CN115529048A - Turbo code decoding method based on linear approximation and sliding window - Google Patents

Turbo code decoding method based on linear approximation and sliding window Download PDF

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CN115529048A
CN115529048A CN202211165730.8A CN202211165730A CN115529048A CN 115529048 A CN115529048 A CN 115529048A CN 202211165730 A CN202211165730 A CN 202211165730A CN 115529048 A CN115529048 A CN 115529048A
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state metric
effective value
window
information
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张佳岩
马一帆
马永奎
赵洪林
郭凯宇
单成兆
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Harbin Institute of Technology
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2957—Turbo codes and decoding
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2771—Internal interleaver for turbo codes

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Abstract

A Turbo code decoding method based on linear approximation and sliding window relates to the technical field of error control coding, aims at the problem of large decoding delay in the prior art, aims at the defects of more nonlinear operation and large decoding delay caused by low parallelism degree of the prior algorithm, and provides a SISO decoder decoding method based on linear approximation and sliding window, well solves the problem of insufficient throughput rate on the premise of ensuring decoding performance, simultaneously approximates nonlinear operation to be linear, greatly reduces calculation complexity, and has excellent stability under a high-speed clock; meanwhile, the sliding window method is introduced, so that the SISO decoder only needs to store the backward state metric effective value of one window length, and does not need to store the forward state metric and the backward state metric of the whole interleaving depth like the traditional algorithm, the use of storage resources is reduced, and the hardware structure is further optimized.

Description

Turbo code decoding method based on linear approximation and sliding window
Technical Field
The invention relates to the technical field of error control coding, in particular to a Turbo code decoding method based on linear approximation and a sliding window.
Background
From ancient times to present, how to realize the effectiveness and reliability of communication is a goal pursued by people. As people step into modern society, the connection between everything becomes increasingly tight, which requires researchers to make innovations more meeting the social requirements for the theory and evolution of communication. In the present society, communication systems are mainly divided into analog and digital communication systems, and compared with the analog communication system, the digital communication system mainly has two modules of source coding for ensuring communication effectiveness and channel coding for ensuring communication reliability. The information source coding module codes the digital signals converted from the analog signals after passing through the AD module, so that the redundancy is removed and the effectiveness of communication is improved; the channel coding module codes the modulated signal, adds a certain redundancy in a specified and controllable way, and searches and corrects error bits generated due to fading and noise in the channel at a receiving end by combining information provided by redundant bits. With the continuous iteration of communication technology, the requirements of various services on the speed and quality of communication are also continuously increasing, and the requirements on channel coding are also increasingly increasing. In 1993, berrou proposed the Turbo coding theory, and channel coding entered a new era of modern coding.
For a core unit SISO decoder in a Turbo code decoder, common decoding methods include a Log-MAP algorithm, a MAX-Log-MAP algorithm, a linear Log-MAP algorithm and the like. The Log-MAP algorithm realizes the calculation of the MAP algorithm on a logarithmic domain in a mapping mode, but is not suitable for being realized on an FPGA; the MAX-Log-MAP algorithm removes all logarithmic operations in the Log-MAP algorithm, thereby reducing the computational complexity, being more convenient to realize on an FPGA, but reducing the decoding performance to some extent; the linear Log-MAP algorithm adopts a linear approximation method, the decoding performance approaches to the Log-MAP algorithm, but the decoding delay is larger. Therefore, the Turbo decoder based on the FPGA has a problem in that both the complexity and the decoding performance need to be considered, and the real-time requirement of the Turbo decoding needs to be solved urgently.
Disclosure of Invention
The purpose of the invention is: aiming at the problem of large decoding delay in the prior art, a Turbo code decoding method based on linear approximation and a sliding window is provided.
