CN114124297B - Text coding method based on RS-LDPC cascade codes - Google Patents

Abstract

The invention discloses a text encoding method based on RS-LDPC cascade codes, which takes a Beidou satellite navigation system B-CNAV1 text as an application object, adopts an RS code as an outer code and adopts a binary LDPC code as an inner code, and comprises the following steps: 1) The original 64-system LDPC codes of the electronic sub-frame 2 and the sub-frame 3 of the Beidou satellite navigation system B-CNAV1 are replaced by the binary LDPC codes, so that the algorithm complexity is reduced; meanwhile, an RS outer code is added before binary LDPC code encoding to resist burst errors caused by fading channels; 2) And defining a new page type 5 for storing check bits of subframe 2 and subframe 3 after RS coding in the previous frame by using the reserved page type of the B-CNAV1 message for subframe 3. The method has the advantages of greatly reducing the complexity of the decoding algorithm, effectively shortening the operation time, and furthest reducing the modification of internal and external interfaces of the telegram caused by the upgrading of the telegram code, thereby reducing the update cost of software and hardware caused by the upgrading of the telegram code.

Description

Message encoding method based on RS-LDPC concatenated code

Technical field

The invention belongs to the field of communication technology and relates to a coding method, in particular a message coding method based on RS-LDPC concatenated code, which can be used for satellite navigation system message coding.

Background technique

Satellite navigation messages are useful information modulated on navigation signals, including satellite broadcast ephemeris, satellite clock offset and other parameters. During the process of satellite navigation signals being transmitted from satellites to the ground, after long-distance transmission in space environments such as the ionosphere and troposphere, the signal power is severely attenuated and is extremely susceptible to various types of noise and interference. In order to improve the probability that the ground receiving terminal obtains correct message information, the satellite navigation system performs error control coding on the message to resist data transmission errors caused by channel noise, interference and fading.

The target application scenario at the beginning of the design of the satellite navigation system was an outdoor open environment. There were no obstacles between the satellite and the receiving terminal. The signal propagated in a line-of-sight manner and the channel state was stable. Therefore, the early satellite navigation message encoding was relatively simple, such as Hamming code. , BCH code, etc. In order to improve the demodulation performance of message data in complex receiving environments such as indoors and cities, satellite navigation message encoding methods are constantly upgraded. In the process of message modernization, the GPS system first introduced convolutional codes into CNAV messages, and then applied binary LDPC codes to CNAV2 in the message to improve the message demodulation performance under low signal-to-noise ratio conditions. Beidou satellite navigation system B-CNAV1, B-CNAV2, B-CNAV3 and other messages use 64-base LDPC codes to improve the adaptability of the messages to fading channels. Taking the B-CNAV1 message as an example, the first 600 bits of subframe 2 are encoded. After encoding with hexadecimal LDPC (200, 100), the length is 1200 bits. The first 264 bits of subframe 3 are encoded, and after hexadecimal LDPC (88,44) encoding, the length is 528 bits. The encoded subframe 2 and subframe 3 are interleaved with 36×48 blocks to improve the message's ability to withstand burst errors.

Polyary LDPC codes have better performance than binary LDPC codes in terms of resisting channel fading, but there is a problem that the decoding algorithm is too complex, which results in a significant increase in the cost and power consumption of receiving terminals in mass application scenarios.

Contents of the invention

In view of the technical problem of excessive algorithm complexity caused by the use of multi-ary LDPC codes in satellite navigation systems in the prior art, the purpose of the present invention is to provide a message encoding method based on RS-LDPC concatenated codes.

In order to achieve the above tasks, the present invention adopts the following technical solutions:

A message encoding method based on RS-LDPC concatenated code, which is characterized in that the method takes the Beidou Satellite Navigation System B-CNAV1 message as the application object, the outer code adopts the RS code, and the inner code adopts the message concatenated coding of the binary LDPC code methods, including:

1) Use binary LDPC codes to replace the original 64-digit LDPC codes in subframe 2 and subframe 3 of the B-CNAV1 message of the Beidou Satellite Navigation System to reduce the complexity of the algorithm; at the same time, add the RS outer code before the binary LDPC code encoding, To combat burst errors caused by fading channels;

2) Use the page type reserved for subframe 3 in the B-CNAV1 message to define a new page type 5 to store the RS-encoded check bits of subframe 2 and subframe 3 in the previous frame.

