Abstract: A memory system includes a non-volatile memory and a memory controller. The memory controller is configured to read a received word from the non-volatile memory, estimate noise by using a plurality of different models for estimating the noise included in the received word to obtain a plurality of noise estimation values, select one noise estimation value from the plurality of noise estimation values, update the received word by using a value obtained by subtracting the selected noise estimation value from the read received word, and decode the updated received word by using a belief-propagation method.

Abstract: According to one embodiment, a learning device includes a noise generation unit, a decoding unit, a generation unit, and a learning unit. The noise generation unit outputs a second code word which corresponds to a first code word to which noise has been added. The decoding unit decodes the second code word and outputs a third code word. The generation unit generates learning data for learning a weight in message passing decoding in which the weight and a message to be transmitted are multiplied, based on whether or not decoding of the second code word into the third code word has been successful. The learning unit determines a value for the weight in the message passing decoding by using the learning data.

Abstract: A learning device includes an encoding unit, a plurality of permutation units, a plurality of decoding units, a selection unit, and a learning unit. The encoding unit is configured generate an encoded word by encoding a transmission word. The permutation units are configured to permutate the encoded word according to different permutation manners to generate a plurality of permutated encoded words. The decoding units are configured to perform message passing decoding on the plurality of permutated encoded words, to generate a plurality of decoded words. The message passing decoding involves weighting of values of a word transmitted during the message passing decoding. The selection unit is configured to select one or more of the decoded words. The learning unit is configured to perform learning of weighting values of the weighting based on the transmission word and the selected one or more of the decoded words.

Abstract: A memory system includes a non-volatile memory and a memory controller. The memory controller is configured to read a received word from the non-volatile memory, estimate noise by using a plurality of different models for estimating the noise included in the received word to obtain a plurality of noise estimation values, select one noise estimation value from the plurality of noise estimation values, update the received word by using a value obtained by subtracting the selected noise estimation value from the read received word, and decode the updated received word by using a belief-propagation method.

Abstract: According to one embodiment, a learning device includes a noise generation unit, a decoding unit, a generation unit, and a learning unit. The noise generation unit outputs a second code word which corresponds to a first code word to which noise has been added. The decoding unit decodes the second code word and outputs a third code word. The generation unit generates learning data for learning a weight in message passing decoding in which the weight and a message to be transmitted are multiplied, based on whether or not decoding of the second code word into the third code word has been successful. The learning unit determines a value for the weight in the message passing decoding by using the learning data.

Abstract: A friction drive belt (B) includes a belt body (10) that is wrapped around pulleys in contact therewith to transmit power. At least a pulley contact portion (15) of the belt main body (10) is made of a rubber composition containing 30-80 parts by mass of at least one layered silicate selected from a smectite group and a vermiculite group, per 100 parts by mass of raw rubber containing an ethylene-?-olefin elastomer.

Abstract: An example information processing device includes first and second receiving units, a deciding unit, and first and second transmitting units. The first receiving unit receives adjustment limit information from a plurality of first external devices. The deciding unit determines adjustment rules on the basis of the adjustment limit information. The first transmitting unit transmits the adjustment rules to second and third external devices. The second receiving unit receives determination information from a fourth external device. The second transmitting unit transmits the adjustment rules to the first external devices when integrated schedule information satisfies a condition. When the integrated schedule information does not satisfy the condition, the deciding unit changes the adjustment rules. When the deciding unit has changed the adjustment rules, the first transmitting unit transmits new adjustment rules to the second and third external devices.

Abstract: An arithmetic device includes an input unit inputting data that are elements of a group; a converting unit is configured, when the input data are in a second representation, to convert the input data into a first representation and to perform arithmetic operation on the converted first representation using an operand in the first representation in which at least one subcomponent is a zero element to convert the converted first representation into first converted data expressed in the first representation, and when the input data are in the first representation, to perform arithmetic operation on the input data using the operand in the first representation in which at least one subcomponent is a zero element to convert the input data into second converted data expressed in the first representation; and an operating unit that performs arithmetic processing on the first or the second converted data using secret information.

Abstract: According to one embodiment, a representation converting unit converts a set of n elements (h0, h1, . . . , hn?1) (hi: a member of a finite field Fp^m, 0?i?n?1) that is a projective representation of a member g of an n-th degree algebraic torus Tn(Fp^m) (n: positive integer, p: prime number, m: positive integer) into a limited projected representation expressed by a set of n elements (h?0, h?1, . . . , h?n?1) (h?i: a member of the finite field Fp^m, 0?i?n?1) in which at least one element out of the n elements is a zero element 0 or an identity element 1. An arithmetic unit omits part of Fp^m operation that is arithmetic operation in the finite field Fp^m based on a fact that an element in the set of n elements (h?0, h?1, . . . , h?n?1) represented by the limited projective representation is a zero element “0” or an identity element “1” when performing Fp^mn operation that is arithmetic operation of a finite field Fp^mn in combination with the Fp^m operation.

Abstract: According to an embodiment, an authority changing device includes a first determiner, a second determiner, and a changing unit. A first authority is defined by a first combination of first to third item values, and a second authority is defined by a second combination of the fourth to sixth item values. The first determiner uses a logical expression to determine whether the change from the first authority to the second authority is possible, not possible, or unknown. The second determiner uses a first table to determine the availability of change from the first authority to the second authority when the availability of the change is determined to be unknown. The changing unit changes the first authority to the second authority when the change is determined to be possible.

