CN104779962B - The minimum segment vectors of Max Log MAP decoding algorithm complexities efficiently produce method - Google Patents

Abstract

Method is efficiently produced the invention discloses a kind of minimum segment vectors of Max Log MAP decoding algorithm complexities, is comprised the following steps：1) according to the minimal trellises M of Max Log MAP decoding algorithms_min, obtain the minimal trellises M_minState vector corresponding to upper each depth and information bit vector；2) according to the minimal trellises M of step 1)_minState vector and information bit vector obtain minimal trellises M corresponding to upper each depth_minIn each section of segment vectors；3) combination step 2) obtained minimal trellises M_minIn each section of segment vectors, obtain for the minimum segment vectors Vetsec of Max Log MAP decoding algorithm computation complexities.The present invention can efficiently generate the minimum segment vectors Vetsec of Max Log MAP decoding algorithm computation complexities.

Description

High Efficiency of Segmented Vectors with Minimum Computational Complexity in Max-Log-MAP Decoding Algorithm generation method

technical field

The invention belongs to the technical field of communication, and relates to a generation method of a segment vector Vetsec, in particular to an efficient generation method of a segment vector with the lowest computational complexity in a Max-Log-MAP decoding algorithm.

Background technique

In baseband transmission, channel coding (error correction code) often consumes a large part of the energy of communication equipment, such as in B.Bougard et al., "Energy-scalability enhancement of wireless local area network transceivers," in Proc.2004IEEE Workshop on In Signal Processing Advances in Wireless Communications, pp.449–453, Viterbi decoding accounts for 35% of the total power consumption of a typical 802.11 receiver. The problem of energy consumption restricts the miniaturization and mobility of communication equipment. How to increase the coding rate so that the generated codeword per unit length can transmit more information bits has great application value. For turbo code decoding, to increase the total code rate, puncturing is generally adopted, such as M.A.Kousa and A.H.Mugaibel, "Puncturing effects on turbo codes," IEEE Proc.Commun., vol.149, no.3, The method described in pp.132-138, June 2002. Another way to increase the total code rate is to use high code rate member codes. For the convolutional code C(n,k,v), this method has the effect of improving the pass rate per unit time and reducing the delay. , but with the increase of k, the complexity of decoding will increase exponentially with the increase of k.

The convolutional code C(n,k,v) can be represented by a semi-infinite trellis graph. This trellis graph is periodic, and its shortest period is called a trellis module. For a grid module with code rate k/n, it contains segments, at depth i there are states, each of which emits side, a _i (0≤i≤n-1) represents the number of bits of the output codeword represented by the edge connecting a certain state of depth i and a certain state of depth i+1, and the total constraint length is v, v _i and b _i are respectively called the state complexity and branch complexity of the grid module at depth i. For the Viterbi algorithm, the complexity of the grid graph module is defined as:

Conventional trellis is one of the most commonly used representations of the convolutional code trellis module, which contains There are 2 ^v initial states and 2 ^v final states, each initial state emanates 2 ^k edges connected to the final state, and each edge represents n bits (see Figure 1).

Another important representation of the convolutional code trellis module is the Minimal trellis, which contains segments, of which _k segments are informative (bi = 1), and the other nk segments are uninformative ( _bi = 0), the minimum grid graph contains 2 ^v initial states and 2 ^v termination states, each edge represents a 1-bit generated codeword (see Figure 2). The minimum trellis graph can be decoded with the lowest complexity method in Viterbi decoding, so the application of the minimum trellis graph can reduce the corresponding energy consumption and improve the utilization rate of hardware. But for other decoding methods, such as Max-Log-MAP decoding, the minimum grid graph does not guarantee that its complexity must be the lowest.

