JP4634423B2 - Information transmission / reception method, encoding apparatus, and decoding apparatus - Google Patents

Description

  The present invention relates to an information transmission / reception method, an encoding device, and a decoding device.

  Conventionally, in information transmission via a noisy communication channel, a code word is generated by adding a mechanism for correcting an error that occurs in the communication channel to the information, input to the communication channel, and the code output from the communication channel Channel decoding that corrects information errors caused by noise and realizes highly reliable information transmission is performed by decoding a word using an added mechanism. That is, in channel coding in a channel having noise, a code word in which “bit for error correction” is added to “information bit” by an encoder is generated, and the code word output from the channel is The decoder performs error correction processing by decoding using “bits for error correction”.

  Here, there are the following three problems in channel coding in a channel having noise.

  The first problem is “to be applied to a communication channel having general noise that is not necessarily additive noise, and to arbitrarily reduce decoding errors”. Here, the communication path having additive noise is, for example, the probability that “0” is erroneously output as “1” when information composed of “0” and “1” is output from the communication path. , And a channel that is modeled like a binary symmetric channel that has a fixed probability of being erroneously output as "0" and has general noise The communication path is a communication path in which the probability that “0” is erroneously output as “1” and the probability that “1” is erroneously output as “0” vary for each information transmission. That is, the first problem is to achieve channel coding that enables encoding and decoding of information that can arbitrarily reduce decoding errors even in a channel having such general noise. is there.

  The second problem is “being able to encode at a transmission rate (encoding rate) close to the channel capacity”. Here, the channel capacity is the maximum amount of information that can be transmitted without error on the channel. The transmission rate (encoding rate) is the ratio of the “number of bits after error correction encoding” to the “number of information bits”. For example, the transmission rate (encoding rate) is “8/9”. , 8 bits of “information bits” and 1 bit of “bits for error correction” are added to generate a 9-bit code word. That is, the second problem is to achieve channel coding that enables coding of information to which “bits for error correction” are added, close to the limit of the maximum amount of information that the channel can transmit without error. That is.

  The third problem is “to enable efficient encoding and decoding in real time”. Specifically, the calculation order of the encoder and decoder in information transmission can be reduced by making the order of polynomials used when encoding information with linear codes fall within the order of the first power to the third power. Thus, it is to achieve channel coding that makes it possible to shorten the time required for information transmission.

  There are many communication path codes that partially solve these three problems, but typical ones include the following.

  As a channel code that solves the first problem and the second problem, a fixed type code (universal code) constituted by random coding is known (see Non-Patent Document 1). A Reed-Solomon code (Read-Solomon Coding) that is a block code is known as a channel code that solves the problem and the third problem (see Non-Patent Document 2).

  The channel code that solves the second and third problems is a block code similar to the Reed-Solomon code, and a low-density parity check that can be decoded by an efficient optimization algorithm such as the sum-product method. A code (LDPC code, LDPC: Low Density Parity Check) is known (see Non-Patent Document 3 and Non-Patent Document 4). Here, the LDPC code is a linear block code defined by a parity check matrix (low density parity check matrix: LDPC matrix) that is a very sparse matrix, and encodes not only a channel code but also an information source. It is also known as a useful technique in information source coding compressed by the above (see Non-Patent Document 5).

  Moreover, it is considered from a theoretical viewpoint that there is a possibility that the first problem may be solved by combining a quantization method with an LDPC code (see Non-Patent Document 6).

  Further, a turbo code that is a convolutional code is known as a channel code having characteristics similar to those of an LDPC code (see Non-Patent Document 7).

Tomohiko Uematsu, "Contemporary Shannon Theory-Information Theory by Type", Baifukan, July 1998, p64-77 Shigeichi Hirasawa, Toshihisa Nishijima, “Introduction to Code Theory”, Baifukan, November 1999, p101-107 Wadayama Tadashi, "Low-density parity check code and its decoding method", Trikeps, June 2002, p23-42, p65-99. D. J. C. MacKay, “Good error-correcting codes based on very separate matrices.”, IEEE Transactions on Information Theory, Vol. IT-45, No. 2, pp.399-431, 1999 S. Miyake and J. Muramatsu, “Construction of a lossy source code using LDPC matrices.”, IEICE Technical Report, Vol. IT2006-51, pp.7-12, 2007 A. Bennatan and D. Burshtein, “On the application of LDPC codes to arbitrary discrete-memoryless-channels.”, IEEE Transactions on Information Theory, Vol. IT-50, No. 3, pp.417-438, 2004 C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: Turbo-Codes.”, IEEE Transactions on Communications, Vol. COM-44, No. 10, pp.1261-1271, 1996

  By the way, the above-described conventional communication path code does not solve all of the first problem, the second problem, and the third problem in terms of practical operation.

  That is, the above-described conventional constant type code is configured by random encoding, and since maximum likelihood estimation and mutual information maximum estimation are used for the decoding method, efficient decoding cannot be performed. The problem cannot be solved.

  The conventional Reed-Solomon code described above is a maximum distance separation code that satisfies the single bound (limit), and in order to make the error probability at the time of decoding as close to “0” as possible, the block length is increased. As a result, the transmission rate inevitably approaches “0”, so the second problem cannot be solved. In addition, many attempts have been made to realize a configuration that simultaneously realizes transmission rate efficiency and calculation efficiency by an encoder and a decoder by combining existing codes such as a Reed-Solomon code and a convolutional code. Although it has been made from an application viewpoint, it can be used without much inconvenience, but information can be transmitted at a transmission rate close to the channel capacity, and the error probability at the time of decoding is “0”. Anything that can reach the Shannon limit that can be close to is still not configured.

