A turbo code decoding method based on linear approximation and sliding window

Abstract

This paper presents a Turbo code decoding method based on linear approximation and a sliding window, relating to the field of error control coding technology. Addressing the problem of large decoding delays in existing technologies, this application proposes a SISO decoder method based on linear approximation and a sliding window, which overcomes the shortcomings of existing algorithms due to numerous nonlinear operations and low parallelism. This method effectively solves the problem of insufficient throughput while maintaining decoding performance. Furthermore, by approximating nonlinear operations as linear, it significantly reduces computational complexity and exhibits excellent stability even under high-speed clocks. Simultaneously, the introduction of the sliding window method allows the SISO decoder to store only the effective value of the backward state metric for a single window length, instead of storing the forward and backward state metrics for the entire interleaving depth as in traditional algorithms. This reduces storage resource usage and further optimizes the hardware structure.

Description

Technical Field

[0001] This invention relates to the field of error control coding technology, specifically a Turbo code decoding method based on linear approximation and sliding window. Background Technology

[0002] Throughout history, achieving effective and reliable communication has been a relentless pursuit. As humanity has entered the modern era, the connections between everything have become increasingly close, demanding that researchers innovate communication theories and evolution to better meet societal needs. Today, communication systems are mainly divided into analog and digital systems. Compared to analog systems, digital systems primarily have two additional modules: source coding to ensure communication effectiveness and channel coding to ensure reliability. The source coding module encodes the digital signal converted from the analog signal by the AD module, removing redundancy and improving communication effectiveness. The channel coding module encodes the modulated signal, adding redundancy in a prescribed and controllable manner. At the receiving end, it combines the information provided by the redundant bits to retrieve and correct erroneous bits caused by fading and noise in the channel. With the continuous iteration of communication technology, the demands for speed and quality from various services are constantly increasing, leading to ever-higher requirements for channel coding. In 1993, Berrou proposed the Turbo coding theory, ushering in a new era of modern channel coding.

[0003] For the SISO decoder, the core unit of a Turbo code decoder, common decoding methods include the Log-MAP algorithm, the MAX-Log-MAP algorithm, and the linear Log-MAP algorithm. The Log-MAP algorithm implements the MAP algorithm calculation in the logarithmic field through mapping, but it is not suitable for implementation on FPGAs. The MAX-Log-MAP algorithm removes all logarithmic operations from the Log-MAP algorithm, thus reducing computational complexity and making it easier to implement on FPGAs, but its decoding performance is somewhat reduced. The linear Log-MAP algorithm uses a linear approximation method, achieving decoding performance close to that of the Log-MAP algorithm, but with a significant decoding delay. Therefore, the implementation of an FPGA-based Turbo decoder faces the challenge of balancing implementation complexity and decoding performance, while also addressing the real-time requirements of Turbo code decoding. Summary of the Invention

[0004] The purpose of this invention is to address the problem of large decoding delay in existing technologies by proposing a Turbo code decoding method based on linear approximation and a sliding window.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A Turbo code decoding method based on linear approximation and sliding window includes the following steps:

[0007] Step 1: Store the information to be decoded into three RAMs as a group of RAMs, then copy them twice to obtain a total of three groups of RAMs;

[0008] Step 2: Divide the information to be decoded in the first group of RAM into N windows, and set the window length. The constraint length of the Turbo encoder is m. Start from the end of the second window and perform pre-calculation of the backward state metric, and normalize the pre-calculation result. The initial value of the pre-calculation of the backward state metric is ln(1 / 2). m );

[0009] Step 3: Divide the information to be decoded in the second group of RAM into N windows and set the window length. Start from the end of the first window and calculate the effective value of the backward state metric. The initial value of the effective value of the backward state metric is the last value of the normalized pre-calculation result in Step 2.