All the states at a certain depth i of the minimum grid graph are removed, and the states at depth i-1 are directly connected to the states at depth i+1, so that a new segment is obtained, which consists of the original The two segments on the minimal grid graph are merged, and the merged grid graph is only left with segments. Generally speaking, this operation of merging multiple segments into one segment is called a segmentation operation, and the grid graph obtained after segmentation is called a segmented grid graph (Sectionalizedtrellis). The segmentation operation is an operation applied on the minimum grid graph to obtain a new grid graph topology. It deletes the state at a certain depth i of the minimum grid graph, and combines the state at the depth i-1 with The states at depth i+1 are reconnected, resulting in a more compact structure. As the number of segments increases, the structure of the grid graph will become more and more compact. Finally, when all intermediate states are deleted, a traditional grid graph will be obtained. For the convolutional code C(n,k,v), there are 2 ^n-1 possible segmentation methods. In order to express various segmentation methods for the minimum grid graph, we define a binary segmentation Segment vector vetsec={vetsec _i }, i=1,...,n-1, when the state of the minimum grid graph at depth i is deleted and the state at depth i-1 is compared with the state at depth i+1 After being directly connected, vetsec _i =1, otherwise, vetsec _i =0 (see FIG. 3 ). We use respectively To represent the number of bits of the generated codeword represented by the edge of the segmented lattice graph from depth i to depth i+1 and the complexity of the state and branch at depth i, For example, Fig. 3 is the segmented grid graph of the minimum grid graph of C(5,3,5) shown in Fig. 2 under the condition of segmentation vector vetsec=(0010), and the minimum grid graph shown in Fig. 2 Segmentation operation is performed on the depth 3 of the trellis, that is, the state on the depth 3 is deleted, and the state on the depth 2 is directly connected to the state on the depth 4. The grid map after the segmentation operation has a total of segment, its edge complexity vector As for the complexity of the grid graph defined by formula (1), it can be obtained that the complexity of the traditional grid graph TC(M _conv )=427.5, the complexity of the minimum grid graph TC(M _min )=74.7, and in the Under the condition of segment vector vetsec=(0010), the complexity of the segmented grid graph is TC(M _sec )=96.

The theoretical complexity of trellis graphs defined in R.J.McEliece and W.Lin, "The trellis complexity of convolutional codes," IEEE Trans.Inf.Theory, vol.42, no.6, pp.1855-1864, Nov.1996 Among them, for Viterbi decoding, the complexity of the minimum trellis graph is smaller than that of the traditional trellis graph, and the use of the minimum trellis graph will not bring any performance loss. But for the Max-Log-MAP decoding algorithm, using the minimum lattice graph for decoding may not necessarily be able to obtain the lowest decoding complexity.

The computational complexity of the Max-Log-MAP decoding algorithm for segmented grid graphs can be expressed by the accumulation of the number of additions, multiplications, and comparisons in each segment. Here we use M, S, and C to represent additions, multiplications, and comparisons, respectively. operation. In Moritz G, Souza R, Pimentel C, et al. "Turbo Decoding Using the Sectionalized Minimal Trellis of the Constituent Code: Performance-Complexity Trade-Off". 2013. The Max-Log-MAP decoding algorithm is given for segmentation Computational complexity of γ _i , α _i , β _i , Λ _i in the i-th segment of the grid diagram and the calculation formula of the total computational complexity. Taking C(5,3,5) as an example, in the Max-Log-MAP decoding, select the appropriate grouping method, under the condition of losing a certain performance, the addition and comparison operations of the segmented method with the lowest computational complexity Compared with the traditional grid graph, the times are respectively reduced by 63.8% and 59.4%, and the complexity is greatly reduced. The existing technical solutions do not have a special method for how to find the segment vector with the lowest computational complexity in the Max-Log-MAP decoding algorithm of the C(n,k,v) code, only 2 ^n-1 kinds of It is obtained after performing traversal operations in a segmented manner.

Contents of the invention

The function of the present invention is to overcome the shortcoming that the above-mentioned existing method needs to perform traversal operation, and provides a method for efficiently generating segmented vectors with the lowest computational complexity in the Max-Log-MAP decoding algorithm, which can efficiently generate Max-Log-MAP decoding algorithm calculates the segment vector Vetsec with the lowest computational complexity.

In order to achieve the above object, the generation method of the segment vector Vetsec with the lowest computational complexity of the Max-Log-MAP decoding algorithm of the present invention comprises the following steps:

1) According to the minimum grid map M _min of the Max-Log-MAP decoding algorithm, obtain the state vector and information bit vector corresponding to each depth on the minimum grid map M _min ;

2) According to the state vector and the information bit vector corresponding to each depth on the minimum grid graph M _min of step 1), obtain the segmentation vector of each segment in the minimum grid graph M _min ;

3) Combining the segment vectors of each segment in the minimum grid graph M _min obtained in step 2), to obtain the segment vector Vetsec with the lowest computational complexity for the Max-Log-MAP decoding algorithm.

