JP6771184B2 - Encoding device, coding method and program - Google Patents

Description

The present invention relates to coding devices , coding methods and programs .

One of the error correction codes is a convolutional code, and several techniques have been proposed in relation to this convolutional code.
For example, in Non-Patent Document 1, a coding device that performs a recursive convolutional Lattice Code (s) (RCLC) for a code alphabet having a lattice structure is arranged in parallel to provide a turbo signal code. A coding technique called (Turbo Signal Code (s)) has been proposed.

By using the technique described in Non-Patent Document 1, communication can be performed using quadrature amplitude modulation relatively easily. Moreover, if the technique described in Non-Patent Document 1 is used, iterative decoding similar to turbo decoding (s) can be performed on the decoding side, whereby decoding can be performed with relatively high accuracy. .. As described above, according to the technique described in Non-Patent Document 1, it is possible to perform communication using quadrature amplitude modulation and obtain a relatively high error correction capability, whereby excellent characteristics (relatively high transmission) can be obtained. Road capacity) can be obtained. On the other hand, in the technique described in Non-Patent Document 1, the coding operation is defined on a finite ring, but in order to obtain higher error correction capability, the four arithmetic operations are defined from the property of the set. Calculation on the body is preferable.

Patrick Mitran, and Hideki Ochiai, "Parallel Concatenated Convolutional Lattice Codes With Constrained States," IEEE Transactions On Communications, April 2015, Vol. 63, No. 4, p. 1081-1090

From the viewpoint of improving the amount of communication, it is desirable that the error correction capability is high and the transmission efficiency is good.
The present invention provides a coding device , a coding method, and a program capable of communication having high error correction capability and higher transmission efficiency.

According to the first aspect of the present invention, the coding apparatus includes a data acquisition unit that acquires data to be transmitted with a code alphabet number associated with a part of a finite number of elements of the integer power of a prime number. a first encoding unit that have a recursive structure, the to the transmission target data that the data acquisition unit has acquired, a first encoding is performed by convolution of the coefficients of elements of the finite field An encoding unit, an interleaver that interleaves the transmission target data acquired by the data acquisition unit, and a second coding unit having a recursive structure, the code for the transmission target data interleaved by the interleaver. The code word of the number of code alphabets obtained by multiplying the number of code alphabets of the output of the second coding unit, the first coding unit, and the number of code alphabets of the output of the second coding unit. The first coding unit and the second coding unit are provided with a transmission unit for transmitting data, the number of code alphabets of each output of the first coding unit and the second coding unit, and the first coding unit and the second code. The number of states of each memory of the conversion unit is the total number of elements of the finite body.

According to the second aspect of the present invention, in the coding method, the data acquisition unit acquires data to be transmitted with a code alphabet number associated with a part of a finite number of elements having an integer power of a prime number. That is, the first coding unit having a recursive structure encodes the transmission target data acquired by the data acquisition unit by a convolution operation using the element of the finite body as a coefficient. The interleaver interleaves the transmission target data, the second coding unit having a recursive structure performs the encoding on the interleaved transmission target data, and the transmission unit performs the first. The first, which includes transmitting with a code word having a code alphabet number obtained by multiplying the code alphabet number of the output of the coding unit of the above and the code alphabet number of the output of the second coding unit. The number of code alphabets of each output of the coding unit and the second coding unit, and the number of states of each memory of the first coding unit and the second coding unit are all described above. The total number of elements in a finite body.

According to a third aspect of the present invention, a program is a data acquisition unit that acquires data to be transmitted with a code alphabet number associated with a part of a finite number of elements of the number of elements of the integer power of a prime number. A first code having a recursive structure, which encodes the data to be transmitted acquired by the data acquisition unit by a convolution operation using the element of the finite body as a coefficient. The conversion unit, the interleaver that interleaves the transmission target data acquired by the data acquisition unit, and the second coding unit having a recursive structure, the encoding is performed on the transmission target data interleaved by the interleaver. The second coding unit and the code word of the code alphabet number obtained by multiplying the code alphabet number of the output of the first coding section by the code alphabet number of the output of the second coding section are transmitted. A program for operating as a transmission unit for performing the above, the number of code alphabets of each output of the first coding unit and the second coding unit, and the first coding unit and the first coding unit. The number of states of each memory of each of the coding portions of 2 is the total number of elements of the finite body.