[0010] Step 4: Divide the information to be decoded in the third group of RAM into N windows and set the window length. Starting from the beginning of the first window, calculate the effective value of the forward state metric and normalize the effective value results. The initial value of the effective value of the forward state metric is:

[0011]

[0012] Step 5: Based on the effective values ​​of the backward state metric obtained in Step 3 and the effective values ​​of the forward state metric obtained in Step 4, obtain the posterior probability log-likelihood ratio and extrinsic information;

[0013] Step 6: Slide the window backward sequentially, repeat steps 2 to 5, and obtain the pre-calculated result of the backward state metric of the (k+1)th window, the effective value calculation result of the backward state metric of the kth window, the effective value calculation result of the forward state metric of the kth window, and the posterior probability log-likelihood ratio and extrinsic information of the kth window, where k = 1, 2, ..., N-1;

[0014] Step 7: Calculate the effective value of the backward state metric for the data containing the tail bit in the last window of the second group of RAM; calculate the effective value of the forward state metric for the data containing the tail bit in the last window of the third group of RAM; obtain the posterior probability log-likelihood ratio and extrinsic information containing the tail bit based on the obtained effective values ​​of the backward and forward state metrics.

[0015] Step 8: Deinterleave the posterior log-likelihood ratio, extrinsic information, posterior log-likelihood ratio including the tail bit, and extrinsic information. Invert the deinterleaved posterior log-likelihood ratio using a hard decision to obtain the final decoded data.

[0016] Furthermore, the information to be decoded includes system information soft bits, check information soft bits, and prior information.

[0017] Furthermore, the pre-computation of the backward state metric in step two is expressed as follows:

[0018]

[0019] Where, Θ β Let γ be the set of all states that can be transitioned to at time k-1 at time k. k (m',m) is the branch metric from time k-1 to time k, β k (m) represents the backward state metric;

[0020]

[0021] Among them, y k,s Let y be the soft bit of the system at time k. k,p For the soft bits of the check sequence at time k, L a (u k ) represents prior information, u k To transmit information, x k,s and x k,p For u k The symbol after BPSK modulation, σ is the conditional probability density, and L c It is a constant.

[0022] Furthermore, the normalized backward state metric pre-calculation result is expressed as follows:

[0023] β k (m)=β k (m)-β k (0)

[0024] Where, β k (0) is the pre-calculated backward state metric when m = 0.

[0025] Furthermore, the effective value of the forward state metric is expressed as:

[0026]

[0027] Where, Θ α α represents the set of all states that can transition to the next time step (k) at time k-1. k-1(m') represents the forward state metric of a state m' at time k-1.

[0028] Furthermore, the normalized effective value of the forward state metric is expressed as follows:

[0029] α k (m)=α k (m)-α k (0)

[0030] Where, α k (0) is the forward state metric of the initial state at time k.

[0031] Furthermore, the posterior probability log-likelihood ratio is expressed as:

[0032]

[0033] Where, Θ + To correspond to the emission u at time 1 k When Θ = 1, the corresponding state change pair of the transmitter encoder register, Θ - To correspond to the emission u at time t k The state change pair of the transmitter encoder register when = 0.

[0034] Furthermore, the external information is represented as follows:

[0035] L e (u k )=L(u k )-L c y k,s -L a (u k )

[0036] in, L(u k ) represents the log-likelihood ratio of the posterior probability, and σ represents the conditional probability density.

[0037] The beneficial effects of this invention are:

[0038] This application addresses the shortcomings of existing algorithms, such as excessive nonlinear operations and low parallelism leading to significant decoding delays. It proposes a SISO decoder method based on linear approximation and a sliding window, which effectively solves the problem of insufficient throughput while maintaining decoding performance. Furthermore, by approximating nonlinear operations as linear, it significantly reduces computational complexity and exhibits excellent stability even under high-speed clocks. The introduction of the sliding window method allows the SISO decoder to store only the effective value of the backward state metric for a single window length, instead of storing the forward and backward state metrics for the entire interleaving depth as in traditional algorithms. This reduces storage resource usage and further optimizes the hardware structure.

[0039] In this application, the fractional part of the calculation uses three-bit quantization, employing the minimum quantization bit width while ensuring decoding performance, thus saving hardware resources and further reducing computational complexity. This application adopts a pipelined design approach, reducing the difficulty of hardware implementation.