The specific implementation steps are as follows:

Let the current frame of the B-CNAV1 message be the i-th frame, the next frame be the i+1-th frame, and i is a natural number;

Step 1: Convert the GF(2) domain binary bit data of subframe 2 and subframe 3 of the i-th frame into GF(2 ⁸ ) domain elements, that is, every 8 bits of binary data corresponds to a GF(2 ⁸ ) domain element, GF The primitive polynomial of the (2 ⁸ ) domain is x ⁸ +x ⁴ +x ³ +x ² +1:

(1) The 600-bit binary data of subframe 2 is converted into 75 GF(2 ⁸ ) domain elements;

(2) The 264-bit binary data of subframe 3 is converted into 33 GF (2 ⁸ ) field elements;

Step 2: Perform RS system coding on the subframe 2 and subframe 3 data of the i-th frame converted into the GF(2 ⁸ ) domain in step 1:

(3) The process of RS(95,75) encoding for subframe 2 is:

First, 160 GF(2 ⁸ ) domain symbols 0 are added in front of the 75 GF(2 ⁸ ) domain information bit symbols in subframe 2, and then the information bits are supplemented to 235 GF(2 ⁸ ) domain symbols in subframe 2. RS (255, 235) encoding, finally delete the first 160 GF (2 ⁸ ) domain symbols after RS (255, 235) encoding, and only retain the last 95 GF (2 ⁸ ) domain encoding symbols;

(4) The encoding process of RS(41,33) for subframe 3 is:

First, 214 GF(2 ⁸ ) domain symbols 0 are added in front of the 33 GF(2 ⁸ ) domain information bit symbols in subframe 3, and then the information bits are supplemented to 247 GF(2 ⁸ ) domain symbols in subframe 3. RS (255, 247) encoding, and finally the first 214 GF (2 ⁸ ) domain symbols after RS (255, 247) encoding are deleted, leaving only the last 41 GF (2 ⁸ ) domain encoding symbols;

Step 3: Convert the GF (2 ⁸ ) domain RS coding symbols of subframe 2 and subframe 3 of the i-th frame obtained in step 2 into binary bits respectively:

(1) The 95-bit GF(2 ⁸ ) domain RS coded symbol of subframe 2 is converted into 760 bits consisting of 600 bits of information bits and 160 bits of check bits;

(2) The 41-bit GF(2 ⁸ ) domain RS coded symbol of subframe 3 is converted into 328 bits consisting of 264 bits of information bits and 64 bits of parity bits;

Step 4: Perform binary LDPC coding on the 600-bit information bits of subframe 2 and the 264-bit information bits of subframe 3 of the i-th frame obtained in step 3 respectively; the binary LDPC check matrices of subframe 2 and subframe 3 are approximate lower triangular matrices. , composed of 6 sparse sub-matrices A, B, C, D, T and E, where T is a lower triangular matrix;

Let s be the information bit vector of subframe 2 or subframe 3, and the parity bit vectors p ₁ and p ₂ can be calculated by the following formula:

In the formula, φ=-E·T ^-1 ·B+D, [] ^T represents transposition. The encoded codeword vector is (s; p ₁ ; p ₂ ).