Abstract: A compressing unit compresses an element on an algebraic torus into affine representation according to a compression map. A determining unit determines whether a target element on the algebraic torus to be compressed is an exceptional point representing an element on the algebraic torus that cannot be compressed by the compression map. The compressing unit generates, when it is determined that the target element is the exceptional point, a processing result including exceptional information indicating that the target element is the exceptional point, and generates, when it is determined that the target element is not the exceptional point, a processing result including affine representation obtained by compressing the target element according to the compression map.

Abstract: In a computing device that calculates a square of an element in a finite field, a vector representation of the element in the finite field is accepted. The vector representation includes a plurality of elements. The computing device performs a multiplication operation on a base field using the accepted elements, and obtains a multiplication value. The multiplication operation is determined by a condition under which the element in the finite field is placed in an algebraic torus. The computing device performs an addition and subtraction operation using the obtained multiplication value and the accepted elements, and obtains a calculation result of the square of the element. The addition and subtraction operation is determined by the condition. The computing device then outputs the calculation result.

Abstract: According to an embodiment, an authority changing device includes a first determiner, a second determiner, and a changing unit. A first authority is defined by a first combination of first to third item values, and a second authority is defined by a second combination of the fourth to sixth item values. The first determiner uses a logical expression to determine whether the change from the first authority to the second authority is possible, not possible, or unknown. The second determiner uses a first table to determine the availability of change from the first authority to the second authority when the availability of the change is determined to be unknown. The changing unit changes the first authority to the second authority when the change is determined to be possible.

Abstract: When converting an affine representation representing a 2r-th degree algebraic torus T2r(Fq) (r is a prime number, and q is an integer) to a projective representation representing a quadratic algebraic torus T2(Fq^r), a representation converting apparatus acquires member (c0, c1, . . . , cr-2), (ci is a member of a finite field Fq, where 0?i?r?2) of a 2r-th degree algebraic torus T2r(Fq) represented by the affine representation. The apparatus performs a multiplication operation on the acquired member. The multiplication operation is determined by a condition under which a member of a quadratic algebraic torus T2(Fq^r) is included in the 2r-th degree algebraic torus T2r(Fq), a modulus and a base of a quadratic extension, and a modulus and a base of an r-th degree extension. The representation converting apparatus then performs an addition and subtraction operation determined by the condition, the moduli, and the bases.

Abstract: An example information processing device includes first and second receiving units, a deciding unit, and first and second transmitting units. The first receiving unit receives adjustment limit information from a plurality of first external devices. The deciding unit determines adjustment rules on the basis of the adjustment limit information. The first transmitting unit transmits the adjustment rules to second and third external devices. The second receiving unit receives determination information from a fourth external device. The second transmitting unit transmits the adjustment rules to the first external devices when integrated schedule information satisfies a condition. When the integrated schedule information does not satisfy the condition, the deciding unit changes the adjustment rules. When the deciding unit has changed the adjustment rules, the first transmitting unit transmits new adjustment rules to the second and third external devices.

Abstract: In a computing device that calculates a square of an element in a finite field, a vector representation of the element in the finite field is accepted. The vector representation includes a plurality of elements. The computing device performs a multiplication operation on a base field using the accepted elements, and obtains a multiplication value. The multiplication operation is determined by a condition under which the element in the finite field is placed in an algebraic torus. The computing device performs an addition and subtraction operation using the obtained multiplication value and the accepted elements, and obtains a calculation result of the square of the element. The addition and subtraction operation is determined by the condition. The computing device then outputs the calculation result.

Abstract: An arithmetic device includes an input unit inputting data that are elements of a group; a converting unit is configured, when the input data are in a second representation, to convert the input data into a first representation and to perform arithmetic operation on the converted first representation using an operand in the first representation in which at least one subcomponent is a zero element to convert the converted first representation into first converted data expressed in the first representation, and when the input data are in the first representation, to perform arithmetic operation on the input data using the operand in the first representation in which at least one subcomponent is a zero element to convert the input data into second converted data expressed in the first representation; and an operating unit that performs arithmetic processing on the first or the second converted data using secret information.

Abstract: An encryption processing unit executes an arithmetic operation decided in advance and outputs an arithmetic result as an element on an algebraic torus. A compressing unit outputs, when the arithmetic result is an exceptional point representing an element on the algebraic torus that cannot be compressed by a compression map for compressing an element on the algebraic torus into affine representation, a compression result obtained by compressing the arithmetic result according to the compression map and outputs, when the arithmetic result is the exceptional point, an element belonging to a specific set decided in advance that does not overlap a set to which a compression result obtained by compressing the arithmetic result, which is not the exceptional point, belongs.

Abstract: According to one embodiment, a representation converting unit converts a set of n elements (h0, h1, . . . , hn?1) (hi: a member of a finite field Fp?m, 0?i?n?1) that is a projective representation of a member g of an n-th degree algebraic torus Tn(Fp?m) (n: positive integer, p: prime number, m: positive integer) into a limited projected representation expressed by a set of n elements (h?0, h?1, . . . , h?n?1) (h?i: a member of the finite field Fp?m, 0?i?n?1) in which at least one element out of the n elements is a zero element 0 or an identity element 1. An arithmetic unit omits part of Fp?m operation that is arithmetic operation in the finite field Fp?m based on a fact that an element in the set of n elements (h?0, h?1, . . . , h?n?1) represented by the limited projective representation is a zero element “0” or an identity element “1” when performing Fp?mn operation that is arithmetic operation of a finite field Fp?mn in combination with the Fp?m operation.

Abstract: A friction drive belt (B) includes a belt body (10) that is wrapped around pulleys in contact therewith to transmit power. At least a pulley contact portion (15) of the belt main body (10) is made of a rubber composition containing 30-80 parts by mass of at least one layered silicate selected from a smectite group and a vermiculite group, per 100 parts by mass of raw rubber containing an ethylene-?-olefin elastomer.