Multiplexed Coding for User Cooperation

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.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a diagram of a two-user cooperative system;

FIG. 2 shows a graph of a low-density parity check (LDPC) code;

FIG. 3 shows a Tanner graph representation of a single parity check code for multiplexing;

FIG. 4 shows a Tanner graph representation of partially multiplexed coding built by irregular repeat accumulate codes; and

FIG. 5 shows a high level block diagram of a computer system which may be used in an embodiment of the invention.

Claims

1. 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

2. 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].

3. A method for decoding a combination of a first message and a second message that were encoded using a generating matrix

4. 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

5. The method of claim 4 wherein the second message is known and the step of decoding comprises: decoding the first message using a component code parity check matrix H1=[P1In-k].

6. The method of claim 4 wherein the first message is known and the step of decoding comprises: decoding the second message using a component code parity check matrix H2=[P2In-k].

7. The method of claim 4 wherein the second message is known, and further comprising the steps: deriving component code parity check matrix H1=[P1In-k] from the generating matrix; anddecoding the first message using the component code parity check matrix.

8. The method of claim 4 wherein the first message is known, and further comprising the steps of: deriving component code parity check matrix H2=[P2In-k] from the generating matrix; and decoding the second message using the component code parity check matrix.

9. 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

10. 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

11. The system of claim 10 wherein the second message is known and the step of decoding comprises: means for decoding the first message using a component code parity check matrix H1=[P1In-k].

12. The system of claim 10 wherein the first message is known and the step of decoding comprises: means for decoding the second message using a component code parity check matrix H2=[P2In-k].

13. The system of claim 10 wherein the second message is known, and further comprising: means for deriving component code parity check matrix H1=[P1In-k] from the generating matrix; andmeans for decoding the first message using the component code parity check matrix.

14. The system of claim 12 wherein the first message is known; and further comprising: means for deriving component code parity check matrix H2=[P2In-k] from the generating matrix; andmeans for decoding the second message using the component code parity check matrix.