According to the present invention, communication having high error correction capability and higher transmission efficiency is possible.

It is a schematic block diagram which shows the example of the functional structure of the coding apparatus which concerns on one Embodiment of this invention. It is explanatory drawing which shows the structural example of the coding part which concerns on the same embodiment. It is a schematic block diagram which shows the example of the functional structure of the coding apparatus which applied puncture ring in the same embodiment. It is explanatory drawing which shows the 1st specific example of the coding part which concerns on the same embodiment. It is a graph which shows the 1st example of the simulation result in the same embodiment. It is explanatory drawing which shows the 2nd specific example of the coding part which concerns on the same embodiment. It is a graph which shows the 2nd example of the simulation result in the same embodiment. It is explanatory drawing which shows the example of the puncture ring matrix in the same embodiment. It is a graph which shows the example of the simulation result including puncture ring in the same embodiment.

Hereinafter, embodiments of the present invention will be described, but the following embodiments do not limit the inventions claimed. Also, not all combinations of features described in the embodiments are essential to the means of solving the invention.
FIG. 1 is a schematic block diagram showing an example of a functional configuration of a coding device according to an embodiment of the present invention. As shown in FIG. 1, the coding device 100 includes a data acquisition unit 110, an interleaver 120, two coding units 130, and a transmission unit 140.

The coding device 100 acquires, encodes, and encodes the transmission target data having the code alphabet number m, and transmits the signal with the symbol number ^aq . Here, m and q are both positive integers, a is a prime number, and m <a ^q .
The data acquisition unit 110 acquires data to be transmitted. In particular, the data acquisition unit 110 acquires transmission target data having a code alphabet number m. Then, the data acquiring unit 110, the m code alphabetic transmission target data, finite number of elements a ^q (Galois field) is a one-to-one mapping to the m elements of the elements of GF (a ^q). By this mapping, the data acquisition unit 110 acquires the transmission target data in which m elements of the GF ( ^aq ) elements are coded alphabets. Then, the data acquisition unit 110 outputs the transmission target data in which m elements of the GF ( ^aq ) elements are code alphabets to the coding unit 130 and the interleaver 120.
In this way, the data acquisition unit 110 acquires the transmission target data having the code alphabet number m associated with a part of the elements of the finite field GF ( ^aq ).

Here, GF (a ^q ) is expressed as {0, 1, α, α ² , ..., α ^x-2 } with α as the primitive element. However, x = 2 ^q . The data acquisition unit 110 converts m alphabets of the data to be transmitted into m elements from 0 to α ^m-2 such as {0, 1, α, α ² , ..., α ^m-2 }. However, it is not limited to this. Data acquisition unit 110, elements of one-to-one mapping of m alphabet of the transmission target ^{data, {0,1, α, α 2} , ···, α x-2} in any of the m elements of the Good.
In the following, a case where the coding unit 130 performs coding using a finite field GF (2 ^q ) having 2 ^q elements will be described as an example. However, the finite field used by the coding unit 130 for coding is not limited to GF (2 ^q ), and may be GF (a ^q ) with a as a prime number as described above.

The interleaver 120 interleaves the transmission target data mapped to the element of the finite field GF (2 ^q ) by the data acquisition unit 110 in symbol units. That is, the interleaver 120 sorts the transmission target data mapped to the elements of the finite field GF (2 ^q ) by the data acquisition unit 110 in symbol units. The interleaving performed by the interleaver 120 is for enabling iterative decoding as well as the interleaving in the turbo code. As the method of interleaving performed by the interleaver 120, a known method such as S-random interleaving can be used.

The coding unit 130 has a recursive structure and performs coding by a convolution operation using an element of the finite field GF (2 ^q ) as a coefficient. The code alphabet of the input to the coding unit 130 is a part of the above finite field GF (2 ^q ), whereas the code alphabet of the output from the coding unit 130 is the whole of the finite field GF (2 ^q ). It is an element. Further, any element of the finite field GF (2 ^q ) is stored in the memory used by the coding unit 130 for the convolution operation. Therefore, the number of states of each memory used by the coding unit 130 for the convolution operation is the total number of elements of the finite field GF (2 ^q ).