  Moreover, although the above-mentioned conventional LDPC code is said to have the possibility of achieving the Shannon limit, since it is based on a linear code, its effectiveness is limited to communication channels under additive noise. Therefore, the first problem cannot be solved.

  In addition, the above-described conventional LDPC code combined with a quantization method includes an encoder asymptotically increased in amount, not only the block length but also the quantization parameter of the encoder. It is difficult.

  In addition, the above-described conventional turbo code is only empirically known to sometimes solve the second and third problems, and theoretical analysis is not progressing like the LDPC code. .

  As described above, the above-described conventional channel code is not a technology that solves all of the first problem, the second problem, and the third problem in terms of practical operation. There is a problem that it is not an efficient channel code that can transmit information at a transmission rate close to the channel capacity and can make the error probability at the time of decoding as close to “0” as possible.

  Therefore, the present invention has been made to solve the above-described problems of the prior art, and asymptotically, while leaving the advantage of the LDPC code that an efficient optimization algorithm such as a sum-product method can be used. By configuring a code whose only parameter is the block length, information can be transmitted at a transmission rate close to the channel capacity of a channel having general noise, and the error probability at the time of decoding is set to “0” as much as possible. An object of the present invention is to provide an information transmission / reception method, an encoding device, and a decoding device that can be set to close values and that can be encoded and decoded in real time.

  In order to solve the above-described problems and achieve the object, the invention according to claim 1 generates a code word obtained by encoding information to be transmitted, inputs the code word to a communication channel having noise, and outputs the code word from the communication channel. An information transmission / reception method for generating a decoded word obtained by decoding an output codeword that is a coded codeword and receiving the information, wherein a sparse matrix for generating a first sparse matrix and a second sparse matrix respectively As a probability distribution imitating the communication path, an input probability distribution storage process of storing an input probability distribution that is a distribution of the appearance probability of the codeword input to the communication path in a first storage unit, A conditional probability distribution storing step of storing a conditional probability distribution in which the output codeword is output when the codeword is input in a second storage unit; and for the information, the sparse matrix generating step The product with the generated first sparse matrix is zero The input probability distribution stored in the first storage unit among the codeword candidates in which the product is a column and the product of the second sparse matrix generated by the sparse matrix generation step is the information. A code word generating step for selecting the largest candidate by the optimization algorithm and generating the selected candidate as the code word of the information, and the output code word generated by the sparse matrix generating step Among the codeword candidates whose product with the first sparse matrix is a zero matrix, when the codeword is input to the communication path, the input probability distribution stored in the first storage unit and the first A candidate that maximizes the probability of output of the output codeword calculated using the conditional probability distribution stored in the second storage unit is selected by the optimization algorithm, and the selected candidate and the sparse matrix According to the production process The product of the second sparse matrix generated Te, characterized in that it includes a decoded word generating step of generating as the decoded word of the output code word, the.

  The invention according to claim 2 is an encoding device that generates a codeword obtained by encoding information to be transmitted and inputs the codeword to a communication channel having noise, and includes a first sparse matrix and a second sparse matrix. Sparse matrix generation means for generating each matrix, input probability distribution storage means for storing an input probability distribution that is a probability distribution appearing as the codeword input to the communication path, and for the information, The product of the first sparse matrix generated by the sparse matrix generation means is a zero matrix, and the product of the second sparse matrix generated by the sparse matrix generation means is the information. Among the candidates, a code word generating unit that selects the one having the maximum input probability distribution stored in the input probability distribution storage unit by an optimization algorithm and generates the selected candidate as the code word of the information And be prepared Characterized in that was.

  Further, the invention according to claim 3 decodes the output codeword that is the codeword output from the communication path after the codeword encoding the information to be transmitted is input to the communication path having noise. A decoding device that generates a decoded word and receives the information, sparse matrix generation means for generating a first sparse matrix and a second sparse matrix, respectively, and the input to the communication path An input probability distribution storage means for storing an input probability distribution, which is a probability distribution that appears as a code word, and the output code word is output when the code word is input as a probability distribution simulating the communication path. Conditional probability distribution storage means for storing a conditional probability distribution, and for the output codeword, the product of the first sparse matrix generated by the sparse matrix generation means is a zero matrix. Among the candidates, it enters the communication channel. The probability that the output codeword calculated using the input probability distribution stored in the input probability distribution storage means and the conditional probability distribution stored in the conditional probability distribution storage means is output. Decoding that selects the largest one by an optimization algorithm and generates a product of the selected candidate and the second sparse matrix generated by the sparse matrix generation means as the decoded word of the output codeword And a word generation means.