(1) Binary LDPC (1200, 600) encoding is performed on subframe 2, and the encoding is 1200 bits; the dimensions of the six sub-matrices A, B, T, C, D, and E of the check matrix of subframe 2 are 599 respectively. ×600, 599×1, 599×599, 1×600, 1×1, 1×599;

(2) Subframe 3 is binary LDPC (528, 264) encoded, and the encoding is 528 bits; the dimensions of the six sub-matrices A, B, T, C, D, and E of the check matrix of subframe 3 are 263×264 respectively. , 263×1, 263×263, 1×264, 1×1, 1×263;

Interleave the obtained encoded subframe 2 and subframe 3, using the original 38×46 size block interleaver of the B-CNAV1 message;

Step 5, create a new subframe 3 page type 5, encode the 160 check bits of subframe 2 of the i-th frame and convert it to the GF(2) domain, and encode the 160 check bits of subframe 3 and convert it to GF(2). The 64 check bits of the domain are put into page type 5 of subframe 3 of the i+1th frame, totaling 224 bits, and the remaining 10 bits are reserved bits; the concatenated encoding process of the i+1th frame is the same as that of the ith frame .

The message encoding method based on the RS-LDPC concatenated code of the present invention has error correction performance similar to the original 64-base LDPC code of the B-CNAV1 message, and at the same time can greatly reduce the computational complexity. Compared with hexadecimal LDPC code, it has the following advantages:

First, the complexity of the decoding algorithm is greatly reduced, effectively shortening the calculation time, and the decoding performance of the two encoding algorithms under the Land Mobile Satellite (LMS) channel and Gaussian White Noise (AWGN) channel is basically the same.

Second, when applying the RS-LDPC concatenated code to B-CNAV1, the page type reserved for the existing B-CNAV1 message subframe 3 is used to store the check bits generated by the RS outer code in the concatenated code, maintaining the B-CNAV1 The frame structure of the CNAV1 message minimizes the modification of the internal and external interfaces of the message caused by the message encoding upgrade, thereby reducing the software and hardware update costs caused by the message encoding upgrade.

Third, the RS outer code adopts the system encoding method. The position of the information bits remains unchanged after RS encoding. The receiving end can implement hierarchical decoding processing according to the actual signal reception quality: after completing the binary LDPC inner code decoding, the decoding can be The product result of the code result and the LDPC check matrix transpose or the CRC check result of each frame determines whether the inner code decoding result is correct. If the inner code decoding result is correct, the decoding ends. Otherwise, RS outer code decoding is required. , thereby further reducing the complexity of the decoding algorithm.

Description of the drawings

Figure 1 is a flow chart of B-CNAV1 message encoding based on RS-LDPC concatenated code of the present invention.

Figure 2 shows the information layout format of page type 5 of B-CNAV1 message subframe 3 defined in the present invention.

Figure 3 is a schematic diagram of the RS (95, 75) encoding process of B-CNAV1 message subframe 2 based on RS-LDPC concatenated code.

Figure 4 is a schematic diagram of the RS (41, 33) encoding process of B-CNAV1 message subframe 3 based on RS-LDPC concatenated code.

Figure 5 is the binary LDPC inner code check matrix structure of B-CNAV1 message subframe 2/subframe 3 based on RS-LDPC concatenated code.

Figure 6 is a schematic diagram of the interleaving and deinterleaving methods of B-CNAV1 message block interleaving.

Figure 7 shows the comparison of the frame error rate simulation results under the AWGN channel based on the RS-LDPC concatenated code and the original 64-base LDPC code of the B-CNAV1 message.

Figure 8 shows the comparison of the frame error rate simulation results based on the RS-LDPC concatenated code and the original 64-base LDPC code of the B-CNAV1 message under the Prieto-Cerdeira two-state LMS channel.

Figure 9 shows a comparison of the computational complexity values based on the RS-LDPC concatenated code and the original 64-base LDPC code of the B-CNAV1 message.

The present invention will be described in further detail below with reference to the accompanying drawings and examples.

Detailed ways

This embodiment provides a message encoding method based on RS-LDPC concatenated code. Taking Beidou Satellite Navigation System B-CNAV1 message as the application object, the instantiated design parameters of the concatenated code are given. The outer code adopts RS code. , the inner code adopts the message concatenation encoding method of binary LDPC code, that is, using binary LDPC code to replace the original 64-digit LDPC code of B-CNAV1 message subframe 2 and subframe 3 to reduce the complexity of the algorithm. At the same time, in the binary LDPC code The RS outer code is added before encoding to combat burst errors caused by fading channels. In order to adapt to the B-CNAV1 message information format, using the page type reserved for subframe 3 in the B-CNAV1 message, a new page type 5 is defined, which is used to store the RS-encoded subframes 2 and 3 in the previous frame. check digit.