In the following, when distinguishing between the two coding units 130, reference numerals 130-1 and 130-2 are used as shown in FIG. The coding unit 130-1 encodes the transmission target data (the transmission target data that is not interleaved and is represented by the element of the finite field GF (2 ^q )) acquired by the data acquisition unit 110. I do. On the other hand, the coding unit 130-2 encodes the transmission target data interleaved by the interleaver 120. The coding unit 130-1 corresponds to the example of the first coding unit. The coding unit 130-2 corresponds to the example of the second coding unit.

The transmission unit 140 uses a code word having a code alphabet number squared to the code alphabet number of the output of one coding unit 130 for the output from the coding unit 130-1 and the output from the coding unit 130-2. Send. That is, the transmission unit 140 transmits with the code word of the code alphabet number obtained by multiplying the code alphabet number of the output of the coding unit 130-1 by the code alphabet number of the output of the coding unit 130-2.
For example, the transmission unit 140, the output of the code alphabet number ^{2 q} from the encoding unit 130-1, an output of the code alphabet number ^{2 q} from the encoding unit ^130-1, and transmits at 2 2q -QAM ..

FIG. 2 is an explanatory diagram showing a configuration example of the coding unit 130. In the example of FIG. 2, the coding unit 130 includes a shift register 131, a recursive convolution calculation unit 132a, and a non-recursive convolution calculation unit 132b. The combination of the recursive convolution calculation unit 132a and the non-recursive convolution calculation unit 132b is referred to as a convolution calculation unit 132.
In the example of FIG. 2, the recursive convolution calculation unit 132a includes P multipliers M1 _{1 to} M1 _P and two adders A1 _{1 to} A1 ₂ . The non-recursive convolution calculation unit 132b includes P + 1 multipliers M2 _{0 to} M2 _P and one adder A2. The multiplication performed by each of the multipliers M1 _{1 to} M1 _P and M2 _{0 to} M2 _P , and the addition performed by the adders A1 _{1 to} A1 ₂ and A22 are all defined on the finite field GF (2 ^q ). .. Therefore, all the operations performed by the convolution operation unit 132 are closed by the finite field GF (2 ^q ).

Further, the shift register 131 includes P memories R1 _{1 to} R1 _P. Therefore, the constraint length K of the convolution operation performed by the coding unit 130 is K = P + 1. Memory _R1 1 _{~R1 P} is a time series of values that the adder A1 ₂ was calculated stores P times. The memory R1 _p stores the value calculated by the adder A1 ₂ p times before. Here, p is a positive integer of 1 ≦ p ≦ P. In FIG. 2, the value of the adder A1 ₂ was calculated before p times denoted as x _i-p.

The multiplier M1 _p (p is a positive integer of 1 ≦ p ≦ P) multiplies the value (x _i−p ) of the memory R1 _{p by} the coefficient h _p . Further, the multiplier M2 ₀ multiplies the output of the adder A1 _{2 by} a coefficient f ₀ . The multiplier M2 _p (p is a positive integer of 1 ≦ p ≦ P) multiplies the value (x _i−p ) of the memory R1 _{p by} the coefficient f _p . The coefficients h _{1 to} h _P and f _{0 to} f _P all take the value of any element of the finite field GF (2 ^q ).
With this configuration, the recursive convolution operation section 132a adds the input symbol u _i the computation result by performing the convolution operation. Further, non-recursive convolution computation unit 132b outputs the operation result by performing the convolution operation as an output symbol c _i.

While the possible values of the input symbol u _i to the encoding unit 130 is m elements of the finite field GF (2 ^q), the output symbol c _i of possible values is finite GF (2 ^q The values of the coefficients h _{1 to} h _P and f _{0 to} f _P are determined so as to be all the elements of). Therefore, the value of at least _one of the coefficients h _{1 to} h _P is set to other than 0. Further, at least one of the coefficients f _{0 to} f _P is set to a value other than 0.