[0040] This application designs a Turbo code decoding algorithm based on linear approximation and sliding window, which reduces the decoding delay of the SISO decoder to 1%-5% of that of traditional algorithms while ensuring decoding performance. Attached Figure Description

[0041] Figure 1 Here is a diagram of the Turbo decoder structure;

[0042] Figure 2 This is the implementation form of the sliding window algorithm in this application;

[0043] Figure 3 This is a block diagram of the Turbo decoder module in this application;

[0044] Figure 4 State diagram of the Turbo decoder;

[0045] Figure 5 This is the timing diagram of the SISO decoder in this application;

[0046] Figure 6 A simulation comparison of the decoding algorithm performance of the SISO decoder;

[0047] Figure 7 This is a comparison chart of the bit error rate between the software simulation of this application and the test version of the previous version. Detailed Implementation

[0048] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0049] Specific implementation method one: Refer to Figure 1 This embodiment describes a Turbo code decoding method based on linear approximation and a sliding window, which includes the following steps:

[0050] Step 1: Store the information to be decoded into three RAMs as a group of RAMs, then copy them twice to obtain a total of three groups of RAMs;

[0051] Step 2: Divide the information to be decoded in the first group of RAM into N windows, with a window length of W and a constraint length of m for the Turbo encoder. During the 0-T0 time period, perform backward state measurement β starting from the end of the second window. k Pre-calculation of (m), and β k(m) The pre-calculated results are normalized, and the backward state metric β k The initial value of (m) is ln(1 / 2) m ), where k represents the window number;

[0052] Step 3: Divide the information to be decoded in the second group of RAM into N windows of length W. During the T0-T1 time period, perform backward state measurement β starting from the end of the first window. k The effective value of (m) is calculated, and the backward state metric β is... k The initial value of the effective value of (m) is the last value of the pre-calculated result after normalization in step two;

[0053] Step 4: Divide the information to be decoded in the third group of RAM into N windows of length W. During the T1-T2 time period, perform forward state measurement α starting from the beginning of the first window. k Calculate the effective value of (m) and then use α k (m) The effective value results are normalized, and the forward state metric α is... k The initial value of the effective value of (m) is:

[0054]

[0055] Step 5: Based on the effective value β of the backward state metric obtained in Step 3 k (m) and the effective value of the forward state metric α obtained in step four k (m) Obtain the posterior probability log-likelihood ratio and external information;

[0056] Step 6: Slide the window backward sequentially, repeating steps 2 to 5, to obtain the backward state metric β of the (k+1)th window. k The pre-calculation results of (m), and the backward state metric β of the k-th window. k The effective value calculation result of (m), and the forward state metric α of the k-th window. k The effective value calculation results of (m) and the posterior probability log-likelihood ratio of the k-th window and external information, where k = 1, 2, ..., N-1;

[0057] Step 7: Calculate the effective value of the backward state metric for the data containing the tail bit in the last window of the second group of RAM; calculate the effective value of the forward state metric for the data containing the tail bit in the last window of the third group of RAM; obtain the posterior probability log-likelihood ratio and extrinsic information containing the tail bit based on the obtained effective values ​​of the backward and forward state metrics.

[0058] Step 8: Deinterleave the posterior log-likelihood ratio, extrinsic information, posterior log-likelihood ratio including the tail bit, and extrinsic information. Invert the deinterleaved posterior log-likelihood ratio using a hard decision to obtain the final decoded data.

[0059] Specific Implementation Method Two: This implementation method is a further explanation of Specific Implementation Method One. The difference between this implementation method and Specific Implementation Method One is that the information to be decoded includes system information soft bits, check information soft bits, and prior information.

[0060] Specific Implementation Method Three: This implementation method is a further explanation of Specific Implementation Method One. The difference between this implementation method and Specific Implementation Method One is that in step two, β... k The pre-calculation of (m) is expressed as:

[0061]

[0062] Where, Θ β γ represents the set of all states that can transition to time k-1 at time k. k (m',m) is the branch metric from time k-1 to time k;

[0063]

[0064]

[0065] Among them, y k,s Let y be the soft bit of the system at time k. k,p For the soft bits of the check sequence at time k, L a (u k ) represents prior information, u k To transmit information, x k,s and x k,p For u k The symbol after BPSK modulation, σ is the conditional probability density, and L c It is a constant.