The following are specific examples given by the inventor.

Example:

This embodiment takes the B-CNAV1 message as an example to describe the RS-LDPC cascade encoding method of the B-CNAV1 message.

Let the current frame of the B-CNAV1 message be the i-th frame, the next frame be the i+1-th frame, and i is a natural number;

Taking subframe 2 and subframe 3 of the i-th frame as an example, the RS-LDPC cascade encoding method of the B-CNAV1 message is introduced; taking subframe 3 of the i+1th frame as an example to introduce the newly defined subframe 3 page type 5 of the present invention. information format.

Referring to Figure 1 and Figure 2, the RS-LDPC cascade encoding method of B-CNAV1 message is implemented as follows:

Step 1: Convert the GF(2) domain binary bit data of subframe 2 and subframe 3 of the i-th frame into GF(2 ⁸ ) domain elements, that is, every 8 bits of binary data corresponds to a GF(2 ⁸ ) domain element, GF The primitive polynomial of the (2 ⁸ ) domain is x ⁸ +x ⁴ +x ³ +x ² +1:

(1) The 600-bit binary data of subframe 2 is converted into 75 GF(2 ⁸ ) domain elements;

(2) The 264-bit binary data of subframe 3 is converted into 33 GF (2 ⁸ ) field elements;

Step 2: Perform RS system coding on the subframe 2 and subframe 3 data of the i-th frame converted into the GF(2 ⁸ ) domain in step 1:

(1) The process of RS(95,75) encoding for subframe 2 is shown in Figure 3:

First, 160 GF(2 ⁸ ) domain symbols 0 are added in front of the 75 GF(2 ⁸ ) domain information bit symbols in subframe 2, and then the information bits are supplemented to 235 GF(2 ⁸ ) domain symbols in subframe 2. RS (255, 235) encoding, and finally the first 160 GF (2 ⁸ ) domain symbols after RS (255, 235) encoding are deleted, leaving only the last 95 GF (2 ⁸ ) domain encoding symbols.

(2) The encoding process of RS(41,33) for subframe 3 is shown in Figure 4. First, 214 GF(2 ⁸ ) domain symbols 0 are added in front of the 33 GF(2 ⁸ ) domain information bit symbols in subframe 3, and then the information bits are supplemented to 247 GF(2 ⁸ ) domain symbols in subframe 3. RS (255, 247) encoding, and finally the first 214 GF (2 ⁸ ) domain symbols after RS (255, 247) encoding are deleted, leaving only the last 41 GF (2 ⁸ ) domain encoding symbols.

Step 3: Convert the GF (2 ⁸ ) domain RS coding symbols of subframe 2 and subframe 3 of the i-th frame obtained in step 2 into binary bits respectively:

(1) The 95-bit GF(2 ⁸ ) domain RS coded symbol of subframe 2 is converted into 760 bits consisting of 600 bits of information bits and 160 bits of check bits;

(2) The 41-bit GF (2 ⁸ ) domain RS encoding symbol of subframe 3 is converted into 328 bits consisting of 264 bits of information bits and 64 bits of parity bits.

Step 4: Perform binary LDPC coding on the 600-bit information bits of subframe 2 and the 264-bit information bits of subframe 3 of the i-th frame obtained in step 3 respectively; the binary LDPC check matrices of subframe 2 and subframe 3 are approximate lower triangular matrices. , composed of 6 sparse sub-matrices A, B, C, D, T and E, where T is a lower triangular matrix;

Let s be the information bit vector of subframe 2 or subframe 3, and the parity bit vectors p ₁ and p ₂ can be calculated by the following formula:

In the formula, φ=-E·T ^-1 ·B+D, [] ^T represents transposition. The encoded codeword vector is (s; p ₁ ; p ₂ ).

