CN104202117B - A kind of structure code method of unique decodable code based on traversal mode - Google Patents
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Abstract
A kind of structure code method of unique decodable code based on traversal mode, the present invention relates to the structure code method of the unique decodable code based on traversal mode.The present invention is to solve prior art can not at the same time with cause under the premise of frequency multi-user and speed be more than 1 and with speed it is not ideal enough the problem of, a kind of and structure code method of the unique decodable code based on traversal mode proposed.This method is the codeword set C by 1, hypothesis user 11For (n, k) linear block codes；The 2nd, the codeword set C of user 2 is set2Initial value be empty set, while the initial value for setting set E is empty set；3rd, obtain | C1| individual ternary vector；Whether the ternary vector the 4th, obtained in judgment step three is in set E；5th, by element x, it is added to set C2In, incite somebody to action simultaneously | C1| in individual ternary vector deposit set E；6th, unique decodable code C is obtained1With unique decodable code C2The step such as the set E of sum of code word realize.Structure code field of the present invention applied to unique decodable code.
Description
Technical Field
The invention relates to a unique decodable code constructing method based on a traversal mode.
Background
With the development of science and technology and the progress of the era, the requirements of people on the information transmission rate are gradually increased. When a plurality of users need to access simultaneously, the prior art, no matter Time Division Multiple Access (TDMA), Frequency Division Multiple Access (FDMA) and Code Division Multiple Access (CDMA), can not make the multi-user sum rate greater than 1 on the premise of simultaneous same frequency. The unique decoding starts from the information theory and the coding angle, firstly, the information coding is carried out on different user information through corresponding unique decoding, and then when a plurality of users access a channel at the same frequency, the information sent by different users is distinguished at a receiving end through a decoding pattern detection mode. Although for each user, the information rate is less than 1 due to the unique decodable encoding scheme; but because the same frequency can simultaneously support the simultaneous transmission of a plurality of users, the sum rate of information is greater than 1 when the users access. Through reasonable construction, unique decoding is realized, and each user sending information has a certain degree of error correction and detection capability. By applying unique decoding not only on wireless multiple access channels but also in wired channels, multiple users can access a common channel simultaneously.
The only decodable code was originally proposed by h.h.j.liao in 1972, and later through research by Lin Shu, j.k.wolf et al, the only decodable code itself has the capability of error correction and error detection, and Lin proposes a code constructing mode for constructing the only decodable code by a coset code constructing mode. Then y.w.wu and s.c.chang propose unique decodable of multiple resources, and j.cheng and k.kamoi and y.watanabe propose unique decodable based on Hadamard matrix with error correction capability for multiple resource construction in 2006. The only decodable code structure mode is coset structure code, but the only decodable code group obtained by the coset structure code is not ideal in rate although the method is simple.
Disclosure of Invention
The invention aims to solve the problems that in the prior art, no matter Time Division Multiple Access (TDMA), Frequency Division Multiple Access (FDMA) or Code Division Multiple Access (CDMA), the sum rate of multiple users is larger than 1 and the sum rate is not ideal enough on the premise of same frequency, and provides a unique decodable code constructing method based on a traversal mode.