[0066] x k is u k The symbol after BPSK modulation, x k It is (x) k,s x k,p ).

[0067] Specific Implementation Method Four: This implementation method is a further explanation of Specific Implementation Method One. The difference between this implementation method and Specific Implementation Method One is that the normalized β... k (m) The pre-calculated results are expressed as follows:

[0068] β k (m)=β k(m)-β k (0)

[0069] Where, β k (0) is the pre-calculated backward state metric when m=0.

[0070] Specific Implementation Method Five: This implementation method is a further explanation of Specific Implementation Method One. The difference between this implementation method and Specific Implementation Method One is that the forward state measurement α is... k The effective value of (m) is expressed as:

[0071]

[0072] Where, Θ α α represents the set of all states that can transition to the next time step (k) at time k-1. k-1 (m') represents the forward state metric of a state m' at time k-1.

[0073] Specific Implementation Method Six: This implementation method is a further explanation of Specific Implementation Method One. The difference between this implementation method and Specific Implementation Method One is that the α... k The normalized effective value of (m) is expressed as follows:

[0074] α k (m)=α k (m)-α k (0)

[0075] Where, α k (0) is the forward state metric of the initial state at time k.

[0076] Specific Implementation Method Seven: This implementation method is a further explanation of Specific Implementation Method One. The difference between this implementation method and Specific Implementation Method One is that the posterior probability log-likelihood ratio is expressed as:

[0077]

[0078] Where, Θ + This indicates that the time corresponding to emission u is... k When Θ = 1, the corresponding state change pair of the transmitter encoder register (m', m); - This indicates that the time corresponding to emission u is... k The state change pair of the transmitter encoder register when = 0.

[0079] Specific Implementation Method Eight: This implementation method is a further explanation of Specific Implementation Method One. The difference between this implementation method and Specific Implementation Method One is that the external information is represented as follows:

[0080] L e (uk )=L(u k )-L c y k,s -L a (u k )

[0081] in, L(u k ) represents the posterior probability log-likelihood ratio.

[0082] Example:

[0083] This application is implemented on an FPGA, using the Xilinx Virtex-7 series XC7VX485T-2FFG1761C chip, and the development board type is VC707, which is responsible for implementing the decoding function of the Turbo code decoder, with a working frequency of 198MHz. Figure 3 This is a block diagram of the Turbo code decoder module.

[0084] The specific implementation steps are as follows:

[0085] Control module: Generates control signals to control the operation of the entire Turbo decoder and controls the decoder's state transitions. The Turbo decoder state diagram is shown below. Figure 4 As shown.

[0086] Interleaving and Deinterleaving Modules: The main functions of the interleaving and deinterleaving modules are to store the soft information of the sequence to be decoded and to interleave and deinterleave the external information of the SISO decoder under the control of the controller. When the number of iterations is reached, the deinterleaving module interleaves the second log-likelihood ratio output by the SISO decoder in this iteration.

[0087] SISO decoder input selection module: Rectifies and combines the outputs of the interleaving and deinterleaving modules into one.

[0088] SISO decoder module: Adopting the concept of multiplexing, the two SISO decoders in the Turbo code decoder are combined into one, and all functions are completed by one SISO decoder. Figure 5 The following is a timing diagram for the SISO decoder. The specific steps of the SISO decoder's operation are as follows:

[0089] Step 1: Data caching:

[0090] The system information soft bits input to the SISO decoder will be y. s =(y 1,s ,y 2,s ,y 3,s ,…,y N,s ), verification information soft bits y p =(y1,p ,y 2,p ,y 3,p ,…,y N,p ) and prior information L a The signals are stored in three RAMs as one group, and two copies of each of the three input signals are written into RAM as the other two groups of RAM.

