As a right node, continuing to participate in the binary tree ascent yields the final decoding result; for node MNⅣ, the resulting decoding estimate will be... Compared with the previously obtained estimates Performing a modulo-2 addition operation, i.e. The obtained value is used as the left node of node MNⅣ and the decoding estimate. As the right node, continuing to participate in the binary tree's ascent will yield the final decoding result.

[0009] Step 3: Once all nodes have been decoded, the decoding result is obtained, and step S4 is executed.

[0010] Step 4: The obtained decoding result is subjected to CRC check, and if the check is passed, the decoding is considered successful, and if the check is failed, the decoding is considered failed.

[0011] After all the MN series nodes and the traditional nodes are decoded, the decoding results of all the nodes are climbed according to the climbing principle of the binary tree to obtain the final decoding result. The final decoding result is subjected to CRC check, and if the check is passed, the decoding is considered successful, and if the check is failed, the decoding is considered failed.

[0012] The present application has the following advantages: the fast decoding method based on SC decoding designed in the present application can decode at the intermediate nodes. Through the identification of the MN nodes, the decoding tree nodes can be reduced by 40%, and the leaf node tree to be decoded can be greatly reduced, thereby achieving the effect of fast decoding. The fast decoding scheme proposed in the present application can greatly improve the decoding speed on the basis of guaranteeing the original block error rate. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 is a flow chart of the low complexity decoding method of MN-FSC decoding in the present application;

[0014] Figure 2 is a simplified schematic diagram of the SC decoding tree of the fast decoding in the present application;

[0015] Figure 3 is the minimum decoding unit of MN I type node;

[0016] Figure 4 is the minimum decoding unit of MN II type node;

[0017] Figure 5 is the minimum decoding unit of MN III type node;

[0018] Figure 6 is the minimum decoding unit of MN IV type node;

[0019] Figure 7 is a complexity simulation comparison diagram of the present application and the comparative algorithm. DETAILED DESCRIPTION

[0020] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0021] Under the conditions of code length N=1024, K=512, code rate R=1 / 2, and CRC length of 16, the present application proposes a fast decoding method based on SC decoding, Figure 1 is a decoding flow chart, Figure 2 which shows the simplification degree of the decoding tree of different decoding algorithms, and the method comprises the following contents:

[0022] Step 1: First, polar coding and CRC code are used to transmit the codewords.

[0023] The polar coding adopts a non-systematic polar code encoding scheme, and the CRC code is a 16-bit CRC checksum. The CRC code is inserted into the information bit stream but does not carry any information itself and is only used for verification.

[0024] Step 2: Perform SC decoding. In the decoding process, different decoding algorithms are used to decode MN series nodes and traditional nodes.

[0025] Given a fixed code rate and code length, the nodes of the decoding tree can be directly determined. During SC decoding, the vast majority of nodes are the MN nodes proposed in the algorithm, such as... Figure 3 The diagram shows the smallest decoding unit of node MNⅠ. Figure 4 The diagram shows the smallest decoding unit of the MNⅡ node. Figure 5 The diagram shows the smallest decoding unit of the MNⅢ node. Figure 6 The diagram shows the smallest decoding unit for the MNⅣ node. The corresponding MN-FSC algorithm is used for the MN series nodes. For the very few traditional nodes, traditional decoding algorithms are used for decoding.

[0026] Step 3: If all nodes have been decoded, the decoding result is obtained and step S4 is executed; otherwise, steps 2 to 4 are executed.

[0027] Since SC decoding is traversal, fast decoding inherits this characteristic of SC decoding. The decoding nodes are also decoded in order. When the entire decoding tree is traversed, the decoding result can be obtained. If the decoding is still in the intermediate layer, the decoding process of steps 2 to 4 needs to be continued.

[0028] Step 4: Perform CRC check on the obtained decoding result. If the check passes, the decoding is considered successful; if it fails, the check is considered unsuccessful.

[0029] Polar codes typically have a code length of 1024 or longer, which is considered a relatively long codeword. Therefore, a 16-bit CRC checksum is used, which can be retrieved from the standard library. A CRC check is performed after decoding; if the checksum passes, decoding is considered successful; otherwise, decoding has failed.

[0030] Under the same simulation environment, i.e., code length N = 1024, K = 512, code rate R = 1 / 2, and CRC length of 16, this invention realizes the complexity simulation of SC decoding, traditional FSC decoding, and MN-FSC decoding. The time step, i.e., the number of operations required for one decoding operation, is used as the metric. Figure 7The decoding performance chart shows that the algorithm proposed by the present application has a significant reduction in complexity under the same conditions. Figure 2 The decoding tree simplification comparison shows that the introduction of MN series nodes with a minimum decoding unit of 16 bits for fast decoding makes the decoding tree level simpler and conducive to fast decoding.

[0031] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope proposed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A fast MN-FSC decoding algorithm for polar codes, characterized in that, The decoding algorithm identifies MN series nodes with a minimum decoding unit of 16 bits, thus improving decoding speed. The decoding algorithm steps are as follows: Step 1: Based on the distribution of information bits and frozen bits in the polar code, nodes that meet the corresponding conditions are considered as MN series nodes; let the leaf node of a certain node after polar code encoding be (u1, u2, ..., u...). N ), where N is the codeword length of the leaf node, and the minimum length of N is 16. Codeword identification is performed on the smallest decoding unit. If u1, u2, u3, u5, and u9 are frozen bits, and the others are information bits, then the node is an MNⅠ node; if u1, u2, u3, u4, u5, u6, and u9 are frozen bits, and the others are information bits, then the node is an MNⅡ node; if u N-8 u N-4 u N-2 u N-1 u N If all bits are information bits and the rest are frozen bits, then this node is an MNⅢ node; if u satisfies N-8 u N-5 u N-4 u N-3 u N-2 u N-1 u N If the bits are information bits and the rest are frozen bits, then this node is MNⅣ node; Step 2 involves using different decoding algorithms to decode the MN series nodes and traditional nodes during the decoding process; among them, For node MNⅠ, the following decoding algorithm is used: Among them, operators The calculation method is as follows y1 and y2 are the LLR values ​​of the receiving channel, and all i and j in the algorithm have 1≤i≤N / 2 and 1≤j≤N / 4. N is the length of the MN series nodes, and the minimum value of N is 16. ε(t) is the step function, and all additions in the operation are modulo 2 additions. Will The value is fed into the Wagner decoder to obtain The value, The estimated value is from get; Calculated by the following formula Will The value can be obtained by feeding it into the Wagner decoder. The value of can be used to obtain the decoding result; For MNⅡ nodes, the following decoding algorithm is used: Will The value is fed into the Wagner decoder to obtain Will The value is fed into the Wagner decoder to obtain The decoding result can then be obtained; For MNⅢ nodes, the following decoding algorithm is used: Will The values ​​are fed into the Wagner decoder to obtain... It can be by get The decoding result can then be obtained; For the MNⅣ node, the following decoding algorithm is used: Will The value is fed into the Wagner decoder to obtain... in The estimated value can be used to obtain the decoding result; For traditional nodes, traditional decoding algorithms are used for decoding; Step 3: Once all nodes have been decoded, the decoding process terminates, and the decoding result is obtained. Step 4: Perform CRC check on the obtained decoding result. If the check passes, the decoding is considered successful; if the CRC check fails, the decoding is considered unsuccessful.

Images