  According to the present invention, a first sparse matrix and a second sparse matrix are generated respectively, and an input probability distribution that is a distribution of the appearance probability of codewords input to the communication path, and a probability distribution that simulates the communication path As a conditional probability distribution in which an output codeword is output when the codeword is input. Then, for the information to be transmitted, the input probability distribution is the largest among the codeword candidates whose product with the first sparse matrix is the zero matrix and the product with the second sparse matrix is the information. Is selected by an optimization algorithm, and the selected candidate is generated as a codeword of the information. Furthermore, among the codeword candidates whose product with the first sparse matrix is the zero matrix for the output codeword, when the input codeword is input to the communication channel, the input probability distribution and the conditional probability distribution are The output codeword that is calculated using the output codeword that has the highest probability of being output is selected by the optimization algorithm, and the product of the selected candidate and the second sparse matrix is the decoded word of the output codeword Generate as Therefore, the first sparse matrix is used as the LDPC matrix for parity check used in the conventional LDPC code, and the second sparse matrix is the transmission target information (transmission message) and the code word. Sum-product, which is usually used only in decoding in the conventional LDPC code, is used as a matrix for giving a correspondence relationship, and further, in encoding, in order to realize a parity check and a correspondence between a transmission message and a code word By using an optimization algorithm such as the method at the time of encoding, the calculation process for associating the transmission message with the code word becomes efficient at the time of decoding. Information can be transmitted at a transmission rate close to the path capacity, and the error probability at the time of decoding should be as close to “0” as possible. Can, and encoding and decoding can be performed in real time.

  Exemplary embodiments of an information transmitting / receiving method, an encoding device, and a decoding device according to the present invention will be described below in detail with reference to the accompanying drawings. In the following, a communication system for executing the information transmitting / receiving method according to the present invention will be described as an embodiment.

[Explanation of terms]
First, main terms used in the following examples will be described. The “communication path” used in the following embodiments is an information transmission medium used for transmission and reception of information, and the “communication path having noise” is a binary symmetric communication path (Binary Symmetric Channel). Thus, when information composed of “0” and “1” is output from the “communication channel”, the probability that “0” is erroneously output as “1” and “1” is erroneously assumed as “0” In addition to the “communication channel with additive noise” such that the probability of being output is a fixed value, “0” is erroneously output as “1”, and “1” is erroneously assumed as “0” It is a “communication channel having a general noise” that includes one in which the probability of being output varies depending on information transmission.

  The “encoder” generates a code word (encoded message) in which “bit for error correction” is added to “information bit” as a transmission message to be transmitted, and the code word is converted to “ It is a device that inputs to the “communication path” and corresponds to the “encoding device” recited in the claims. In the following, “encoded message” may be described as “communication path input message”. In addition, the “decoder” is a codeword (communication channel output message) output from the “communication channel”, and generates a decoded word in which error correction is performed using “bits for error correction”. A device that outputs a decrypted message obtained by decrypting a transmission message to an information reception target, and corresponds to a “decryption device” recited in the claims. The “communication path output message” corresponds to the “output codeword” recited in the claims.

  The transmission rate (encoding rate) is the ratio of the “number of bits after error correction encoding” to the “number of information bits”, and the transmission rate (encoding rate) is “k / n”. This means that “bits for error correction” of “(n−k) bits” are added to “information bits” of k bits to generate an “n bit” code word. “Channel capacity” refers to the maximum amount of information that can be transmitted without error, and “Shannon limit” refers to “Transmission rate” close to “Channel capacity”. This means that the error probability at the time of decoding can be set to a value close to “0” as much as possible ”.

The alphabet used in the following description belongs to “field: Z _q (where q is a prime number)”, which is a set closed by addition / subtraction / division / division. In the present embodiment, a case where “q = 2” and “body” is a set of numbers including “0” and “1” will be described. Further, “X” is a random variable of “code word” input to the communication path, and “Y” is a random variable of “code word” output from the communication path. Further, “x ⁿ ” and “y ⁿ ” respectively indicate the actual values (n bits) of the random variables “X” and “Y”, and these belong to “field: Z _q ”.

Also, the transmission message "k bits", expressed as "u ^k", "u ^k" is intended to belong to the set "{Z _q} ^k". In addition, “encoder” is represented by the Greek letter “phi”. In this embodiment, “encoder: phi” represents “k bits” of the transmitted message “{Z _q } ^k ” and “n bits”. Is encoded into the code word “{Z _q } ⁿ ”. In addition, “decoder” is represented by the Greek letter “Psai”. In this embodiment, “decoder: Psai” represents “n bits” code word “{Z _q } ⁿ ” and “k bits”. It is assumed that the decrypted message “{Z _q } ^k ” is decrypted. In the following, the decrypted message is represented by adding “^: hat” symbol on “u” of “u ^k ”.

[Outline and features of communication system in this embodiment]
Next, the outline and main features of the communication system in the present embodiment will be specifically described with reference to FIGS. 1 and 2. FIG. 1 is a diagram for explaining an outline of a communication system in the present embodiment, and FIG. 2 is a diagram for explaining characteristics of the communication system in the present embodiment.

  As shown in FIG. 1, the communication system according to the present embodiment converts a “communication path input message”, which is a code word obtained by encoding a “transmission message”, into a “transmission rate (encoding rate):“ k / n ”” and input to the “channel having noise”, and the “channel output message” which is a code word output from the “channel having noise” is decoded by the “decoder”. The outline is to generate a decrypted message that is a decrypted word. Note that the alphabetical symbols shown in FIG. 1 are in accordance with the above-mentioned [Terminology].