[0091] Step 2: Backward state metric β pre-computation module:

[0092] The information to be decoded in the first group of RAM is divided into N windows, each with a length of W. The constraint length of the Turbo encoder is m. At the beginning of time period T0, β is performed backward from the end of the second window. k (m) Pre-calculation, initial value set as ln(1 / 2) m ).

[0093] Step 2.1: β k (m) Pre-calculation:

[0094] The recursive formula for calculating the backward state metric is:

[0095]

[0096] Where, Θ β This indicates that it is possible to jump to time S at time k-1. k-1 =m's all S k = The set of m states;

[0097]

[0098]

[0099] Step 2.2: β k (m) Pre-computation normalization:

[0100]

[0101] Step 3: Backward state metric β effective value calculation module:

[0102] The information to be decoded in the second set of RAM is divided into N windows, each with a length of W. At the beginning of time period T1, β is processed backward from the end of the first window. k (m) Calculation of effective value, the initial value is β obtained in step 2. k (m) The last value pre-calculated.

[0103] Step 4: Forward state measurement α k (m) RMS value calculation module:

[0104] The information to be decoded in the third group of RAM is divided into N windows, each with a window length of W. At the beginning of time period T2, α is performed sequentially from the beginning of the first window. k (m) Calculation of effective value, initial value:

[0105]

[0106] Step 4.1: α k (m) Calculation of effective value:

[0107] The formula for calculating the forward state metric is:

[0108]

[0109] Where, Θ α This indicates that it is possible to transition to the next time step, i.e., time k, at time k-1. k = The set of all states of m.

[0110] Step 4.2: α k (m) RMS value normalization:

[0111]

[0112] Step 5: Obtain the posterior probability log-likelihood ratio L and external information L e :

[0113] Based on the effective value β of the backward state metric in the first window of steps 3 and 4. k (m) and the effective value of the forward state metric α k (m) is used to obtain the posterior probability log-likelihood ratio and extrinsic information. The calculation of the posterior probability log-likelihood ratio adopts a pipelined design to reduce latency.

[0114] The formula for calculating the posterior probability log-likelihood ratio is:

[0115]

[0116] The formula for calculating external information is:

[0117] L e (u k )=L(u k )-L c y k,s -L a (u k )

[0118] in,

[0119] Step 6: Slide the calculation window backward sequentially, repeating steps 2 to 5, to obtain the backward state metric β of the (k+1)th window. k (m) Pre-computed backward state metric β for the k-th window k (m) Effective value, forward state metric α of the k-th window k (m) The effective value and the log-likelihood ratio of the posterior probability of the k-th window, along with external information. Where k = 1, 2, ..., N-1.

[0120] Step 7: The last window contains the calculation of the tail bits:

[0121] The effective value β of the backward state metric is calculated for the data containing the tail bits in the last window of the second group of RAM. k (m) Calculate the forward state metric effective value α for the data containing the tail bits in the last window of the third group of RAM. k (m) Calculate the effective value β of the backward state metric based on the data in the last window containing the tail bits. k (m) and the effective value of the forward state metric α k (m) yields the posterior probability log-likelihood ratio and extrinsic information of the data containing the tail bits in the last window.

[0122] SISO decoder output selection module: Distributes the output of data and control information of the SISO decoder to the interleaving and deinterleaving modules.

[0123] Hard decision module: Inverts the input posterior probability log-likelihood ratio data to obtain the final decoded data.

[0124] Figure 6 The simulation comparison diagram of the SISO decoder algorithm shows that the algorithm used in this application has a significantly lower bit error rate than the second-best traditional algorithm, MAX-Log-MAP, and almost no decrease in bit error rate compared to the best traditional algorithm, Log-MAP, demonstrating good performance.

[0125] This application implements a Turbo code decoder based on linear approximation and a sliding window, with an interleaving depth of 2048, a window length of 32, a window number of 64, 8 iterations, a quantization scheme of [7,3], and a running clock of 198MHz. Figure 7 As can be seen, the decoder designed in this application has good performance, and the actual bit error rate curve basically coincides with the theoretical bit error rate curve. From the implementation results, the Turbo code decoding achieved by this invention has low latency and a throughput of up to 20 Mbps, enabling high-speed decoding in engineering applications.