(1) Binary LDPC (1200, 600) encoding is performed on subframe 2, and the encoding is 1200 bits. In this embodiment, the dimensions of the six sub-matrices A, B, T, C, D, and E of the check matrix of subframe 2 are 599×600, 599×1, 599×599, 1×600, and 1×1 respectively. , 1×599.

(2) Subframe 3 is encoded with binary LDPC (528, 264), and the encoding is 528 bits. In this embodiment, the dimensions of the six sub-matrices A, B, T, C, D, and E of the check matrix of subframe 3 are 263×264, 263×1, 263×263, 1×264, 1×1, 1×263.

The obtained encoded subframe 2 and subframe 3 are interleaved. In this embodiment, the original 38×46 size block interleaver of the B-CNAV1 message as shown in Figure 6 is still used.

Step 5, create a new subframe 3 page type 5 (PageID is 000101), RS-encode and convert the i-th subframe 2 to the 160 check digits of the GF(2) domain and RS-encode and convert subframe 3 The 64 check bits to the GF(2) field are placed in subframe 3 (page type 5) of the i+1th frame, totaling 224 bits, and the remaining 10 bits are reserved bits. The data format of subframe 3 page type 5 is shown in Figure 2. The concatenated encoding process of frame i+1 is the same as that of frame i.

With the upgrading of satellite navigation systems, message coding is developing towards the performance limit. However, the use of more advanced single codes (such as multi-ary LDPC codes) will introduce the problem of excessive computational complexity. Concatenated codes (such as the RS-LDPC concatenated code proposed by the present invention) can effectively improve error correction performance and reduce decoding complexity by combining two short component codes with relatively low decoding complexity to construct an equivalent long code.

Figures 7 and 8 respectively show the original 64-ary LDPC code based on RS-LDPC concatenated code and B-CNAV1 message in the AWGN channel (representing an open environment) and the Prieto-Cerdeira two-state LMS channel (representing a complex environment). The frame error rate simulation results, in which the Prieto-Cerdeira two-state LMS channel model selects scene parameters under the conditions of urban environment, satellite elevation angle of 60°, and average terminal rate of 50km/h. It can be seen from Figures 7 and 8 that when the frame error rate is 1E-2, the demodulation performance of RS-LDPC and 64-ary LDPC codes is basically the same.

Figure 9 shows the comparison of the computational complexity when B-CNAV1 message subframe 2 is based on RS-LDPC concatenated code and the original 64-base LDPC code. Since the complexity of the encoding and decoding algorithm mainly depends on the decoding algorithm, only the decoding algorithms are compared here. The RS code uses the Berlekamp-Massey decoding algorithm, the binary LDPC uses the LLR-BP decoding algorithm, and the 64-ary LDPC code uses Extended minimum sum (EMS) decoding algorithm with truncated information vector length 16. It can be seen that, in the message encoding method based on RS-LDPC concatenated codes given in this embodiment, the total number of decoding operations of the RS-LDPC code is less than 1/5 of the total number of decoding operations of the hexadecimal LDPC code.

Claims (1)

1. A text encoding method based on RS-LDPC cascade codes is characterized in that the method takes a Beidou satellite navigation system B-CNAV1 text as an application object, adopts an RS code as an outer code and adopts a binary LDPC code as an inner code, and comprises the following steps:

1) The original 64-system LDPC codes of the electronic sub-frame 2 and the electronic sub-frame 3 of the Beidou satellite navigation system B-CNAV1 are replaced by the binary LDPC codes, and meanwhile, the RS outer codes are added before the binary LDPC codes are coded;

2) Defining a new page type 5 for storing check bits of subframe 2 and subframe 3 after RS coding in the previous frame by using the reserved page type of the B-CNAV1 message for subframe 3;

the specific implementation steps are as follows:

let the current frame of B-CNAV1 message be the i-th frame, the next frame be the i+1th frame, i is a natural number;

step 1, converting GF (2) domain binary bit data of an ith frame subframe 2 and subframe 3 into GF (2) ⁸ ) The field element, i.e. one GF (2) for every 8 bits of binary data ⁸ ) Domain element, GF (2 ⁸ ) The primitive polynomial of the domain is x ⁸ +x ⁴ +x ³ +x ² +1：