  Here, the present invention can transmit information at a transmission rate close to the channel capacity of a channel having general noise, and can make the error probability at the time of decoding as close to “0” as possible, and The main feature is that encoding and decoding can be performed in real time. Briefly describing this main feature, as shown in FIG. 2A, the communication system in the present embodiment further includes a “sparse matrix generation device” in addition to an “encoder” and a “decoder”. The sparse matrix generator generates a first sparse matrix (A) and a second sparse matrix (B), respectively, and generates the generated first sparse matrix (A) and second sparse matrix (B). Are output to the “encoder” and “decoder”. Here, the first sparse matrix (A) is an LDPC matrix of “n rows and 1 columns”, and the second sparse matrix (B) is an LDPC matrix of “n rows and k columns”. In addition, the fact that these are sparse matrices is a necessary condition for efficiently executing an efficient optimization algorithm such as the sum-product method. A specific method for generating the first sparse matrix (A) and the second sparse matrix (B) will be described in detail later.

Further, the “encoder” and “decoder” constituting the communication system in the present embodiment store an input probability distribution that is a distribution of appearance probabilities of codewords input to the communication path. For example, as shown in FIG. 2A, the “encoder” and the “decoder” store an input probability distribution, which is a probability distribution of “x ⁿ ”, as “Px ⁿ ”. The input probability distribution used in the present embodiment is preset by the administrator of the communication system, and an optimal probability distribution is used to achieve the “Shannon limit”. For example, the input probability distribution used in the present embodiment is a probability distribution in which the mutual information amount (the amount of information that can be transmitted through the communication channel) is smaller than the “communication channel capacity” corresponding to the constant type code. For example, it can be obtained by using the Arimoto-Blahut algorithm (see RW Yeung, “A First Course in Information Theory”, Springer, 2002).

In addition, the “decoder” constituting the communication system according to the present embodiment outputs a “communication path output message” when a “communication path input message” is input as a probability distribution simulating the “communication path”. Store the conditional probability distribution. For example, as shown in FIG. 2A, when the “decoder” receives a random variable “X” of “codeword” input to the communication channel, the random variable “Y” from the communication channel. Is stored as “W _{Y | X} ” (hereinafter, “X” in the conditional probability distribution shown in FIG. 2A as “W _{Y | X} ”). And the superscript “n” in “Y” is omitted). Here, the conditional probability distribution used in the present embodiment is given as unique to each “communication channel”, but experience obtained by actually transmitting / receiving information for each “communication channel” Based on the value, the administrator of the communication system may calculate and set the value.

Note that H (X) is entropy that is an amount defined by “Px ⁿ ”, and H (X | Y) is a conditional condition that is an amount defined by “P _XY = P _x W _{Y | X} ”. In the case of entropy, the natural numbers “n”, “k” and “l” satisfy “l / n> H (X | Y)” and “(l + k) / n <H (X ) ”. This is necessary as a condition for approaching the Shannon limit.

Then, as shown in FIG. 2B, the “encoder” constituting the communication system in the present embodiment has a product of the transmission message “u ^k ” and the first sparse matrix (A). Among the candidate codewords that have a zero matrix and a product of “u ^k ” with the second sparse matrix (B), the one having the maximum input probability distribution is selected by the optimization algorithm, and the selected The candidate is generated as “communication path input message: x ⁿ ” which is a codeword of the information, and is output to “communication path”. As shown in FIG. 2B, codeword candidates are represented by adding “˜: tilde” symbols on “x” of “x ⁿ ”. Belongs to {Z _q } ⁿ ".

Then, as shown in FIG. 2C, the “decoder” that configures the communication system in the present embodiment has the first sparse matrix (A) and “communication path output message: y ⁿ ” If the codeword candidate is input to the communication channel among the candidate codewords whose product is a zero matrix, it is calculated using the input probability distribution “Px ⁿ ” and the conditional probability distribution “W _{Y | X} ” An optimization algorithm is used to select the output codeword with the highest probability “P _XY = P _x W _{Y | X} ”, and the selected candidate (ie, the estimated “communication path input message”). ) And the second sparse matrix (B) as a decrypted message ("^: hat" symbol added above "u" of "u ^k "), which is a restoration of "sent message" And output to the information reception target. In (C) of FIG. 2, similar to (B) of FIG. 2, codeword candidates to be error-corrected from “communication channel output message: y ⁿ ” are displayed above “x” of “x ⁿ ”. "~: Tilde" is added to the codeword, and among the candidate codewords that are error-corrected, the one selected by the optimization algorithm is displayed above "x" in " ^xn " It is shown with the “^: hat” symbol.

  For this reason, in the communication system according to the present embodiment, the first sparse matrix (A) is used as the LDPC matrix for parity check used in the conventional LDPC code, and the second sparse matrix ( B) is used as a matrix that gives the correspondence between transmission messages and codewords. Further, in order to realize a parity check and correspondence between transmission messages and codewords at the time of encoding, a conventional LDPC code is usually used. By using an optimization algorithm such as a sum-product method used only at the time of decoding at the time of encoding, calculation processing for associating a transmission message with a code word at the time of decoding becomes efficient. Therefore, as described above, information can be transmitted at a transmission rate close to the channel capacity of a channel having general noise. Both can be a value close to "0" as possible the error probability during decoding and encoding and decoding can be performed in real time.

[Configuration of sparse matrix generation apparatus in this embodiment]
Next, the configuration of the sparse matrix generation device according to the present embodiment will be described with reference to FIGS. FIG. 3 is a block diagram illustrating a configuration of the sparse matrix generation apparatus according to the present embodiment, and FIG. 4 is a diagram for explaining a sparse matrix generation unit.