The above-mentioned invention purpose is realized through the following technical scheme:
step one, assume the code word set C of user 11Is (n, k) linear block code, where n is code length, k is effective information bit, code word set C1Is provided with 2kAvailable code word | C1I.e. C1L is C1The number of code words, n ═ 1,2, 3 …;
step two, setting a code word set C of a user 22Setting the initial value of the set E as an empty set; the cyclic variable j is 1;
step three, taking out VnThe jth element x of (a), the element x and the codeword set C1All of | C in1The | elements are summed according to bit to obtain | C1| three ternary vectors, and | C obtained simultaneously1Storing | ternary vectors into a set E, wherein the length of each ternary vector is n; x is an n-dimensional vector; cyclic variable j-1, 2, 3 …,2n；VnSet of n-dimensional vectors representing all GF (2) in the Galois field, C1And C2Is VnTwo subsets of (a);
step four, let j become j +1, and judge | C obtained in step three1If all ternary vectors are transferred to the step five in the set E; if all the ternary vectors are not in the set E, C corresponding to the ternary vectors not in the set E is obtained2Turning to the third step;
step five, adding the element x into the set C2Simultaneously adding | C obtained in the third step1Storing | ternary vectors into a set E;
step six, judging whether j is equal to 2n+1, if not, go j to step three; if yes, the method ends to obtain the only user 1Decodable C1User 2's unique decodable C2And a unique decodable C1And a unique decodable C2A set E of sums of codewords of; and assume that the code rates of user 1 and user 2 are R, respectively1And R2Definition of R1＝(log2|C1|)/n，R2＝(log2|C2|)/n；R1+R2＝log2(C1|×|C2I)/n; namely, a unique decodable code constructing method based on a traversal mode is completed.
Effects of the invention
The invention constructs the unique decodable pair by adopting a traversing mode aiming at two users, so that the information and the speed of the two users are improved compared with the unique decodable pair constructed by the coset structure code, the information and the speed of a multi-access system are increased, and the throughput is improved. Furthermore, in the case that one of the user code word sets is known, the present invention can select a plurality of code word sets which are used by another user and satisfy the unique interpretable condition through the traversal method.
Compared with the traditional coset structure code, the invention assumes a code word set C1And C2The code length n of (2) is 4. C1In the case of linear block codes, C is not present1Is 0000,0011,1100,1111, namely C1Code rate R of10.5, a codeword set C of a conventional coset-structured code construction2Is 0000,0001,0100,1010,1110,1011,0101. So according to the conventional coset-structured code scheme C2Having 7 elements, C2Code rate R of2Is (log)27) 0.702 for/4, and rate R1+R2＝1.202。
For the same C1The invention provides a unique decodable code constructing method based on traversal, and a code word set C is obtained2Is {0000,0001,0010,0100,0101,0110,1000,1001,1010}, at which time C2Having 9 elements, C2Code rate R of2Is (log)29) 0.792, so the resulting sum rate is R1+R2Is 1.292. Therefore, compared with the traditional coset code constructing method, the unique decodable code constructing method based on traversal provided by the invention has higher sum rate, so that the system has higher throughput.
Drawings
FIG. 1 is a schematic diagram of a unique decodable application environment according to the fourth embodiment;
fig. 2 is a flowchart of a unique decodable code constructing method based on a traversal manner according to an embodiment.
Detailed Description
The first embodiment is as follows: the unique decodable code constructing method based on the traversal mode is specifically prepared according to the following steps:
step one, assume the code word set C of user 11Is (n, k) linear block code, where n is code length, k is effective information bit, code word set C1Is provided with 2kAvailable code word | C1I.e. C1L is C1The number of code words, n ═ 1,2, 3 …;
step two, setting a code word set C of a user 22Setting the initial value of the set E as an empty set; the cyclic variable j is 1;
step three, taking out VnThe jth element x of (a), the element x and the codeword set C1All of | C in1The | elements are summed according to bit to obtain | C1L ternary vectors (taking C)1All of (A) to (B)1Respectively carrying out bitwise summation with x to obtain | C1| ternary n-dimensional vectors) and the resultant | C' s1The | ternary vectors, each of which is long, are stored in a set EDegree n (i.e. C)1And C2The code length of (1) is n); x is an n-dimensional vector; cyclic variable j-1, 2, 3 …,2n；VnSet of n-dimensional vectors representing all GF (2) in the Galois field, C1And C2Is VnTwo subsets of (a);
step four, let j become j +1, and judge | C obtained in step three1If all ternary vectors are transferred to the step five in the set E; if all the ternary vectors are not in the set E, C corresponding to the ternary vectors not in the set E is obtained2Turning to the third step;
step five, adding the element x into the set C2Simultaneously adding | C obtained in the third step1Storing | ternary vectors into a set E;
step six, judging whether j is equal to 2n+1, if not, go j to step three; if so, the unique decodable (code word set) C of the user 1 is obtained1User 2's unique decodable (codeword set) C2And a unique decodable C1And a unique decodable C2A set E of sums of codewords of; and assume that the code rates of user 1 and user 2 are R, respectively1And R2Definition of R1＝(log2|C1|)/n，R2＝(log2|C2|)/n；R1+R2＝log2(|C1|×|C2I)/n; a unique decodable code constructing method based on a traversal mode is completed as shown in fig. 2.