The technical scheme adopted by the invention to solve the technical problems is as follows:
a Turbo code decoding method based on linear approximation and a sliding window comprises the following steps:
the method comprises the following steps: respectively storing information to be decoded into three RAMs as a group of RAMs, and then copying two parts to obtain three groups of RAMs;
step two: dividing information to be decoded in a first group of RAM (random access memory) into N windows, setting the window length, setting the constraint length of a Turbo encoder to be m, carrying out forward precomputation on backward state measurement from the tail of a second window, and normalizing the precomputation result, wherein the precomputation initial value of the backward state measurement is ln (1/2) m )；
Step three: dividing the information to be decoded in the second group of RAM into N windows, setting the window length, and calculating the effective value of the backward state metric from the tail of the first window to the front, wherein the initial value of the effective value of the backward state metric is the last value of the precomputed result after normalization in the step two;
step four: dividing information to be decoded in a third group of RAM into N windows, setting window length, calculating an effective value of forward state metric from the beginning of a first window to the back, and normalizing the effective value result, wherein the initial value of the effective value of the forward state metric is as follows:
Figure BDA0003861270920000021
step five: obtaining posterior probability log-likelihood ratio and external information according to the effective value of the backward state metric obtained in the third step and the effective value of the forward state metric obtained in the fourth step;
step six: the windows sequentially slide backwards, and the steps from the second step to the fifth step are repeated to obtain a pre-calculation result of the backward state metric of the k +1 th window, an effective value calculation result of the backward state metric of the k-th window, an effective value calculation result of the forward state metric of the k-th window, and the posterior probability log-likelihood ratio and the extrinsic information of the k-th window, wherein k =1,2, \8230; \, N-1;
step seven: carrying out backward state metric effective value calculation on data containing tail bits in the last window in the second group of RAM; carrying out forward state metric effective value calculation on data containing tail bits in the last window in the third group of RAM; obtaining a posterior probability log-likelihood ratio containing tail bits and external information according to the obtained backward state metric effective value and forward state metric effective value;
step eight: and de-interleaving the posterior probability log-likelihood ratio, the extrinsic information, the posterior probability log-likelihood ratio containing tail bits and the extrinsic information, and obtaining final decoding data by inverting the de-interleaved posterior probability log-likelihood ratio through hard decision.
Further, the information to be decoded includes system information soft bits, check information soft bits, and prior information.
Further, the pre-calculation of the backward state metric in the second step is represented as:
Figure BDA0003861270920000022
wherein, theta β To be able to jump to the set of all states at time k-1, γ k (m', m) is the branch metric from time k-1 to time k, β k (m) representing a backward state metric for the backward state metric;
Figure BDA0003861270920000031
wherein, y k,s For systematic soft bits at time k, y k,p Checking the sequence for time kSoft bit, L a (u k ) As a priori information, u k For transmitting information, x k,s And x k,p Is u k Symbol after BPSK modulation, σ is conditional probability density, L c Is a constant.
Further, the normalized backward state metric pre-calculation result is expressed as:
β k (m)＝β k (m)-β k (0)
wherein, beta k (0) Pre-computed for the backward state metric for the m =0 state.
Further, the effective value of the forward state metric is represented as:
Figure BDA0003861270920000032
wherein, theta α Representing the set of all states that can be transferred to the next instant, i.e. k instant, at instant k-1, alpha k-1 (m ') represents the forward state metric for some state m' at time k-1.
Further, the result of the normalized effective value of the forward state metric is represented as:
α k (m)＝α k (m)-α k (0)
wherein alpha is k (0) Is the forward state metric value of the initial state at time k.
Further, the posterior probability log-likelihood ratio is expressed as:
Figure BDA0003861270920000033
wherein, theta + To correspond at a time instant to a transmission u k The state change pair of the corresponding transmitting end encoder register at the time of =1, theta - To correspond in time to the emission u k And =0, the state change pair of the corresponding encoder register at the transmitting end.
Further, the extrinsic information is expressed as:
L e (u k )＝L(u k )-L c y k,s -L a (u k )
wherein the content of the first and second substances,
Figure BDA0003861270920000034
L(u k ) σ is the conditional probability density for the posterior probability log-likelihood ratio.
The invention has the beneficial effects that:
aiming at the defects that the existing algorithm has more nonlinear operations and low parallelism degree and causes larger decoding delay, the application provides a SISO decoder decoding method based on linear approximation and a sliding window, the problem of insufficient throughput rate is well solved on the premise of ensuring decoding performance, and meanwhile, nonlinear operation is approximate to linearity, so that the calculation complexity is greatly reduced, and the SISO decoder has excellent stability under a high-speed clock; meanwhile, the sliding window method is introduced, so that the SISO decoder only needs to store the backward state metric effective value of one window length, and does not need to store the forward state metric and the backward state metric of the whole interleaving depth like the traditional algorithm, the use of storage resources is reduced, and the hardware structure is further optimized.