Thus, while the possible values of the input symbol u _i to the encoding unit 130 is m elements of the finite field GF (2 ^q), finite field can take the value of the output symbol c _i All elements of GF (2 ^q ). As a result, redundancy is added to one input symbol even if the output is one symbol, and a coding gain can be obtained.

Here, if the transmission rate r is defined as in the equation (1), the convolutional code by the coding unit 130 is the transmission rate 1 (r = 1).

Further, assuming that the number of elements of the input symbol is m = ^2p , the number of transmission bits per output symbol is r × p bits. Further, the number of states of the trellis required for decoding the coding by the coding unit 130 is (2 ^q ) ^P = 2 ^{q × P.}

Further, in the configuration in which the coding units 130 shown in FIG. 1 are connected in parallel, any of the coding units 130-1 and 130-2 can obtain the coding gain as described above. Therefore, in the parallel connection coding in the entire parallel connection configuration shown in FIG. 1, it is not necessary to transmit the organizational elements (organization symbols) as in the case of the general turbo code. The overall rate of the two coding units 130 after being connected in parallel is r = 1/2. While the transmission rate in the case of a general turbo code is 1/3, the transmission rate is improved in the coding device 100.

It should be noted that puncturing may be further applied to the configuration of the coding device 100 shown in FIG. The puncturing referred to here is a process of periodically omitting (deleting) the output code word symbol.
FIG. 3 is a schematic block diagram showing an example of a functional configuration of a coding device to which puncturing is applied. As shown in FIG. 3, the coding device 200 includes a data acquisition unit 110, an interleaver 120, two coding units 130, a deinterleaver 250, a puncture processing unit 260, and a transmission unit 140. Of the parts of FIG. 3, parts having the same functions corresponding to the parts of FIG. 1 are designated by the same reference numerals (110, 120, 130, 130-1, 130-2, 140) and the description thereof will be omitted. To do.
In the configuration of the coding device 200 shown in FIG. 3, in addition to the coding device 100 configuration shown in FIG. 1, a deinterleaver 250 and a puncture processing unit 260 are further provided.

The deinterleaver 250 performs a deinterleave on the interleave performed by the interleaver 120. That is, the deinterleaver 250 performs the reverse conversion of the interleave performed by the interleaver 120.
The puncturing processing unit 260 punctures one or both of the output from the coding unit 130-1 and the output from the deinterleaver 250. That is, the puncturing processing unit 260 periodically omits one or both of the code word symbol output from the coding unit 130-1 and the code word symbol output from the deinterleaver 250. Do.

It should be noted that it is not essential for the transmitting side to perform deinterleaving before puncturing as in the coding device 200 of FIG. 3, and the receiving side may perform deinterleaving. On the other hand, by performing deinterleaving before puncturing on the transmitting side, the omission of the code word symbol becomes periodic in the state after deinterleaving. As a result, the decrease in the decoding success rate on the receiving side due to the deinterleave can be small.
The puncturing performed by the puncturing processing unit 260 is represented by the puncturing matrix exemplified in the equation (2).

Each row of the puncturing matrix corresponds to one coding unit. In the example of the equation (2), the upper row of the puncturing matrix P corresponds to the coding unit 130-1, and the lower row corresponds to the coding unit 130-2.
Further, the element "0" of the puncturing matrix indicates that the code word symbol is omitted, and the element "1" indicates that the code word symbol is not omitted. In the case of the example of the equation (2), since the elements in the upper row are "1" and "1", the puncture processing unit 260 transmits all the code word symbols output by the coding unit 130-1. Output to 140. On the other hand, since the elements in the lower row are "1" and "0", the coding device 200 outputs every other code word symbol output by the coding unit 130-2 to the transmitting unit 140. .. In this case, puncturing improves the transmission rate from r = 1/2 to r = 2/3.
The number of columns in the puncturing matrix is called the puncturing period and is represented by T. In the case of the puncturing matrix shown in equation (2), the puncturing period is T = 2.