The effect of the embodiment is as follows:
the embodiment adopts a traversal mode to construct the unique decodable pair aiming at two users, so that the information and the speed of the two users are improved compared with the unique decodable pair constructed by the coset structure code, the information and the speed of a multi-access system are increased, and the throughput is improved. Furthermore, in the case where one of the user code word sets is known, the present embodiment may select, through the traversal method, a plurality of code word sets that are intended for another user and satisfy the unique interpretable condition.
This embodiment is compared with the conventional coset structure code, and this embodiment assumes a codeword set C1And C2The code length n of (2) is 4. C1In the case of linear block codes, C is not present1Is 0000,0011,1100,1111, namely C1Code rate R of10.5, a codeword set C of a conventional coset-structured code construction2Is 0000,0001,0100,1010,1110,1011,0101. So according to the conventional coset-structured code scheme C2Having 7 elements, C2Code rate R of2Is (log)27) 0.702 for/4, and rate R1+R2＝1.202。
For the same C1The unique decodable code constructing method based on traversal provided by the embodiment obtains a code word set C2Is {0000,0001,0010,0100,0101,0110,1000,1001,1010}, at which time C2Having 9 elements, C2Code rate R of2Is (log)29) 0.792, so the resulting sum rate is R1+R2Is 1.292. Therefore, compared with the traditional coset code constructing method, the unique decodable code constructing method based on traversal provided by the embodiment has higher sum rate, so that the system has higher throughput.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: step one is | C1I is:
|C1|＝2kwherein k is 1,2, 3 …. Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: v in step IIInThe elements of the set are ordered from all 0 s to all 1 s, i.e. by VnBinary value corresponding to each element of the setIn order from small to large. Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: unique decodable C in step six1And C2The specific derivation process is as follows:
(1) if u ∈ C1，v∈C2，C1And C2The code length of (a) is n, and the code lengths of u and v are also n; wherein u and V are VnTwo vectors in, u in the codeword set C1V is in codeword set C2In (u) ═ u1,u2,…,un) And v ═ v (v)1,v2,…,vn)；
(2) The set E is the set of all E (u, v); the E (u, v) code length is also n;
(3) definition E (u, v) denotes an n-dimensional vector (E (u)1,v1),E(u2,v2),…,E(un,vn) E (u ', v') represents an n-dimensional vector (E (u)1',v1'),E(u'2,v'2),…,E(u'n,v'n) For the ith element, E (u)i,vi)＝ui+vi，E(ui',vi')＝ui'+vi', so E (u, v) is an n-dimensional vector with each element belonging to {0,1,2 };
(4) each user has a corresponding encoder, the information sent by each user is distinguished through a decoder of a receiving end, a user 1 obtains u through a unique translatable encoder 1, a user 2 obtains v through the unique translatable encoder 1, u and v are sent to a multiple access channel to obtain E (u, v), and the E (u, v) is obtained through the decoderAndthen holdIs sent to the data link 1 corresponding to the user 1To the data link 2 corresponding to user 2, if and only if for any u, u' ∈ C1(u and u' are optionally C1Two different codewords) and arbitrary v, v' ∈ C2(v and v' are optionally C2Two different codewords) satisfying codewords (u, v) and (u ', v') satisfying E (u, v) ≠ E (u ', v') (C)1,C2) Is uniquely decodable; c1And C2The code length of (A) is n; if (C)1,C2) Is uniquely decodable, then C1And C2At most, only one identical vector; i.e. a set of code words C1And a codeword set C2Constitute the only decodable code as in FIG. 1; wherein,representing the results after u and v decoding, respectively. Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: unique decodable (codeword set) C in step six1Has | C1I codewords, uniquely decodable (codeword set) C2Has | C2| codewords, set E has | C1|×|C2L elements. Other steps and parameters are the same as in one of the first to fourth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the unique decodable code constructing method based on the traversal mode is specifically prepared according to the following steps:
assume a codeword set C1And C2The code length n is 4; c1In the case of linear block codes, C1Is 0000,0011,1100,1111, namely C1Code rate R of10.5, a codeword set C of a conventional coset-structured code construction2Is 0000,0001,0100,1010,1110,1011,0101. So according to the conventional coset-structured code scheme C2Having 7 elements, C2Code rate R of2Is (log)27) 0.702 is set to/4, so the sum rate is R1+R2＝1.202。
For the same C1The invention provides a unique decodable code constructing method based on traversal, and a code word set C is obtained2Is {0000,0001,0010,0100,0101,0110,1000,1001,1010}, at which time C2Having 9 elements, C2Code rate R of2Is (log)29) 0.792, so the resulting sum rate is R1+R2Is 1.292. Therefore, compared with the traditional coset code constructing method, the unique decodable code constructing method based on traversal provided by the invention has higher sum rate, so that the system has higher throughput. At this time C1，C2And set E, shown in table 1:
TABLE 1 coded C of the invention1，C2And set E
Step one, assume the code word set C of user 11Is (4, 2) linear block code, where 4 is code length, 2 is effective information bit, code word set C1Is provided with 22One available codeword, | C1L is C1Number of code words, i.e. | C1|＝4；
Step two, setting a code word set C of a user 22Is an empty set, while a set is setThe initial value of E is a null set; the cyclic variable j is 1;
step three, taking out V4The jth element x of (a), the element x and the codeword set C1All 4 elements in the set are summed according to bit to obtain 4 ternary vectors, and the obtained 4 ternary vectors are stored in a set E, wherein each ternary vector has a length of 4 (namely C)1And C2The code length of (2) is 4); x is a 4-dimensional vector; cyclic variable j-1, 2, 3 …,24；V4Represents the set of all 4-dimensional vectors in the Galois field GF (2), and V4The elements of the set are sorted from all 0 to all 1, and are arranged according to the sequence from small to large of the binary value corresponding to each element; c1And C2Is V4Two subsets of (a);
step four, making j equal to j +1, and judging 4 ternary vectors obtained in the step three, if all the ternary vectors are transferred to the step five in the set E; if all the ternary vectors are not in the set E, C corresponding to the ternary vectors not in the set E is obtained2Turning to the third step;
step five, adding the element x into the set C2Storing the 4 ternary vectors obtained in the step three into a set E;
step six, judging whether j is equal to 24+1, if not, go j to step three; if yes, ending obtaining the code word set C of the user 11Codeword set C for user 22And C1And C2E, the set of sums of codewords. Wherein, the code word set C1There are 4 codewords, codeword set C2Has | C2| codewords, set E has 4| C2L elements.
Let C1Is a first order RM code with a code length of 16. Then, C1Wherein each row vector represents an available codeword, C1Code rate R of15/16-0.312.