According to the method and the device, the bit width decimal part is calculated by three-bit quantization, the minimum quantization bit width is adopted on the premise of ensuring the decoding performance, the consumption of hardware resources is saved, and the calculation complexity is further reduced. The design idea of a production line is adopted, and the hardware implementation difficulty is reduced.
The application designs a Turbo code decoding algorithm based on linear approximation and a sliding window, which ensures the decoding performance and reduces the decoding delay of a SISO decoder to 1% -5% of that of the traditional algorithm.
Drawings
FIG. 1 is a block diagram of a Turbo decoder;
FIG. 2 is a sliding window algorithm implementation of the present application;
FIG. 3 is a block diagram of a Turbo decoder module according to the present application;
FIG. 4 is a Turbo decoder state diagram;
FIG. 5 is a timing diagram of the operation of a SISO decoder of the present application;
FIG. 6 is a comparison diagram of simulation of decoding algorithm performance of a SISO decoder;
FIG. 7 is a comparison graph of bit error rate between simulation and test of the present application
Detailed Description
It should be noted that, in the present invention, the embodiments disclosed in the present application may be combined with each other without conflict.
The first embodiment is as follows: referring to fig. 1, a Turbo code decoding method based on linear approximation and a sliding window according to this embodiment is specifically described, and includes the following steps:
the method comprises the following steps: respectively storing information to be decoded into three RAMs as a group of RAM, and then copying two parts to obtain three groups of RAM;
step two: dividing information to be decoded in a first group of RAM into N windows, wherein the window length is W, the constraint length of a Turbo encoder is m, and the constraint length is 0-T 0 During the time period, the backward state metric β is performed from the end of the second window onwards k (m) and converting beta k (m) normalizing the pre-computed result, the backward state metric β k (m) has a pre-calculated initial value of ln (1/2) m ) K represents the window number;
step three: dividing the information to be decoded in the second group of RAM into N windows with the window length W at T 0 -T 1 During the time period, the backward state metric β is performed from the end of the first window onwards k (m) calculating an effective value of said backward state metric β k (m) the initial value of the valid value is the last value of the pre-calculation result after normalization in the step two;
step four: dividing the information to be decoded in the third group of RAM into N windows with the window length of W and T 1 -T 2 During the time period, the forward state metric α is performed backward from the beginning of the first window k (m) calculating the effective value of (m), and converting alpha k (m) normalizing the result of the significant value, the forward state metric α k The initial values of the effective values of (m) are:
Figure BDA0003861270920000051
step five: according to the effective value beta of the backward state metric obtained in the step three k (m) and the forward state metric valid value α obtained in step four k (m) obtaining a posterior probability log-likelihood ratio and extrinsic information;
step six: the windows sequentially slide backwards, the second step to the fifth step are repeated, and the backward state measurement beta of the (k + 1) th window is obtained k (m) pre-computed result, k-th window backward state metric β k (m) a result of the calculation of the effective value, a forward state metric α for the kth window k (m) a result of the computation of the effective values and a posterior probability log-likelihood ratio and extrinsic information of a kth window, wherein k =1,2, \8230;, N-1;
step seven: carrying out backward state metric effective value calculation on data containing tail bits in the last window in the second group of RAM; carrying out forward state metric effective value calculation on data containing tail bits in the last window in the third group of RAM; obtaining a posterior probability log-likelihood ratio containing tail bits and external information according to the obtained backward state metric effective value and forward state metric effective value;
step eight: and de-interleaving the posterior probability log-likelihood ratio, the extrinsic information, the posterior probability log-likelihood ratio containing tail bits and the extrinsic information, and negating the de-interleaved posterior probability log-likelihood ratio through hard decision to obtain final decoding data.
The second embodiment is as follows: the present embodiment is a further description of the first specific embodiment, and a difference between the present embodiment and the first specific embodiment is that the information to be decoded includes system information soft bits, check information soft bits, and prior information.