  As shown in FIG. 3, the sparse matrix generation device 10 in the present embodiment includes a communication control I / F unit 11 and a processing unit 12, and is further connected to an encoder 20 and a decoder 40 via a network. Is done.

  The communication control I / F unit 11 is an interface that controls transfer of data transmitted through the network. Specifically, the sparse matrix generation request from the administrator of the communication system is received via the network, or the sparse matrix generated by the sparse matrix generation unit 12a described later is transmitted via the network to the encoder 20 and Transmit to the decoder 40.

  As shown in FIG. 3, the processing unit 12 performs various processes, and particularly includes a sparse matrix generation unit 12a as closely related to the present invention.

The sparse matrix generation unit 12a generates a first sparse matrix (A) and a second sparse matrix (B), and generates the generated first sparse matrix (A) and second sparse matrix (B). Is transmitted to the encoder 20 and the decoder 40 via the communication control I / F unit 11. Here, the sparse matrix generation unit 12a generates the first sparse matrix (A), which is an LDPC matrix of “n rows and 1 columns”, for example, by the method shown in FIG. First, all the elements of A in “n rows and l columns” are set to “0”, and the numbers “1 to l” are randomly extracted “t” times. Here, “t” is an order obtained by the natural logarithm of “n” (Order). Then, the sparse matrix generation unit 12a adds “1” to “column” corresponding to the extracted number on “body: Z _q ”. As a result, the first sparse matrix (A) having many “0” s in the elements of “n rows and 1 columns” is generated.

Also, the sparse matrix generation unit 12a shows the second sparse matrix (B), which is an LDPC matrix of “n rows and k columns”, as in the first sparse matrix (A), as shown in FIG. Generate by the method. First, all elements of B in “n rows and k columns” are set to “0”, and numbers “1 to k” are randomly extracted “t” times. Then, the sparse matrix generation unit 12a adds “1” to “column” corresponding to the extracted number on “body: Z _q ”. As a result, a second sparse matrix (B) with many “0” s in the elements of “n rows and k columns” is generated. The numerical value defined by the order “O” is defined by the relational expression shown in FIG.

[Configuration of encoder in this embodiment]
Then, the structure of the encoder in a present Example is demonstrated using FIG. 5 and FIG. FIG. 5 is a block diagram showing a configuration of the encoder in the present embodiment, and FIG. 6 is a diagram for explaining a diagram for explaining a codeword generation unit.

  As shown in FIG. 5, the encoder 20 in this embodiment includes an input unit 21, an output unit 22, a communication control unit 23, an input / output control I / F unit 24, a storage unit 25, and a processing unit 26. Are further connected to the sparse matrix generation device 10 via a network and connected to the communication path 30.

  The input unit 21 inputs various information. For example, a keyboard, a touch panel, and the like correspond to this, and particularly those closely related to the present invention include an input probability distribution set by an administrator of the communication system and stored in the input probability distribution storage unit 25b described later. Input from the keyboard operated by the administrator of the communication system.

  The output unit 22 outputs various information. For example, a display, a speaker, etc. correspond to this, for example, the sparse matrix which the sparse matrix production | generation apparatus 10 transmitted is displayed on the screen of a display.

  The communication control unit 23 controls communication with other devices. For example, the transfer of data transmitted and received through the network is controlled, and particularly as closely related to the present invention, data reception of a transmission message to be transmitted is controlled, or generated and transmitted by the sparse matrix generation device 10 The data reception of the sparse matrix is controlled, and the data transmission when the communication channel input message generated by the codeword generation unit 26a described later is output to the communication channel 30 is controlled.

  The input / output control I / F unit 24 controls data transfer between the input unit 21, the output unit 22, the communication control unit 23, the storage unit 25, and the processing unit 26.

  The storage unit 25 stores data used for various types of processing by the processing unit 26, and particularly those closely related to the present invention include a sparse matrix storage unit 25a and an input probability distribution storage unit 25b as shown in FIG. With.

  The sparse matrix storage unit 25a stores the first sparse matrix (A) and the second sparse matrix (B) generated by the sparse matrix generation device 10 and received by the communication control unit 23.

The input probability distribution storage unit 25 b stores an input probability distribution that is a distribution of appearance probabilities of codewords input to the communication path 30. Here, the input probability distribution is set in advance by the administrator of the communication system, input via the input unit 21, and input to the input probability distribution storage unit 25 b via the input / output control I / F unit 24. For example, as shown in FIG. 2A, an input probability distribution that is a probability distribution of occurrence of “x ⁿ ” is stored as “Px ⁿ ”. The input probability distribution can be obtained by using, for example, the Arimoto-Blahut algorithm.

The processing unit 26 executes various processes based on the transmission message “u ^k ” transferred from the input / output control I / F unit 24, and particularly as closely related to the present invention, as shown in FIG. A codeword generator 26a is provided.

In accordance with the definition shown in FIG. 6, the codeword generation unit 26 a has a zero product of the product of the transmission message “u ^k ” and the first sparse matrix (A) stored in the sparse matrix storage unit 25 a. Among the codeword candidates whose product with the second sparse matrix (B) stored in the matrix storage unit 25a is “u ^k ”, the input probability distribution stored in the input probability distribution storage unit 25b is the maximum. Is selected by an optimization algorithm, and the selected candidate is generated as “communication path input message: x ⁿ ” which is a codeword of the information, and is output to the communication path 30 via the communication control unit 23. . As shown in FIG. 6, codeword candidates are represented by adding “˜: tilde” symbols on “x” of “ ^xn ”, and codeword candidates are represented by “{Z _q } ^n. Belongs to.