The concrete process of step 2) is:

Judging the size of state vector v _i and information bit vector b _i corresponding to depth i on the minimum grid graph M _min and state vector v i+1 corresponding to depth i+ ₁ , where i=0,1,.. ., n-2, n is the total number of depths on the minimum grid map M _min ;

When v _i =v _i+1 -1, then the segmentation vector vetsec i+1 of segment i+1 in the minimum grid graph M _min is vetsec _i+1 =1;

When v _i =v _i+1 +1, then the segmentation vector vetsec _i+1 of segment i+1 in the minimum grid graph M _min is 0;

When v _i =v _i+1 , and the corresponding information bit vector b _i on the depth i on the minimum grid graph M _min =1, then the segmentation vector vetsec _i of the i+1 segment in the minimum grid graph M _{min +1} = 0;

When v _i =v _i+1 , and the information bit vector b _i corresponding to the depth i on the minimum grid graph M _min =0, then the segmentation vector vetsec _i of the i+1 segment in the minimum grid graph M _{min +1} =1.

The present invention has the following beneficial effects:

In the Max-Log-MAP decoding algorithm described in the present invention, the efficient generation method of the segment vector with the lowest computational complexity only needs to be based on the state vector v _i corresponding to each depth on the minimum grid map M _min and The comparison and judgment of the information bit vector b _i is used to obtain the segment vector vetsec _i of each segment in the minimum grid graph M _min , and then the segment vectors of each segment can be combined, which is the same as the traditional generation of the segment vector Vetsec with the lowest complexity Compared with the need to perform traversal operations, the present invention improves the efficiency of finding the segmentation mode with the lowest computational complexity of the Max-Log-MAP decoding algorithm. In addition, theoretically speaking, for the application of time-varying generator matrix, under the condition of knowing its minimum grid graph, this method can quickly select a group of segment vectors with the lowest complexity online and in real time.

Description of drawings

Fig. 1 is the traditional grid diagram of C (5,3,5) sign indicating number;

Fig. 2 is the minimum grid figure of C (5,3,5) code;

Fig. 3 is the segmentation grid figure of C (5,3,5) code under the condition of segmentation vector vetsec=(0010);

Fig. 4 is the minimum grid diagram of C(7,4,4);

Fig. 5 is a diagram of the complexity calculation results of C(7,4,4) in various segmentation methods obtained by traversal calculation.

Detailed ways

The present invention is described in further detail below in conjunction with accompanying drawing:

The efficient generation method of the segment vector with the lowest computational complexity in the Max-Log-MAP decoding algorithm of the present invention comprises the following steps:

1) According to the minimum grid map M _min of the Max-Log-MAP decoding algorithm, obtain the state vector and information bit vector corresponding to each depth on the minimum grid map M _min ;

2) According to the state vector and the information bit vector corresponding to each depth on the minimum grid graph M _min of step 1), obtain the segmentation vector of each segment in the minimum grid graph M _min ;

3) Combining the segment vectors of each segment in the minimum grid graph M _min obtained in step 2), to obtain the segment vector Vetsec with the lowest computational complexity for the Max-Log-MAP decoding algorithm.

The concrete process of step 2) is:

Judging the size of the state vector v _i and the information bit vector b _i corresponding to the depth i on the minimum grid graph M _min and the state vector v _i +1 corresponding to the depth i+1, where i=0,1,... , n-2, n is the total number of depths on the minimum grid map M _min ;

When v _i =v _i+1 -1, then the segmentation vector vetsec i+1 of segment i+1 in the minimum grid graph M _min is vetsec _i+1 =1;

When v _i =v _i+1 +1, then the segmentation vector vetsec _i+1 of segment i+1 in the minimum grid graph M _min is 0;

When v _i =v _i+1 , and the information bit vector b _i corresponding to depth i on the minimum grid map M _min =1, then the segmentation vector _{vetsec i+ 1} = 0;

When v _i =v _i+1 , and the information bit vector b _i corresponding to depth i on the minimum grid graph M _min =0, then the segmentation vector vetsec _i+ of segment i+1 in the minimum grid graph M _{min 1} = 1.