Next, the simulation result of coding will be described. In the simulation, the first m symbol {0,1, ... α ^m-2 } among the elements of the finite field GF (2 ^q ) is used as the input code alphabet. Here, m = 2 ^p (p is a positive integer). Therefore, each input symbol has p-bit information.
As information to be input to the coding device (coding device 100 or 200), three pieces of information having symbol lengths 1024, 2048, and 4096 are used, and simulation is performed for each of them. Since the coding apparatus performs coding at a rate r = 1/2, the output symbol lengths are 2048, 4096, and 8192.

The output symbol is a signal point in Euclidean space consisting of 2 ^q points. In the following, for the sake of simplicity, one-dimensional PAM (Pulse Amplitude Modulation) is used as the transmission method, and therefore evaluation is performed based on the frequency utilization efficiency (information rate) per dimension. However, the transmission method used by the coding apparatus is not limited to the one-dimensional PAM, and various transmission methods can be used. For example, the frequency efficiency can be doubled by assigning PAM to a two-dimensional plane (complex plane) (that is, using QAM (Quadrature Amplitude Modulation) as a transmission method).

Further, for each of the output symbol lengths of 2048 and 4096, S random interleavers having spread values of 22, 32 and 45 are used as interleavers. Further, the coding unit 130 has a memory number of 1 (P = 1, therefore, a constraint length of 2).
The BCJR algorithm using the trellis structure of the code is used for decoding in the same manner as the decoding of a normal binary turbo code. However, the calculation of the metric needs to be performed by the finite field GF (2 ^q ). Since P = 1 here, the number of states of the trellis used for decoding is 2 ^q .
As for the coefficients used for the multiplier of the coding unit 130, simulation was performed for all possible combinations of coefficients to search for all solutions, and the combination of coefficients having the smallest error rate was used.

The trellis termination process is performed by repeatedly transmitting the final state four times. Therefore, in a configuration in which the coding units are connected in parallel, termination processing is performed by additionally transmitting a total of 8 symbols. By this termination processing, the block lengths are 2056, 4054, and 8200.
Hereinafter, the simulation described with reference to FIGS. 4 and 5 and the simulation described with reference to FIGS. 6 and 7 do not perform puncturing. On the other hand, in the simulation described with reference to FIGS. 8 and 9, puncturing is performed.

FIG. 4 is an explanatory diagram showing a first specific example of the coding unit 130. The coding unit 130 shown in FIG. 4 is a specific example of the coding unit 130 shown in FIG. 2, and the parts corresponding to the parts of FIG. 2 among the parts of FIG. 4 have the same reference numerals (130, 131, 132, _{132a, 132b, R1 1, M1} 1, M2 0, M2 1, are denoted by A1 2, A2).

In the example of FIG. 4, in the recursive convolution calculation unit 132a, the multiplier M1 ₁ multiplies the value of the memory R1 _{1 by} the coefficient α ² . The adder A1 ₂ adds an output from the multiplier M1 ₁ to the input symbol _{u i.} The memory R1 ₁ stores the previous value of the output from the adder A1 ₂ .
In the non-recursive convolution calculation unit 132b, the multiplier M2 ₀ multiplies the output from the adder A1 ₂ by the coefficient α ⁰ (= 1). The multiplier M2 ₁ multiplies the value of the memory R1 _{1 by} the coefficient α ³ . The adder A2 adds the output of the multiplier M2 _{0 and} the output of the multiplier M2 ₁ . The output of the multiplier M2 ₁ is an output _{c i} of the encoder 130.

In the example of FIG. 4, the input is a symbol of m = 4 (p = 2 bits), and the code alphabet of the input is {0,1, α, α ² }. The coding unit 130 converts this input symbol into an output symbol (q = 3) on the GF (8). Code alphabet outputs are ^{{0,1, α, α 2,} ···, α 6}. The coding device 100 maps the code alphabet of the output to 8-PAM modulation. The number of states of each trellis is eight.
The coefficients shown in FIG. 4 are the coefficients showing the best results at the constraint length 2 when the primitive polynomial g (x) = x ³ + x + 1.
In the example of FIG. 4, the frequency utilization efficiency per dimension is p / 2 = 1 (bit / dimension) excluding the terminating symbol.