[Configuration of Decoder in this Embodiment]
Subsequently, the configuration of the decoder in the present embodiment will be described with reference to FIGS. FIG. 7 is a block diagram showing the configuration of the decoder in the present embodiment, and FIG. 8 is a diagram for explaining the decoded message generation unit.

  As shown in FIG. 7, the decoder 40 in this embodiment includes an input unit 41, an output unit 42, a communication control unit 43, an input / output control I / F unit 44, a storage unit 45, and a processing unit 46. Are further connected to the sparse matrix generation device 10 via a network and connected to the communication path 30.

  The input unit 41 inputs various information. For example, a keyboard, a touch panel, and the like correspond to this, and particularly as closely related to the present invention, an input probability distribution set by an administrator of the communication system and stored in an input probability distribution storage unit 45b described later, The conditional probability distribution stored in the conditional probability distribution storage unit 45c described later is input from a keyboard or the like operated by the administrator of the communication system.

  The output unit 42 outputs various information. For example, a display, a speaker, etc. correspond to this, for example, the sparse matrix which the sparse matrix production | generation apparatus 10 transmitted is displayed on the screen of a display.

  The communication control unit 43 controls communication with other devices. For example, the transfer of data transmitted and received through the network is controlled, and particularly as closely related to the present invention, the data reception of the communication path output message output from the communication path 30 is controlled, or the sparse matrix generation device 10 Controls the reception of sparse matrix data generated and transmitted, and controls data transmission when a decoded message generated by a decoded message generation unit 46a described later is output as a transmission target.

  The input / output control I / F unit 44 controls data transfer between the input unit 41, the output unit 42, the communication control unit 43, the storage unit 45, and the processing unit 46.

  The storage unit 45 stores data used for various types of processing by the processing unit 46, and particularly those closely related to the present invention include a sparse matrix storage unit 45a and an input probability distribution storage unit 45b as shown in FIG. And a conditional probability distribution storage unit 45c.

  Similar to the sparse matrix storage unit 25a in the encoder 20, the sparse matrix storage unit 45a generates the first sparse matrix (A) and the second sparse matrix generated by the sparse matrix generation device 10 and received by the communication control unit 43. (B) is stored, and the input probability distribution storage unit 45b stores an input probability distribution, which is a distribution of the appearance probabilities of codewords input to the communication path 30, in the same manner as the input probability distribution storage unit 25b in the encoder 20. Remember.

The conditional probability distribution storage unit 45c is a conditional distribution that outputs “communication path output message: y ⁿ ” when “communication path input message: x ⁿ ” is input as a probability distribution simulating “communication path”. Memorize the probability distribution. Here, the conditional probability distribution is input by the administrator of the communication system via the input unit 41 and stored in the conditional probability distribution storage unit 45c via the input / output control I / F unit 44. As shown in FIG. 2A, the “decoder” outputs the random variable “Y” from the communication path when the random variable “X” of the “code word” input to the communication path is input. Is stored as “W _{Y | X} ”. The conditional probability distribution used in the present embodiment is set as a unique one given for each “communication path”, but can be obtained by actually transmitting / receiving information for each “communication path”. The administrator of the communication system may calculate and set based on the experience value.

  The processing unit 46 executes various processes based on the “communication path input message” transferred from the input / output control I / F unit 44, and particularly as closely related to the present invention, as shown in FIG. A decrypted message generator 46a is provided.

In accordance with the definition shown in FIG. 8A, the decryption message generation unit 46a multiplies the “communication channel output message: y ⁿ ” by the product of the first sparse matrix (A) stored in the sparse matrix storage unit 45a. Is a zero matrix, and when it is input to the communication channel, the input probability distribution “Px ⁿ ” stored in the input probability distribution storage unit 45 b and the conditional probability distribution storage unit 45 c store them. The optimization algorithm selects the one with the highest probability (see FIG. 8C) that the output codeword calculated using the conditional probability distribution “W _{Y | X} ” is output.

Then, as illustrated in FIG. 8B, the decrypted message generation unit 46 a converts the product of the selected candidate and the second sparse matrix (B) stored in the sparse matrix storage unit 45 a into the decrypted message (“ ^: A “hat” symbol added to “u” of “u ^k ”) and output it to the information reception target.

[Procedure of processing by sparse matrix generation apparatus in this embodiment]
Next, processing performed by the sparse matrix generation device 10 in this embodiment will be described with reference to FIG. FIG. 9 is a diagram for explaining a processing procedure of the sparse matrix generation device according to the present embodiment.

  As shown in FIG. 9, first, the sparse matrix generation device 10 in the present embodiment receives a sparse matrix generation request from the communication system administrator via the communication control I / F unit 11 (Yes in step S901). The sparse matrix generation unit 12a generates a first sparse matrix (A) and a second sparse matrix (B), respectively (step S902).

  For example, the sparse matrix generation unit 12a generates a first sparse matrix (A) that is an LDPC matrix of “n rows and 1 columns” by the method illustrated in FIG. A second sparse matrix (B) that is an LDPC matrix is generated by the method shown in FIG.