(1) 600-bit binary data conversion of subframe 2 into 75 GF (2 ⁸ ) A domain element;

(2) 264-bit binary data conversion of subframe 3 into 33 GF (2 ⁸ ) A domain element;

step 2, converting step 1 into GF (2 ⁸ ) RS system coding is respectively carried out on the data of the subframe 2 and the subframe 3 of the ith frame of the domain:

(1) The RS (95, 75) encoding process for subframe 2 is:

first at 75 GF (2 ⁸ ) The field information bit sign is prepended with 160 GF (2) ⁸ ) Domain symbol 0, then complements the information bits with 235 GF (2 ⁸ ) Subframe 2 of the field symbol is RS (255, 235) encoded, and finally the first 160 GFs (2) encoded by RS (255, 235) ⁸ ) Domain symbolNumber deletion, leaving only the last 95 GF (2 ⁸ ) Domain coding symbols;

(2) The coding process of RS (41, 33) for subframe 3 is:

first at 33 GF (2) of subframe 3 ⁸ ) The field information bit sign is prepended by 214 GF (2) ⁸ ) Field symbol 0, then the information bits are complemented with 247 GF (2 ⁸ ) Subframe 3 of the field symbol is RS (255, 247) encoded, and finally the first 214 GFs (2) after RS (255, 247) encoding are performed ⁸ ) The field symbol is deleted, and only the last 41 GF (2 ⁸ ) Domain coding symbols;

step 3, GF (2) of the ith frame sub-frame 2 and sub-frame 3 obtained in step 2 ⁸ ) The domain RS code symbols are converted into binary bits, respectively:

(1) 95 bits GF (2) of subframe 2 ⁸ ) The domain RS code symbol is converted into 760 bits consisting of 600 bits of information bits and 160 bits of check bits;

(2) 41 bits GF (2) of subframe 3 ⁸ ) The domain RS code symbol is converted into 328 bits composed of 264-bit information bits and 64-bit check bits;

step 4, respectively performing binary LDPC coding on the 600 bit information bits of the ith frame subframe 2 and the 264 bit information bits of the subframe 3 obtained in the step 3; the binary LDPC check matrix of the subframe 2 and the subframe 3 is an approximate lower triangular matrix, and consists of 6 sparse submatricesAnd->Composition of->Is a lower triangular matrix;

order theFor the information bit vector of subframe 2 or subframe 3, check bit vector +.>And->Can be calculated by the following formula:

in the method, in the process of the invention,[] ^T representing the transpose, the encoded codeword vector is +.>

(1) Binary LDPC (1200, 600) encoding of subframe 2, with 1200 bits after encoding; check matrix six sub-matrices of sub-frame 2The dimensions of (2) are 599×600, 599×1, 599×599, 1×600, 1×1, 1×599, respectively;

(2) Subframe 3 is binary LDPC (528, 264) coded, 528 bits after coding; check matrix six sub-matrices of sub-frame 3The dimensions of (2) are 263×264, 263×1, 263×263, 1×264, 1×1, 1×263, respectively;

interleaving the obtained encoded sub-frame 2 and sub-frame 3, and adopting a block interleaver with the original size of 38 multiplied by 46 of the B-CNAV1 telegram;

step 5, newly creating a sub-frame 3 page type 5, namely putting 160 check bits of an ith frame sub-frame 2 which is subjected to RS coding and is converted to a GF (2) domain and 64 check bits of the sub-frame 3 which are subjected to RS coding and are converted to the GF (2) domain into the page type 5 of the ith+1th frame sub-frame 3, wherein 224 bits are total, and the rest 10 bits are reserved bits; the concatenated coding process of the i+1th frame is the same as that of the i frame.