[0126] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A Turbo code decoding method based on linear approximation and sliding window, characterized in that... Includes the following steps: Step 1: Store the information to be decoded into three RAMs as a group of RAMs, then copy them twice to obtain a total of three groups of RAMs; Step 2: Divide the information to be decoded in the first group of RAM into N windows, and set the window length. The constraint length of the Turbo encoder is m. Start from the end of the second window and perform pre-calculation of the backward state metric, and normalize the pre-calculation result. The initial value of the pre-calculation of the backward state metric is ln(1 / 2). m ); Step 3: Divide the information to be decoded in the second group of RAM into N windows and set the window length. Start from the end of the first window and calculate the effective value of the backward state metric. The initial value of the effective value of the backward state metric is the last value of the normalized pre-calculation result in Step 2. Step 4: Divide the information to be decoded in the third group of RAM into N windows and set the window length. Starting from the beginning of the first window, calculate the effective value of the forward state metric and normalize the effective value results. The initial value of the effective value of the forward state metric is: Step 5: Based on the effective values ​​of the backward state metric obtained in Step 3 and the effective values ​​of the forward state metric obtained in Step 4, obtain the posterior probability log-likelihood ratio and extrinsic information; Step 6: Slide the window backward sequentially, repeat steps 2 to 5, and obtain the pre-calculated result of the backward state metric of the (k+1)th window, the effective value calculation result of the backward state metric of the kth window, the effective value calculation result of the forward state metric of the kth window, and the posterior probability log-likelihood ratio and extrinsic information of the kth window, where k = 1, 2, ..., N-1; Step 7: Calculate the effective value of the backward state metric for the data containing the tail bit in the last window of the second group of RAM; calculate the effective value of the forward state metric for the data containing the tail bit in the last window of the third group of RAM; obtain the posterior probability log-likelihood ratio and extrinsic information containing the tail bit based on the obtained effective values ​​of the backward and forward state metrics. Step 8: Deinterleave the posterior log-likelihood ratio, extrinsic information, posterior log-likelihood ratio including the tail bit, and extrinsic information. Invert the deinterleaved posterior log-likelihood ratio using a hard decision to obtain the final decoded data.

2. The Turbo code decoding method based on linear approximation and sliding window as described in claim 1, characterized in that... The information to be decoded includes system information soft bits, check information soft bits, and prior information.

3. The Turbo code decoding method based on linear approximation and sliding window as described in claim 1, characterized in that... The pre-calculation of the backward state metric in step two is represented as follows: Where, Θ β Let γ be the set of all states that can be transitioned to at time k-1 at time k. k (m',m) is the branch metric from time k-1 to time k, β k (m) represents the backward state metric; Among them, y k,s Let y be the soft bit of the system at time k. k,p For the soft bits of the check sequence at time k, L a (u k ) represents prior information, u k To transmit information, x k,s and x k,p For u k The symbol after BPSK modulation, σ is the conditional probability density, and L c It is a constant.

4. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, characterized in that... The normalized backward state metric pre-calculation result is expressed as follows: b k (m)=β k (m)-b k (0) Where, β k (0) is the pre-calculated backward state metric when m = 0.

5. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, characterized in that... The effective value of the forward state metric is represented as follows: Where, Θ α α represents the set of all states that can transition to the next time step (k) at time k-1. k-1 (m') represents the forward state metric of a state m' at time k-1.

6. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, characterized in that... The normalized effective value of the forward state metric is represented as follows: a k (m)=a k (m)-a k (0) Where, α k (0) is the forward state metric of the initial state at time k.

7. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, characterized in that... The posterior probability log-likelihood ratio is expressed as: Where, Θ + To correspond to the emission u at time t k When Θ = 1, the corresponding state change pair of the transmitter encoder register, Θ - To correspond to the emission u at time 1 k The state change pair of the transmitter encoder register when = 0.

8. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, characterized in that... The external information is represented as follows: L e (u k )=L(u k )-L c y k,s -L a (u k ) in, L(u k ) represents the log-likelihood ratio of the posterior probability, and σ represents the conditional probability density.

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