  Then, the sparse matrix generation unit 12a transmits the generated first sparse matrix (A) and second sparse matrix (B) from the communication control I / F unit 11 to the encoder 20 and the decoder 40 via a network. (Step S903), and the process ends.

[Procedure for Processing by Encoder in this Embodiment]
Next, processing by the encoder 20 in the present embodiment will be described with reference to FIG. FIG. 10 is a diagram for explaining the processing procedure of the encoder in the present embodiment.

As shown in FIG. 10, first, when the encoder 20 in the present embodiment receives the transmission message “u ^k ” via the communication control unit 23 (Yes in step S1001), the codeword generation unit 26a receives the message. From the transmitted message “u ^k ”, a code word “communication path input message: x ⁿ ” is generated using an optimal algorithm (step S1002).

That is, according to the definition shown in FIG. 6, the codeword generation unit 26a has a product of the transmission message “u ^k ” and the first sparse matrix (A) stored in the sparse matrix storage unit 25a as a zero matrix, Among the codeword candidates whose product with the second sparse matrix (B) stored in the sparse matrix storage unit 25a is “u ^k ”, the input probability distribution stored in the input probability distribution storage unit 25b is the largest. Is selected by an optimization algorithm, and the selected candidate is generated as “communication path input message: x ⁿ ” which is a codeword of the information.

Then, the codeword generation unit 26a inputs the generated codeword “communication path input message: x ⁿ ” to the communication path 30 via the communication control unit 23 (step S1003), and ends the process. .

[Procedure of processing by the decoder in this embodiment]
Next, processing performed by the decoder 40 in this embodiment will be described with reference to FIG. FIG. 11 is a diagram for explaining the processing procedure of the decoder in the present embodiment.

As shown in FIG. 11, first, when the decoder 40 in this embodiment outputs an output codeword “communication path output message: y ⁿ ” from the communication path 30 (Yes in step S1101), the decoding message is output. The generation unit 46a selects an optimal codeword from the received output codeword using an optimal algorithm (step S1102).

That is, the decryption message generation unit 46a determines the first sparse matrix (A) stored in the sparse matrix storage unit 45a for the “communication channel output message: y ⁿ ” according to the definition shown in FIG. Among the codeword candidates whose product is a zero matrix, the input probability distribution “Px ⁿ ” stored in the input probability distribution storage unit 45 b and the conditional probability distribution storage unit 45 c are stored in the channel. The optimization algorithm is used to select the one that maximizes the probability (see FIG. 8C) that the output codeword calculated using the stored conditional probability distribution “W _{Y | X} ” is output.

  Then, the decrypted message generation unit 46a generates a decrypted message (step S1103). That is, as shown in FIG. 8B, the decrypted message generating unit 46a generates a product of the selected candidate and the second sparse matrix (B) stored in the sparse matrix storage unit 45a as a decrypted message. To do.

  After that, the decrypted message generation unit 46a outputs the generated decrypted message to the information reception target (step S1104) and ends the process.

[Effect of this embodiment]
As described above, according to the present embodiment, the first sparse matrix (A) is used as the LDPC matrix for parity check used in the conventional LDPC code, and the second sparse matrix (B). Is used as a matrix that gives the correspondence between transmission messages and codewords, and in order to realize a parity check and correspondence between transmission messages and codewords at the time of encoding, it is usually decoded in a conventional LDPC code. Since an optimization algorithm such as a sum-product method used only at the time of encoding is also used at the time of encoding, calculation processing for associating a transmission message with a code word becomes efficient at the time of decoding Information can be transmitted at a transmission rate close to the channel capacity of a channel having general noise, and the error probability at the time of decoding is set to “0” as much as possible. It can be had values, and encoding and decoding can be performed in real time.

  In this embodiment, the first sparse matrix (A) and the second sparse matrix (B) generated by the sparse matrix generation apparatus 10 are transmitted to the encoder 20 and the decoder 40 via the network. However, the present invention is not limited to this. For example, the first sparse matrix (A) and the second sparse matrix (B) generated by the sparse matrix generation device 10 May be directly input to the encoder 20 and the decoder 40 by the administrator of the communication system.

  In addition, the first sparse matrix (A) and the second sparse matrix (B) generated by the sparse matrix generation device 10 may be the same in all communication channels to which the present invention is applied. For example, in each communication channel to which the present invention is applied, even when the sparse matrix generation device 10 generates and uses the first sparse matrix (A) and the second sparse matrix (B). Good.

  In addition, among the processes described in this embodiment, all or part of the processes described as being performed automatically can be performed manually, or the processes described as being performed manually can be performed. All or a part can be automatically performed by a known method. In addition, the processing procedure, control procedure, specific name, and information including various data and parameters shown in the above-described document and drawings can be arbitrarily changed unless otherwise specified.

  Further, each component of each illustrated apparatus is functionally conceptual, and does not necessarily need to be physically configured as illustrated. In other words, the specific form of distribution / integration of each device is not limited to that shown in the figure, and all or a part thereof may be functionally or physically distributed or arbitrarily distributed in arbitrary units according to various loads or usage conditions. Can be integrated and configured. Further, all or any part of each processing function performed in each device may be realized by a CPU and a program analyzed and executed by the CPU, or may be realized as hardware by wired logic.