The third concrete implementation mode: this embodiment mode is a further description of the first embodiment mode, and the difference between this embodiment mode and the first embodiment mode is β in the second step k The precomputation of (m) is expressed as:
Figure BDA0003861270920000052
wherein, theta β Representing the set of all states that can jump to the time k-1 at the time k, gamma k (m', m) is the branch metric from time k-1 to time k;
Figure BDA0003861270920000053
Figure BDA0003861270920000061
wherein, y k,s For the systematic soft bits at time k, y k,p Checking the sequence soft bits for time k, L a (u k ) Is a priori information, u k For transmitting information, x k,s And x k,p Is u k Symbol after BPSK modulation, σ is conditional probability density, L c Is a constant.
x k Is u k Symbol after BPSK modulation, x k Is (x) k,s ，x k,p )。
The fourth concrete implementation mode: this embodiment mode is a further description of the first embodiment mode, and the difference between this embodiment mode and the first embodiment mode is the normalized β k (m) the pre-calculation results are expressed as:
β k (m)＝β k (m)-β k (0)
wherein, beta k (0) Is a backward state metric pre-calculated value for the m =0 state.
The fifth concrete implementation mode is as follows: this embodiment is a further description of the first embodiment, and the difference between this embodiment and the first embodiment is that the forward state metric α is k The effective value of (m) is expressed as:
Figure BDA0003861270920000062
wherein, theta α Representing the set of all states that can be transferred to the next instant, i.e. k instant, at instant k-1, alpha k-1 (m ') represents the forward state metric for some state m' at time k-1.
The sixth specific implementation mode is as follows: this embodiment mode is a further description of the first embodiment mode, and the difference between this embodiment mode and the first embodiment mode is that α is k (m) the normalized effective value results are expressed as:
α k (m)＝α k (m)-α k (0)
wherein alpha is k (0) Is the forward state metric value for the initial state at time k.
The seventh embodiment: this embodiment is a further description of the first embodiment, and is different from the first embodiment in that the posterior probability log-likelihood ratio is expressed as:
Figure BDA0003861270920000063
wherein, theta + Indicating that at a time corresponds to a transmission u k Pair (m', m) of state changes of the corresponding transmitter encoder register at time = 1; theta - Indicating that at a time corresponds to a transmission u k And =0, the state change pair of the corresponding encoder register at the transmitting end.
The specific implementation mode is eight: this embodiment mode is a further description of the first embodiment mode, and is different from the first embodiment mode in that the extrinsic information is expressed as:
L e (u k )＝L(u k )-L c y k,s -L a (u k )
wherein the content of the first and second substances,
Figure BDA0003861270920000071
L(u k ) Is a posterior probability log likelihood ratio.
The embodiment is as follows:
the method is realized on an FPGA, the model of an adopted FPGA chip is an XC7VX485T-2FFG1761C chip of Virtex-7 series of Xilinx company, the type of a development board is VC707, the development board is responsible for realizing the decoding function of a Turbo code decoder, and the working dominant frequency adopts 198MHz. FIG. 3 is a block diagram of a Turbo code decoder module.
The specific implementation steps are as follows:
a control module: and generating a control signal for controlling the operation of the whole Turbo decoder and controlling the state jump of the decoder. A Turbo decoder state diagram is shown in figure 4.
An interleaving and de-interleaving module: the storage interleaving module and the de-interleaving module are mainly used for storing soft information of a sequence to be decoded and interleaving and de-interleaving external information of the SISO decoder under the control of the controller, and when the number of iterations is reached, the de-interleaving module interleaves a second log-likelihood ratio output by the SISO decoder in the iteration.
SISO decoder input selection module: and the outputs of the interleaving module and the de-interleaving module are rectified and combined into one.
SISO decoder module: the multiplexing idea is adopted, two SISO decoders in the Turbo code decoder are combined into one, and one SISO decoder is used for completing all functions. Fig. 5 is a timing diagram of the operation of the SISO decoder. The operation of the SISO decoder is as follows:
step 1: data caching:
soft bits y of system information to be input to SISO decoder s ＝(y 1,s ,y 2,s ,y 3,s ,…,y N,s ) Checking the soft bit y of the information p ＝(y 1,p ,y 2,p ,y 3,p ,…,y N,p ) And a priori information L a And respectively storing the three input signals into three RAMs as one group, and copying two copies of each of the three input signals into the RAMs as the other two groups of RAMs.