FIG. 5 is a graph showing a first example of the simulation result. The horizontal axis of FIG. 5 shows the signal-to-noise ratio (SNR) [unit: decibel (dB)]. The vertical axis indicates the frame error rate (FER). FIG. 5 shows the relationship between the signal-to-noise ratio and the frame error rate in the simulation of communication using the coding unit 130 having the configuration shown in FIG.
Line L11 shows the channel capacity under signal point constraint when the frequency utilization efficiency is 1 bit / dimension and the 8-PAM signal point arrangement is used. Line L21 shows the frame error rate at the block length 2048. Line L22 shows the frame error rate at block length 4096. Line L23 shows the frame error rate at the block length 8192.

As shown by line L23, a frame error rate of ^10-2 can be achieved at a block length of 8200 with a signal-to-noise ratio 0.75 dB away from the limit (line L11). Also, as with normal turbo codes, an error floor is observed, which is below the frame error rate of ^10-2 .
Further, as shown by the lines L21 and L22, a good frame error rate is obtained even when the input symbol length is relatively short.

FIG. 6 is an explanatory diagram showing a second specific example of the coding unit 130. The coding unit 130 shown in FIG. 6 has the same configuration as that in the case of FIG. 4, and the value of the coefficient used by the multiplier is different. In the configuration of FIG. 6, the coefficients of the multipliers M1 ₁ , M2 ₀ , and M2 ₁ are set to α ² , α ⁹ , and α ⁰ (= 1), respectively.
In the example of FIG. 6, the input is a symbol of m = 8 (p = 3 bits), the code alphabet input is ^{{0,1, α, α 2,} ···, α 6}. The coding unit 130 converts this input symbol into an output symbol (q = 4) on the GF (16). The code alphabet of the output is {0, 1, α, α ² , ..., α ¹⁴ }. The coding device 100 maps the code alphabet of the output to 16-PAM modulation.
The coefficients shown in FIG. 6 are the coefficients showing the best results at the constraint length 2 when the primitive polynomial g (x) = x ⁴ + x + 1.
In the example of FIG. 6, the frequency utilization efficiency per dimension is p / 2 = 1.5 (bit / dimension) excluding the terminating symbol.

FIG. 7 is a graph showing a second example of the simulation result. The horizontal axis of FIG. 7 indicates the signal-to-noise ratio [unit: dB]. The vertical axis shows the frame error rate. FIG. 7 shows the relationship between the signal-to-noise ratio and the frame error rate in the simulation of communication using the coding unit 130 having the configuration shown in FIG.
Line L31 shows the channel capacity under signal point constraint when the frequency utilization efficiency is 1.5 bit / dimension and the 16-PAM signal point arrangement is used. Line L41 shows the frame error rate at the block length 2048. Line L42 shows the frame error rate at the block length of 4096. Line L43 shows the frame error rate at the block length 8192.

As shown by line L43, a frame error rate of ^10-2 can be achieved at a block length of 8200 with a signal-to-noise ratio 0.9 decibels away from the limit (line L31). Also, as with normal turbo codes, an error floor is observed, which is below the frame error rate of ^10-2 .
Further, as shown by lines L41 and L42, a good frame error rate is obtained even when the input symbol length is relatively short.

FIG. 8 is an explanatory diagram showing an example of a puncturing matrix. In the simulation described with reference to FIGS. 8 and 9, a simulation including puncturing was performed by the coding apparatus 200 using the coding unit 130 having the configuration shown in FIG. Simulations were performed for each of the two types of puncture ring shown in FIG.
In the puncturing (transmission rate 2/3, frequency utilization efficiency 1.3 bit / dimension) shown in line L51 of FIG. 8, the number of transmission symbols is 3072. In the puncture ring (transmission rate 4/5, frequency utilization efficiency 1.6 bit / dimension) shown in line L52, the number of transmission symbols is 2560.

