Compress-forward Coding with N-PSK Modulation for the Half-duplex Gaussian Relay Channel

Abstract

Systems and methods that implement compress-forward (CF) coding with N-PSK modulation for the relay channel are disclosed, where N is greater than or equal to two. In the CF scheme, Wyner-Ziv coding is applied at the relay to exploit the joint statistics between signals at the relay and the destination. Quantizer design and selection of channel code parameters are discussed. Low-density parity check (LDPC) codes are used for error protection at the source, and nested scalar quantization (NSQ) and irregular repeat accumulate (IRA) codes for Wyner Ziv coding (or more precisely, distributed joint source-channel coding) at the relay. The destination system decodes original message information using (a) a first signal received from the source in a first interval and (b) a second signal that represents a mixture of transmissions from the source and relay in the second interval.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

The following detailed description makes reference to the accompanying drawings, which are now briefly described.

FIG. 1A illustrates one embodiment of a source encoder system.

FIG. 1B illustrates one embodiment of a source encoding method.

FIG. 2A illustrates one embodiment of a relay system.

FIG. 2B illustrates one embodiment of compressing information from a source system and forwarding the compressed information to a destination system.

FIG. 3 illustrates one embodiment of a destination decoder system.

FIG. 4 illustrates one embodiment of a method for recovering message information from signals received from a source system and a relay system.

FIG. 5 shows one embodiment of the relay channel with three nodes: the source, the relay and the destination.

FIG. 6 illustrates one embodiment of the relay channel, where the relay is located along the line between the source and the destination.

FIG. 7 illustrates one embodiment of the CF coding scheme for half-duplex relaying based on WZC (Wyner-Ziv coding).

FIG. 8 shown an example of the conditional distribution of Y_r given particular values of Y_d1, with d=9 m.

FIG. 9 illustrates the distributed joint source-channel coding (DJSCC) of binary source X with decoder side information Y using systematic IRA codes that are designed for both the physical noisy channel and the “virtual” correlation channel between X and Y.

FIG. 10 shows operational distortion-rate curves of SWC-NSQ (assuming ideal SWC after NSQ) of Y_r with decoder side information Y_d1 for several different nesting ratios N, where each curve is generated by varying the quantization stepsize q while fixing N. The lower envelope of these curves is the operational distortion-rate function of SWC-NSQ. The relay is 9 m away from the source, and |c_sd|²=0.85|c_sr|².

FIG. 11A illustrates the conditional probabilities of different NSQ indices given the side information Y_d1 when the nesting ratio is N=4 in the Gaussian relay setup with d=8 m.

FIG. 1B illustrates soft input for iterative decoding of DJSCC as L_ch⁽¹⁾(y_d1) for the first bit plane. For the second bit plane, since the IRA code rate is approximately 1, there is no need to evaluate the information for iterative decoding.

FIGS. 12A and 12B are tables that present the conditional entropy and the corresponding degree distribution polynomials λ(x) and ρ(x) for each bit plane of CF for Gaussian relay channels using nested scalar quantization when (A) d=7 m and (B) d=9 m.

Claims

1. A method for encoding a message m, the method comprising: performing a first low-density parity check (LPDC) channel encoding on a first portion m1 of the message m to obtain first encoded data;performing a second LPDC channel encoding on a second portion m2 of the message m to obtain second encoded data;converting the first encoded data into a first stream of N-PSK constellation points, wherein N is greater than one;converting the second encoded data into a second stream of N-PSK constellation points;generating a first output signal, for transmission to a relay and a destination in a first interval, based on the first stream on N-PSK constellation points;generating a second output signal, for transmission to the destination in a second interval, based on the second stream of N-PSK constellation points.

2. The method of claim 1, wherein the first interval and second interval are disjoint intervals in time.

3. The method of claim 1 wherein said generating the first output signal includes modulating an RF carrier using the first stream of N-PSK constellation points during the first interval in time, wherein said generating the second output signal includes modulating the RF carrier using the second stream of N-PSK constellation points during the second interval in time.

4. The method of claim 1, wherein the first interval and second interval are disjoint bands of frequency.

5. The method of claim 1 wherein said generating the first output signal includes modulating a first RF carrier in the first band of frequency using the first stream of N-PSK constellation points, wherein said generating the second output signal includes modulating a second RF carrier in the second band of frequency using the second stream of N-PSK constellation points.

6. A method comprising: receiving an input signal from a channel in a first interval;recovering from the input signal a stream Yr of N-PSK constellation points, wherein N is greater than one, wherein the stream Yr corresponds to a stream Xs1 of N-PSK constellation points transmitted onto the channel by a source system using N-PSK modulation;performing nested lattice quantization on the stream Yr to generate a quantization value W;performing joint source-channel encoding on the quantization value W to obtain encoded data;converting the encoded data into a stream Xr of N-PSK constellation points;generating an output signal, for transmission to a destination system in a second interval, based on the stream Xr of N-PSK constellation points.