For C(n,k,v), use the Max-Log-MAP algorithm to decode it in segments. If you need to select the segmentation method with the lowest complexity, you need to perform 2 ^n-1 segmentation methods Traverse and calculate the number of additions, multiplications and comparisons required for each segmentation method. However, the method used in the present invention only needs to know the state vector V={v _i } and the information bit vector B={b _i } of the minimum grid graph, and can obtain its complex A segmented method with the lowest degree, the total number of judgment operations is not more than 2*(n-1) times, while using traditional traversal operations requires operations, where and Respectively represent the computational complexity of γ, α, β, Λ and the total number of segments in the i+1th segment of the segmented grid graph under the jth segmentation method, which is the lowest for quickly finding out the computational complexity The amount of calculation saved by the Max-Log-MAP decoding algorithm is significant, and as n,k increases, the advantages of this method will become more obvious. In addition, for the application of time-varying generator matrix, under the condition of knowing its minimum grid map, this method can quickly select a group of segment vectors with the lowest complexity online and in real time, which greatly improves the efficiency of finding the Max-Log-MAP The decoding algorithm calculates the speed of the least complex segmented way. The determination of the segmented method with the lowest computational complexity is suitable for applications that are sensitive to computational complexity, and it is considerable in terms of reducing energy consumption of communication equipment and improving computational efficiency. The C(7,4, 4) Code as an example, use the above generation method:

v ₀ =v ₁ -1, so the segmentation vector vetsec ₁ of the first segment in the minimum grid graph M _min =1;

v ₁ =v ₂ -1, so the segmentation vector vetsec ₂ of the second segment in the minimum grid graph M _min =1;

v ₂ =v ₃ +1, so the segmentation vector vetsec ₃ of the third segment in the minimum grid graph M _min =0;

v ₃ =v ₄ , and the information bit vector b ₃ corresponding to depth 3 on the minimum grid graph M _min is 1, so the segmentation vector vetsec ₄ of the fourth segment in the minimum grid graph M _min is 0;

v ₄ =v ₅ +1, so the segmentation vector vetsec ₅ of the fifth segment in the minimum grid graph M _min is 0.

v ₅ =v ₆ -1, so the segmentation vector vetsec ₆ of the sixth segment in the minimum grid map M _min is 1;

The segmentation method vetsec=[110001] with the lowest computational complexity obtained according to the above generation method is the same as the segmentation method vetsec=[110001] with the lowest computational complexity obtained through the traversal operation shown in Figure 5, and its operation Reps save rate About 99.99%.

In Figure 5, S, M, and C represent the number of addition, multiplication, and comparison operations, and Tr, Ta, Tb, and Tv represent the calculation of α, β, and γ in the corresponding segmented Max-Log-MAP decoding algorithm. , the number of operands required by Λ.

Note: Figures 1 to 3 are extracted from Moritz G L, Demo Souza R, Pimentel C, et al. Turbodecoding using the sectionalized minimal trellis of the constituent code: performance-complexity trade-off[J]. Communications, IEEE Transactions on, 2013, 61(9):3600-3610. Figure 4 is excerpted from Benchimol I, Pimentel C, Demo Souza R. Sectionalization of the minimal trellis module for convolutional codes[C]//Telecommunications and Signal Processing (TSP), 2012 35th International Conference on. IEEE, 2012 :227-232.

Claims (1)

1. a kind of minimum segment vectors of Max-Log-MAP decoding algorithms complexity efficiently produce method, its feature It is, comprises the following steps：

1) according to the minimal trellises M of Max-Log-MAP decoding algorithms_min, obtain the minimal trellises M_minUpper each depth pair State vector and the information bit vector answered；

2) according to the minimal trellises M of step 1)_minState vector and information bit vector obtain minimum net corresponding to upper each depth Trrellis diagram M_minIn each section of segment vectors；

3) combination step 2) obtained minimal trellises M_minIn each section of segment vectors, obtain decoding for Max-Log-MAP and calculate The minimum segment vectors Vetsec of method computation complexity；

The detailed process of step 2) is：

Judge minimal trellises M_minState vector v corresponding on upper depth i_iAnd information bit vector b_iIt is corresponding with depth i+1 State vector v_i+1Size, wherein, i=0,1 ..., n-2, n be minimal trellises M_minThe sum of upper depth；

Work as v_i=v_i+1When -1, then minimal trellises M_minThe segment vectors vetsec of middle i+1 section_i+1=1；

Work as v_i=v_i+1When+1, then minimal trellises M_minThe segment vectors vetsec of middle i+1 section_i+1=0；

Work as v_i=v_i+1, and minimal trellises M_minInformation bit vector b corresponding on upper depth i_iWhen=1, then minimal trellises M_minThe segment vectors vetsec of middle i+1 section_i+1=0；

Work as v_i=v_i+1, and minimal trellises M_minInformation bit vector b corresponding on upper depth i_iWhen=0, then minimal trellises M_minThe segment vectors vetsec of middle i+1 section_i+1=1.