FIG. 9 is a graph showing an example of simulation results including puncturing. The horizontal axis of FIG. 9 indicates the signal-to-noise ratio [unit: dB]. The vertical axis shows the frame error rate.
Line L61 shows the channel capacity under signal point constraint when puncturing is not performed (transmission rate 1, frequency utilization efficiency 1 bit / dimension, 8-PAM). The number of output symbols in this case is 4096.
Line L62 shows the channel capacity under signal point constraint in the case of puncturing of line L51 (transmission rate 2/3, frequency utilization efficiency 1.3 bit / dimension, 8-PAM).
Line L63 shows the channel capacity under signal point constraint in the case of puncturing of line L52 (transmission rate 4/5, frequency utilization efficiency 1.6 bit / dimension, 8-PAM).

Line L71 shows the frame error rate when puncturing is not performed. Line L72 shows the frame error rate when puncturing line L51. Line L73 shows the frame error rate when puncturing line L52.
Good results have been obtained in both cases, and the transmission rate can be easily changed by applying puncturing without degrading the error rate characteristics. In any case, it has a limit (line L61, L62, L63) from the frame error rate ^10-2 within one decibels.
In this way, good results were also obtained when puncturing was performed.

As described above, the data acquisition unit 110 acquires the transmission target data having the number of code alphabets associated with a part of the elements of the finite field. The coding unit 130 has a recursive structure and performs coding by a convolution operation using the element of the finite field as a coefficient. Then, the number of code alphabets of the output of the coding unit 130 and the number of states of each memory of the coding unit 130 are both the total number of elements of the finite field.
As a result, in the coding performed by the coding unit 130, redundancy is added to one input symbol even if the output is one symbol, and a coding gain can be obtained. Due to this coding gain, it is not necessary to transmit a systematic element when the coding unit 130 is used to configure the coding for iterative decoding. It has high error correction capability in that it can be repeatedly decoded, and has high transmission efficiency in that it does not require transmission of organizational elements.
As described above, according to the coding devices 100 and 200, it is possible to perform communication having high error correction capability and higher transmission efficiency.

Here, in the previous application (Japanese Patent Application No. 2016-130872), the applicant performs encoding using a convolution operation that takes a binary symbol as an input and outputs an L element symbol that is two or more elements. An encoding unit, a conversion unit that converts the series of L-source symbols output by the first coding unit into a series of L-th-order square matrix elements, and an interleaver that interleaves the series of L-th-order square matrix elements. , A second coding unit that performs a convolution operation that outputs the elements of the L-th order square matrix with the elements interleaved by the interleaver as input, and feeds back the output of the convolution operation to the input side of the convolution operation. And proposed a coding device equipped with.
In the coding apparatus according to the previous application, there is room for further improvement in transmission efficiency in that coding is performed by inputting a binary symbol.
On the other hand, in the coding apparatus according to the present embodiment, excellent transmission efficiency can be obtained by using non-binary symbols. Further, in the coding apparatus according to the present embodiment, since the coding unit has a feedback structure, it is possible to obtain an effect that the coding unit has a high error correction capability in a configuration in which the coding units are connected in parallel.

Further, a binary turbo code or LDPC code is a strong error correction code that approaches the Shannon limit when a sufficiently long code length is sufficiently long, but an error rate characteristic in the case of a medium to short code length. Is not good. Further, when a modulation method consisting of multi-valued signal points is used to improve frequency utilization efficiency, the error rate characteristic largely depends on how the binary code is mapped to multi-valued modulation.
On the other hand, in the non-binary symbol (multidimensional symbol) used by the coding apparatus according to the present embodiment, only when the code length (input symbol length) is long as described with reference to FIGS. 5 and 7. It is possible to obtain the effect of having excellent error correction ability even when the error is relatively short.

Further, the coding unit 130-1 encodes the transmission target data acquired by the data acquisition unit 110. The interleaver 120 interleaves the transmission target data acquired by the data acquisition unit 110. The coding unit 130-2 encodes the transmission target data interleaved by the interleaver 120.
As a result, iterative decoding on the decoding side can be performed, and transmission of systematic elements is not required for iterative decoding. It has high error correction capability in that it can be repeatedly decoded, and has high transmission efficiency in that it does not require transmission of organizational elements.
As described above, according to the coding devices 100 and 200, it is possible to perform communication having high error correction capability and higher transmission efficiency.

