Multiplexed Coding for User Cooperation
AssigneeNEC Laboratories America, Inc.
InventorsGuosen Yue, Xiaodong Wang, Mohammad Madihian
Life of this patent
Estimating the term…
Abstract
A method and system for decoding a combination of a first message and a second message that were encoded using a generating matrix of a systematic linear block code is described. The combination of the first message and the second message may be decoded using a parity check matrix. If the second message is known, the first message is decoding using a first component code parity check matrix. If first message is known, the second message is decoded using a second component code parity check matrix. The parity check matrix can be derived from the generating matrix and the first message or the second message can be decoded using the first or second component code parity check matrix.
Claims14
A method for constructing component codes of a partially multiplexed code from a binary systematic (n, k) code, where k=k1+k2=n(R1+R2), with a parity check matrix given by H=└P(n-k)×kIn-k┘=[P1P2I], where P=[P1P2] with dimensions of P1 and P2 given by (n−k)×k1 and (n−k)×k2, respectively, and a generator matrix is then given by
- G
- =
- [
- I
- k
- P
- T
- ]
- =
- [
- I
- k
- 1
- 0
- P
- 1
- T
- 0
- I
- k
- 2
- P
- 2
- T
- ]
- comprising the steps of:
- separating the parity check matrix P=[P1, P2];
- forming the component code G1=[Ik1P1T] using submatrices Ik1, P1T from G;
- form the component code G2=[Ik2P2T] using submatrices Ik2, P2T from G;
- and
- deriving parity check matrices of H1=[P1In-k], H2=[P2In-k].
A method to build a multiplex code from G, a (n−k2, k1) code with the generator G1=[IkaP1T] and a (n−k1, k2) code with the generator G2=[Ik2P2T] comprising the step of:
- deriving component code parity check matrices given by the formula
- H1=[P1In-k], H2=[P2In-k].
A method for decoding a combination of a first message and a second message that were encoded using a generating matrix
- G
- =
- [
- I
- k
- P
- T
- ]
- =
- [
- I
- k
- 1
- 0
- P
- 1
- T
- 0
- I
- k
- 2
- P
- 2
- T
- ]
- of a systematic linear block code comprising the step of:
- decoding the combination of the first message and the second message using a parity check matrix H=└P(n-k)×kIn-k┘=[P1P2I].
A method for decoding one of a first or a second message when the other message is known and wherein both the first message and the second message were encoded using a generating matrix
- G
- =
- [
- I
- k
- P
- T
- ]
- =
- [
- I
- k
- 1
- 0
- P
- 1
- T
- 0
- I
- k
- 2
- P
- 2
- T
- ]
- of a systematic linear block code comprising the step of:
- decoding said one of a first message or a second messages using a component code parity check matrix.
A method for generating multiplexed component codes for a generating matrix G=└I,PAT(PB−1)T┘, comprising:
- generating a generator matrix for a multiplexed code Gmp=└I(k1+k2)×(k1+k2),PZT(PB−1)T;
- separating PA into two parts where PA=[PA;1;
- PA;2], and PA;1:
- m×k1;
- PA;2:
- m×k2 so that
- P
- A
- T
- =
- [
- P
- A
- ,
- 1
- T
- P
- A
- ,
- 2
- T
- ]
- ,
- and
-
-
- G
- mp
- =
- [
- I
- k
- 1
- 0
- P
- A
- ,
- 1
- T
-
- (
- P
- B
- -
- 1
- )
- T
- 0
- I
- k
- 2
- P
- A
- ,
- 2
- T
-
- (
- P
- B
- -
- 1
- )
- T
- ]
- ;
- obtaining component codes with the generator matrices given by
- G
- 1
- =
- [
- I
- k
- 1
- ,
-
- P
- A
- ,
- 1
- T
-
- (
- p
- B
- -
- 1
- )
- T
- ]
- G
- 2
- =
- [
- I
- k
- 2
- ,
-
- P
- A
- ,
- 2
- T
-
- (
- P
- B
- -
- 1
- )
- T
- ]
- with the corresponding parity check matrices given by
- H
- 1
- =
- ⌊
- P
- A
- ,
- 1
- ,
-
- P
- B
- ⌋
- H
- 2
- =
- [
- P
- A
- ,
- 2
- ,
-
- P
- B
- ]
- .
A system for decoding one of a first or a second message when the other message is known and wherein both the first message and the second message were encoded using a generating matrix
- G
- =
- [
- I
- k
-
-
- P
- T
- ]
- =
- [
- I
- k
- 1
- 0
- P
- 1
- T
- 0
- I
- k
- 2
- P
- 2
- T
- ]
- of a systematic linear block code comprising the step of:
- means for decoding said one of a first message or a second messages using a component code parity check matrix.
Dependencies are inferred from the claim text.