7. The method of claim 6, wherein the first interval and second interval are disjoint intervals in time.

8. The method of claim 6, wherein the first interval and second interval are disjoint bands of frequency.

9. The method of claim 6, wherein a Voronoi volume q of a fine lattice of the nested lattice quantization is optimized to minimize a Wyner-Ziv operational distortion-rate function subject to a rate constraint.

10. The method of claim 6, wherein said performing joint source-channel encoding includes performing an irregular repeat accumulate (IRA) encoding on the quantization value W to obtain the encoded data.

11. The method of claim 6, wherein said performing joint source-channel encoding includes performing a plurality of irregular repeat accumulate (IRA) encodings on corresponding bit planes of the quantization value W to obtain the encoded data.

12. A method for decoding received information in order to recover a message m, the system comprising: receiving a first input signal in a first interval and a second input signal in a second interval;recovering from the first input signal a first stream Yd1 of data and from the second input signal a second stream Yd2 of data, wherein the first stream Yd1 is a first channel-modified version of a stream Xs1 transmitted in the first interval by a source system using N-PSK modulation, wherein N is greater than one, wherein the second stream Yd2 is a mixture including a channel-modified version Vs of stream Xs2 transmitted in the second interval by the source system using said N-PSK modulation and a channel-modified version Vr of a stream Xr transmitted in the second interval by a relay system using said N-PSK modulation, wherein the relay system is configured to (a) receive stream Yr which is a second channel-modified version of the stream Xs1 transmitted by the source system, (b) perform nested lattice quantization on the stream Yr to obtain index W and (b) perform joint source-channel encoding on the index W to obtain the stream Xr;generating an estimate for the index W using the first stream Yd1 and the second stream Yd2;generating an estimate for the stream Yr using the estimate for the index W;performing maximum ratio combining based on the first stream Yd1 and the estimate for the stream Yr in order to obtain likelihood information;performing channel decoding on the likelihood information to generate an estimate for a first portion m1 of the message m.

13. The method of claim 12 further comprising: performing said joint source-channel encoding on the index estimate to obtain an estimate for the stream Xr;scaling the estimate for the stream Xr to obtain an estimate for the channel-modified version Vr;performing channel decoding on a difference between the second stream Yd2 and the estimate of the version Vr to generate an estimate for a second portion m2 of the message m.

14. The method of claim 12, wherein the first interval and second interval are disjoint intervals in time.

15. The method of claim 12, wherein the first interval and second interval are disjoint bands of frequency.

16. The method of claim 12, wherein the iterative decoder is configured to reverse an effect of said joint source-channel encoding of the relay system.

17. A computer system comprising: a memory medium configured to store program instructions;a processor configured to access the program instructions from the memory medium and execute the program instructions, wherein the program instructions are executable to implement: receiving an input signal from a channel in a first interval;recovering from the input signal a stream Yr of data, wherein the stream Yr corresponds to a stream Xs1 of N-PSK constellation points transmitted onto the channel by a source system using N-PSK modulation, wherein N is greater than one;performing nested lattice quantization on the stream Yr to generate a quantization value W;performing joint source-channel encoding on the quantization value W to obtain encoded data;converting the encoded data into a stream Xr of N-PSK constellation points;generating an output signal, for transmission to a destination system in a second interval, based on the stream Xr of N-PSK constellation points.

18. The computer system of claim 17, wherein the first interval and second interval are disjoint intervals in time.

19. The computer system of claim 17, wherein the first interval and second interval are disjoint bands of frequency.

20. The computer system of claim 17, wherein said performing joint source-channel encoding includes performing a plurality of irregular repeat accumulate (IRA) encodings on corresponding bit planes of the quantization value W to obtain the encoded data.

21. A computer-readable memory medium configured to stored program instructions, wherein the program instructions are executable to implement: receiving an input signal from a channel in a first interval;recovering from the input signal a stream Yr of data, wherein the stream Yr corresponds to a stream Xs1 of N-PSK constellation points transmitted onto the channel by a source system using N-PSK modulation, wherein N is greater than one;performing nested lattice quantization on the stream Yr to generate a quantization value W;performing joint source-channel encoding on the quantization value W to obtain encoded data;converting the encoded data into a stream Xr of N-PSK constellation points;generating an output signal, for transmission to a destination system in a second interval, based on the stream Xr of N-PSK constellation points.

22. The memory medium of claim 21, wherein the first interval and second interval are disjoint intervals in time.

23. The memory medium of claim 21, wherein the first interval and second interval are disjoint bands of frequency.