Further, the transmission unit 140 transmits with a code word having a code alphabet number obtained by multiplying the code alphabet number of the output of the coding unit 130-1 by the code alphabet number of the output of the coding unit 130-2. Be prepared.
As a result, according to the coding devices 100 and 200, the outputs from the coding units 130-1 and 130-2 can be relatively easily associated with the transmission symbol.

A program for realizing all or part of the functions of the arithmetic and control performed by the encoding device 100 or 200 is recorded on a computer-readable recording medium, and the program recorded on the recording medium is stored in the computer system. The processing of each part may be performed by reading and executing. The term "computer system" as used herein includes hardware such as an OS and peripheral devices.
In addition, the "computer system" includes a homepage providing environment (or display environment) if a WWW system is used.
Further, the "computer-readable recording medium" refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, or a CD-ROM, or a storage device such as a hard disk built in a computer system. Further, a "computer-readable recording medium" is a communication line for transmitting a program via a network such as the Internet or a communication line such as a telephone line, and dynamically holds the program for a short period of time. In that case, it also includes the one that holds the program for a certain period of time, such as the volatile memory inside the computer system that becomes the server or client. Further, the above-mentioned program may be a program for realizing a part of the above-mentioned functions, and may be a program for realizing the above-mentioned functions in combination with a program already recorded in the computer system.

Although the embodiments of the present invention have been described in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and design changes and the like within a range not deviating from the gist of the present invention are also included.

100, 200 Encoding device 110 Data acquisition unit 120 Interleaver 130 Coding unit 140 Transmission unit 250 Deinterleaver 260 Puncturing processing unit

Claims (3)

A data acquisition unit that acquires data to be transmitted with a code alphabet number associated with a part of a finite field element having a prime number integer power.
A first encoding unit that have a recursive structure, the to the transmission target data that the data acquisition unit has acquired, a first encoding is performed by convolution of the coefficients of elements of the finite field Encoding part and
An interleaver that interleaves the transmission target data acquired by the data acquisition unit, and
A second coding unit having a recursive structure, the second coding unit that performs the coding on the transmission target data interleaved by the interleaver, and
A transmission unit that transmits with a code word having a code alphabet number obtained by multiplying the code alphabet number of the output of the first coding unit by the code alphabet number of the output of the second coding unit.
With
The number of code alphabets of each output of the first coding unit and the second coding unit, and the number of states of each memory of the first coding unit and the second coding unit are , All of which are the total number of elements of the finite field. The data acquisition unit acquires the data to be transmitted with the number of code alphabets associated with a part of the finite field elements of the prime number to the integer power.
The first coding unit having a recursive structure encodes the transmission target data acquired by the data acquisition unit by a convolution operation using the element of the finite field as a coefficient.
When the interleaver interleaves the data to be transmitted,
A second coding unit having a recursive structure performs the coding on the interleaved data to be transmitted.
The transmission unit transmits with a code word having a code alphabet number obtained by multiplying the code alphabet number of the output of the first coding unit by the code alphabet number of the output of the second coding unit.
Including
The number of code alphabets of each output of the first coding unit and the second coding unit, and the number of states of each memory of the first coding unit and the second coding unit are , All of which are the total number of elements of the finite field. Computer,
A data acquisition unit that acquires data to be transmitted with a code alphabet number associated with a part of a finite field element having a prime number integer power.
A first coding unit having a recursive structure, which encodes the data to be transmitted acquired by the data acquisition unit by a convolution operation using the element of the finite field as a coefficient. Kabu,
An interleaver that interleaves the transmission target data acquired by the data acquisition unit,
A second coding unit having a recursive structure, the second coding unit that performs the coding on the transmission target data interleaved by the interleaver, and
A transmission unit that transmits with a code word having a code alphabet number obtained by multiplying the code alphabet number of the output of the first coding unit by the code alphabet number of the output of the second coding unit.
It is a program to operate as
The number of code alphabets of each output of the first coding unit and the second coding unit, and the number of states of each memory of the first coding unit and the second coding unit are , All of which are the total number of elements of the finite field.

Images