  The information transmission / reception method described in this embodiment can be realized by executing a program prepared in advance on a computer such as a personal computer or a workstation. This program can be distributed via a network such as the Internet. The program can also be executed by being recorded on a computer-readable recording medium such as a hard disk, a flexible disk (FD), a CD-ROM, an MO, and a DVD and being read from the recording medium by the computer.

  As described above, the information transmission / reception method, the encoding device, and the decoding device according to the present invention generate a codeword obtained by encoding information to be transmitted, input it to a communication channel having noise, and output from the communication channel This is useful when receiving information by generating a decoded word obtained by decoding an output codeword that is a coded codeword, and transmitting information at a transmission rate close to the channel capacity of a channel having general noise. In addition, the error probability at the time of decoding can be made as close to “0” as possible, and encoding and decoding can be performed in real time.

It is a figure for demonstrating the outline | summary of the communication system in a present Example. It is a figure for demonstrating the characteristic of the communication system in a present Example. It is a block diagram which shows the structure of the sparse matrix production | generation apparatus in a present Example. It is a figure for demonstrating a sparse matrix production | generation part. It is a block diagram which shows the structure of the encoder in a present Example. It is a figure for demonstrating a codeword production | generation part. It is a block diagram which shows the structure of the decoder in a present Example. It is a figure for demonstrating a decoding message production | generation part. It is a figure for demonstrating the procedure of a process of the sparse matrix production | generation apparatus in a present Example. It is a figure for demonstrating the procedure of the process of the encoder in a present Example. It is a figure for demonstrating the procedure of the process of the decoder in a present Example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Sparse matrix production | generation apparatus 11 Communication control I / F part 12 Processing part 12a Sparse matrix production | generation part 20 Encoder 21 Input part 22 Output part 23 Communication control part 24 Input / output control I / F part 25 Memory | storage part 25a Sparse matrix memory | storage part 25b Input probability distribution storage unit 26 Processing unit 26a Codeword generation unit 30 Communication path 40 Decoder 41 Input unit 42 Output unit 43 Communication control unit 44 Input / output control I / F unit 45 Storage unit 45a Sparse matrix storage unit 45b Input probability distribution storage Unit 45c conditional probability distribution storage unit 46 processing unit 46a decrypted message generation unit

Claims (3)

Generate a codeword that encodes information to be transmitted and input it to a communication channel having noise, generate a decoded word by decoding an output codeword that is the codeword output from the communication channel, and An information transmission / reception method for receiving information,
A sparse matrix generation step for generating a first sparse matrix and a second sparse matrix respectively;
An input probability distribution storage step of storing an input probability distribution, which is a distribution of the appearance probability of the codewords input to the communication path, in a first storage unit;
A conditional probability distribution storage step of storing, in a second storage unit, a conditional probability distribution in which the output codeword is output when the codeword is input as a probability distribution imitating the communication path;
The product of the information and the first sparse matrix generated by the sparse matrix generation step is a zero matrix, and the product of the second sparse matrix generated by the sparse matrix generation step is the Among the codeword candidates to be information, the one that maximizes the input probability distribution stored in the first storage unit is selected by an optimization algorithm, and the selected candidate is the codeword of the information A codeword generation step to generate as
When the output codeword is input to the communication channel among the codeword candidates whose product of the first sparse matrix generated by the sparse matrix generation step is a zero matrix with respect to the output codeword The probability that the output codeword calculated using the input probability distribution stored in the first storage unit and the conditional probability distribution stored in the second storage unit is output is maximized. A decoding word generation step of generating a product of the selected candidate and the second sparse matrix generated by the sparse matrix generation step as the decoding word of the output codeword ,
An information transmission / reception method comprising: An encoding device that generates a code word obtained by encoding information to be transmitted and inputs the code word to a communication channel having noise,
Sparse matrix generation means for generating a first sparse matrix and a second sparse matrix respectively;
Input probability distribution storage means for storing an input probability distribution which is a distribution of the probability of appearing as the codeword input to the communication path;
The product of the information and the first sparse matrix generated by the sparse matrix generation means is a zero matrix, and the product of the second sparse matrix generated by the sparse matrix generation means is the Among the codeword candidates to be information, the one that maximizes the input probability distribution stored by the input probability distribution storage means is selected by an optimization algorithm, and the selected candidate is the codeword of the information Codeword generation means for generating
An encoding device comprising: After a codeword obtained by encoding information to be transmitted is input to a communication channel having noise, a decoded word obtained by decoding an output codeword that is the codeword output from the communication channel is generated to generate the information. A decryption device for receiving
Sparse matrix generation means for generating a first sparse matrix and a second sparse matrix respectively;
Input probability distribution storage means for storing an input probability distribution which is a distribution of the probability of appearing as the codeword input to the communication path;
Conditional probability distribution storage means for storing a conditional probability distribution in which the output codeword is output when the codeword is input as a probability distribution imitating the communication path;
Among the codeword candidates in which the product of the output codeword and the first sparse matrix generated by the sparse matrix generation means is a zero matrix, the input codeword is input to the communication channel The probability that the output codeword calculated using the input probability distribution stored in the input probability distribution storage unit and the conditional probability distribution stored in the conditional probability distribution storage unit is output is maximized. Decoding word generating means for selecting an object by an optimization algorithm and generating a product of the selected candidate and the second sparse matrix generated by the sparse matrix generating means as the decoded word of the output codeword When,
A decoding apparatus comprising:

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