And 2, step: a backward state metric beta pre-calculation module:
dividing information to be decoded in the first group of RAM into N windows, wherein the window length is W. The constraint length of the Turbo encoder is m at T 0 The starting time of the time interval is carried out from the end of the second window and onwards by beta k (m) precomputed with an initial value of ln (1/2) m )。
Step 2.1: beta is a beta k (m) precalculating:
the recursive formula of the backward state metric is as follows:
Figure BDA0003861270920000072
wherein, theta β Indicating that at time k can jump to time S of k-1 k-1 All S of = m k Set of = m states;
Figure BDA0003861270920000081
Figure BDA0003861270920000082
step 2.2: beta is a k (m) pre-calculation normalization:
Figure BDA0003861270920000083
and step 3: the backward state metric beta effective value calculation module:
and dividing the information to be decoded in the second group of RAM into N windows, wherein the window length is W. At T 1 The starting time of the time interval, from the end of the first window onwards k (m) calculating an effective value, wherein the initial value is beta obtained in the step 2 k (m) the last value pre-calculated.
And 4, step 4: forward state metric alpha k (m) an effective value calculation module:
and dividing the information to be decoded in the third group of RAM into N windows, wherein the window length is W. At T 2 Starting from the beginning of the first window and proceeding backward by a k (m) calculating an effective value, wherein the initial value is as follows:
Figure BDA0003861270920000084
step 4.1: alpha is alpha k (m) calculation of the effective value:
the forward state metric is calculated as:
Figure BDA0003861270920000085
wherein, theta α Indicating that at time k-1 the transition to the next time, i.e., time k, S is possible k Set of all states of = m.
Step 4.2: alpha is alpha k (m) effective value normalization:
Figure BDA0003861270920000086
and 5: obtaining the posterior probability log-likelihood ratio L and the extrinsic information L e ：
Backward state metric valid value beta according to the first window in step 3 and step 4 k (m) and forward state metric valid value α k And (m) obtaining the posterior probability log-likelihood ratio and the extrinsic information. The method for realizing the computation of the posterior probability log-likelihood ratio adopts a pipeline design, and the delay is reduced.
The posterior probability log-likelihood ratio is calculated by the following formula:
Figure BDA0003861270920000091
the formula for calculating the extrinsic information is as follows:
L e (u k )＝L(u k )-L c y k,s -L a (u k )
wherein the content of the first and second substances,
Figure BDA0003861270920000092
step 6: the calculation windows are sequentially backwardSliding, repeating the operations from step 2 to step 5 to obtain the backward state metric beta of the k +1 th window k (m) precomputed, k-th window backward state metric β k (m) a valid value, a forward state metric α for the kth window k (m) the effective value and the posterior probability log-likelihood ratio and extrinsic information of the kth window. Wherein k =1,2, \8230;, N-1.
And 7: the last window contains the computation of the tail bits:
backward state metric valid value beta is carried out on data containing tail bits in the last window in the second group of RAM k (m) calculating; carrying out forward state metric effective value alpha on data of which the last window in the third group of RAM contains tail bits k (m) calculating; backward state metric effective value beta based on data with tail bits in the last window k (m) and forward state metric valid value α k And (m) obtaining the posterior probability log-likelihood ratio and extrinsic information of the data of which the last window contains tail bits.
SISO decoder output selection module: the output of the data and control information for the SISO decoder is assigned to the interleaving and deinterleaving modules for use.
A hard decision module: and taking the input posterior probability log-likelihood ratio data as negation to obtain final decoding data.
Fig. 6 is a simulation comparison diagram of the SISO decoder algorithm, and it can be seen that the error rate of the algorithm adopted in the present application is significantly reduced compared with that of the sub-optimal algorithm MAX-Log-MAP algorithm in the conventional algorithm, and the error rate is hardly reduced and the performance is good compared with that of the optimal algorithm Log-MAP algorithm in the conventional algorithm.
The Turbo code decoder based on linear approximation and sliding window has the interleaving depth of 2048, the window length of 32, the window number of 64, the iteration times of 8, the quantization scheme of [7,3] and the operation clock of 198MHz. As can be seen from FIG. 7, the decoder designed by the present application has good performance, and the actual error rate curve is basically coincident with the theoretical error rate curve. The Turbo code decoding delay completed by the invention is small, the throughput can reach 20Mbps, and the high-speed decoding can be realized in engineering.
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.