Through the unique decodable code constructing scheme based on traversal provided by the patent, the constructed code word is shown as appendix C2Is 33945, then C2Has a code rate of (log)233945) And/16 is 0.941. So that the sum rate at this time is R1+R2Is 1.253. Therefore, the method is suitable for code words with different code lengths, and when the code length is long, the code rate is still better, and when the code length is longer, the code rate of one user can be approximate to 1.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (5)
1. A unique decodable code constructing method based on traversal mode is characterized in that: a unique decodable code constructing method based on a traversal mode is specifically carried out according to the following steps:
step one, assume the code word set C of user 11Is (n, k) linear block code, where n is code length, k is effective information bit, code word set C1Is provided with 2kAvailable code word | C1I.e. C1L is C1The number of codewords of the code, n 1,2, 3.;
step two, setting up user 2Set of code words C2Setting the initial value of the set E as an empty set; the cyclic variable j is 1;
step three, taking out VnThe jth element x of (a), the element x and the codeword set C1All of | C in1The | elements are summed according to bit to obtain | C1| three ternary vectors, and | C obtained simultaneously1Storing | ternary vectors into a set E, wherein the length of each ternary vector is n; x is an n-dimensional vector; cyclic variable j-1, 2, 3 …,2n；VnSet of n-dimensional vectors representing all GF (2) in the Galois field, C1And C2Is VnTwo subsets of (a);
step four, let j become j +1, and judge | C obtained in step three1If all ternary vectors are transferred to the step five in the set E; if all the ternary vectors are not in the set E, C corresponding to the ternary vectors not in the set E is obtained2Turning to the third step;
step five, adding the element x into the set C2Simultaneously adding | C obtained in the third step1Storing | ternary vectors into a set E;
step six, judging whether j is equal to 2n+1, if not, go j to step three; if yes, the unique decipherable C of the user 1 is obtained1User 2's unique decodable C2And a unique decodable C1And a unique decodable C2A set E of sums of codewords of; and assume that the code rates of user 1 and user 2 are R, respectively1And R2Definition of R1＝(log2|C1|)/n，R2＝(log2|C2|)/n；R1+R2＝log2(|C1|×|C2I)/n; namely, a unique decodable code constructing method based on a traversal mode is completed.
2. The unique decodable code constructing method based on traversal manner as claimed in claim 1, wherein: step one is | C1I is:
|C1|＝2kwherein k is 1,2, 3.
3. The unique decodable code constructing method based on traversal manner as claimed in claim 1, wherein: v in step IIInThe elements of the set are ordered from all 0 s to all 1 s, i.e. by VnThe binary values corresponding to each element of the set are arranged in order from small to large.
4. The unique decodable code constructing method based on traversal manner as claimed in claim 1, wherein: unique decodable C in step six1And C2The specific derivation process is as follows:
(1) if u ∈ C1，v∈C2，C1And C2The code length of (a) is n, and the code lengths of u and v are also n; wherein u and V are VnTwo vectors in, u in the codeword set C1V is in codeword set C2In (u) ═ u1,u2,…,un) And v ═ v (v)1,v2,…,vn)；
(2) The set E is the set of all E (u, v); the E (u, v) code length is also n;
(3) definition E (u, v) denotes an n-dimensional vector (E (u)1,v1),E(u2,v2),…,E(un,vn) And E (u ', v ') represents an n-dimensional vector (E (u '1,v′1),E(u'2,v'2),…,E(u'n,v'n) For the ith element, E (u)i,vi)＝ui+vi，E(ui',vi')＝ui'+vi', so E (u, v) is an n-dimensional vector with each element belonging to {0,1,2 };
(4) user 1 gets u through the unique translatable encoder 1, user 2 gets v through the unique translatable encoder 1, u and v are sent to a multiple access channel to get E (u, v), and E (u, v) is obtained through a decoderAndthen holdIs sent to the data link 1 corresponding to the user 1To the data link 2 corresponding to user 2, if and only if for any u, u' ∈ C1And optionally v, v' ∈ C2(C) when codewords (u, v) and (u ', v') satisfy E (u, v) ≠ E (u ', v') (C)1,C2) Is uniquely decodable; c1And C2The code length of (A) is n; wherein,representing the results after u and v decoding, respectively.
5. The unique decodable code constructing method based on traversal manner as claimed in claim 1, wherein: unique decodable C in step six1Has | C1L codewords, uniquely decodable C2Has | C2| codewords, set E has | C1|×|C2L elements.
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