Claims (8)

1. A Turbo code decoding method based on linear approximation and a sliding window is characterized by comprising the following steps:
the method comprises the following steps: respectively storing information to be decoded into three RAMs as a group of RAM, and then copying two parts to obtain three groups of RAM;
step two: dividing information to be decoded in a first group of RAM into N windows, setting the window length, wherein the constraint length of a Turbo encoder is m, carrying out forward precomputation of backward state measurement from the end of a second window, and normalizing the precomputation result, wherein the precomputation initial value of the backward state measurement is ln (1/2) m )；
Step three: dividing the information to be decoded in the second group of RAM into N windows, setting the window length, and calculating the effective value of the backward state metric from the end of the first window to the front, wherein the initial value of the effective value of the backward state metric is the last value of the precomputation result after normalization in the second step;
step four: dividing information to be decoded in a third group of RAM into N windows, setting window length, calculating an effective value of forward state metric from the beginning of a first window to the back, and normalizing the effective value result, wherein the initial value of the effective value of the forward state metric is as follows:
Figure FDA0003861270910000011
step five: obtaining posterior probability log-likelihood ratio and external information according to the effective value of the backward state metric obtained in the third step and the effective value of the forward state metric obtained in the fourth step;
step six: the windows sequentially slide backwards, and the second step to the fifth step are repeated to obtain a pre-calculation result of the backward state metric of the k +1 th window, a calculation result of the effective value of the backward state metric of the k-th window, a calculation result of the effective value of the forward state metric of the k-th window, and a posterior probability log-likelihood ratio and extrinsic information of the k-th window, wherein k =1,2, \ 8230; \8230;, N-1;
step seven: carrying out backward state metric effective value calculation on data containing tail bits in the last window in the second group of RAM; carrying out forward state metric effective value calculation on data containing tail bits in the last window in the third group of RAM; obtaining a posterior probability log-likelihood ratio containing tail bits and external information according to the obtained backward state metric effective value and forward state metric effective value;
step eight: and de-interleaving the posterior probability log-likelihood ratio, the extrinsic information, the posterior probability log-likelihood ratio containing tail bits and the extrinsic information, and obtaining final decoding data by inverting the de-interleaved posterior probability log-likelihood ratio through hard decision.
2. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, wherein 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 according to claim 1, wherein the pre-calculation of the backward state metric in the second step is represented as:
Figure FDA0003861270910000021
wherein, theta β To be able to jump to the set of all states at time k-1, γ k (m', m) is the branch metric from time k-1 to time k, β k (m) representing a backward state metric for the backward state metric;
Figure FDA0003861270910000022
wherein, y k,s For the systematic soft bits at time k, y k,p Checking the sequence soft bits for time k, L a (u k ) Is a priori information, u k For transmitting information, x k,s And x k,p Is u k Symbol after BPSK modulation, σ is conditional probability density, L c Is a constant.
4. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, wherein the pre-calculation result of the normalized backward state metric is represented as:
β k (m)＝β k (m)-β k (0)
wherein beta is k (0) Pre-calculated for backward state metrics for the m =0 state.
5. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, wherein the effective value of the forward state metric is represented as:
Figure FDA0003861270910000023
wherein, theta α Representing the set of all states that can be transferred to the next instant, i.e. k instant, at instant k-1, alpha k-1 (m ') represents the forward state metric for some state m' at time k-1.
6. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, wherein the result of the effective value after the forward state metric normalization is represented as:
α k (m)＝α k (m)-α k (0)
wherein alpha is k (0) Is the beginning of time kForward state metric values for the starting state.
7. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, wherein the posterior probability log-likelihood ratio is expressed as:
Figure FDA0003861270910000031
wherein, theta + To correspond in time to the emission u k The state change pair of the corresponding transmitting end encoder register at the time of =1, theta - To correspond at a time instant to a transmission u k And (= 0) corresponding pair of state changes of the encoder register at the transmitting end.
8. The Turbo code decoding method based on linear approximation and sliding window according to claim 1, wherein the extrinsic information is expressed as:
L e (u k )＝L(u k )-L c y k,s -L a (u k )
wherein the content of the first and second substances,
Figure FDA0003861270910000032
L(u k ) σ is the conditional probability density for the posterior probability log-likelihood ratio.
CN202211165730.8A 2022-09-23 2022-09-23 Turbo code decoding method based on linear approximation and sliding window Pending CN115529048A (en)

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