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User Cooperation via Rateless Coding

Mahyar Shirvanimoghaddam, Yonghui Li, and Branka Vucetic

The University of Sydney, Australia

IEEE GLOBECOM 2012 & IEEE ISIT(International Symposium on Information Theory) 2012

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Outlines

• Introduction• Rateless coded cooperation• Degree distribution optimization of PCC scheme• Simulation results• Conclusion

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Introduction

• User cooperation allows users to not only transmit their own information, but also help other users in forwarding their messages– Multiple transmission– Cooperative diversity

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Introduction

• Coded cooperation is a user cooperation scheme where each user broadcasts its coded messages, tries to decode its partners’ codeword and calculates additional parity symbols before forwarding them to the destination.– Cooperative diversity – Coding gain

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Introduction

• Aim of this paper – This paper aims to design and optimize rateless

coded cooperation in two-user cooperative multiple access channel (MAC) to maximize system throughput.

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Introduction• Rateless codes have shown to significantly improve the transmission

efficiency when applied to coded cooperation– Simple design & implementation – Low complexity encoding & decoding – Unlimited parity bit generation – Self-adaptation to channel condition – No pre-determined rate

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System Model

• Two-user cooperative multiple access channel, where each user (U1 or U2) wants to transmit information symbols to the destination, D, via the help of the other user.

• Let e1, e2 and e denote the erasure probability of the channel between U1 and D, U2 and D, and that between U1 and U2, respectively.

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Significance

• Increases cellular capacity and coverage area• Increases WLAN capacity and coverage area• High link stability in Vehicle-to-Vehicle

communication• Increases coverage area of wireless sensor

networks and optimizes their life time in respect to power constraints

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Advantages of Cooperation

• Large system performance gain relative to diversity and multiplexing gain

• Increases capacity and coverage• Provides equal QoS to all users• No need for a predefined structure• Cost effective

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Conventional schemes

• There are two separate transmission phases :– 1) Broadcast phase: Each user encodes k

information symbols using a LT code and keeps transmitting the coded symbols until it receives an acknowledgement from the other user.• Fully Coded Cooperation (FCC)

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Conventional schemes

– 2) Cooperative phase: Each user applies a LT code to perform joint encoding of 2k information symbols

• Drawbacks– 1) Requires feedback between users– 2) Requires separate degree distribution in each phase– 3) Starts cooperation phase only after users have

completely decoded one another– 4) Never starts cooperation phase in cases with poor

inter-user channel

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Proposed schemes

• Partially Coded Cooperation (PCC), as soon as each user has decoded even one bit of another user, coded bits are generated from its own information and the recovered bits.

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Proposed schemes

• Each user first generates N coded symbols from its own information symbols using a LT code with the degree distribution Ω(x), and transmits them to the other user and the destination in its allocated time slot in in the first time frame (TF1)

• Upon receiving coded symbols in TF1, each user starts the decoding process to recover other user’s information symbols.

• Assume that Ui has recovered sl (i) information symbols from the

other user in TFl, where

• In the next time frame, TF2, Ui generates N coded symbols using its k information symbols as well as s1

(i) information symbols from the other user, and transmits these coded symbols to the other user and the destination.

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Proposed schemes

• In each time frame, each user generates coded symbols from its own information symbols and those from the other user which have been recovered in previous time frames, and broadcast them.

• At a same time, each user tries to recover more information symbols from the other user by overhearing its transmission and performing LT decoding process in each time frame.

• When the destination successfully decodes both users’ information symbols, it sends an acknowledgment and users start broadcasting new messages

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Advantages over FCC

• Requires NO feedback between users • Starts cooperation phase even when users can

decode only one bit • Adds NO additional complexity to FCC • Capable of user cooperation even with poor

inter user channel • Achieves higher throughput • Requires only one degree distribution

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Degree distribution optimization of PCC scheme

• The overall codeword received at the destination consists of – 1) the coded symbols transmitted in the broadcast phase with

the degree distribution Ω1(x)

– 2) in the cooperative phase with the degree distribution Ω2(x)– the degree distribution of the overall codeword at the

destination are different• In [14], a linear programming optimization problem has

been formulated to find the optimum degree distribution in the broadcast phase and the cooperative phase.

[14] M. Shirvanimoghaddam, Y. Li, and B. Vucetic, “Distributed rateless coding with cooperative sources,” in Proceedings. IEEE International Symposum on Information Theory (ISIT), July 2012.

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Degree distribution optimization of PCC scheme

• In PCC, each user transmits N coded symbols in each time frame and some of them may be erased by the channel, each users receives on average N(1 - e) coded symbols from the other user.

• Consider that each user can recover si information symbols in TFi.

• In the next time frame, each user encodes the partially decoded symbols of the other user, together with its own information symbols, to generate a new packet of length N, and transmits it to the destination.

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Degree distribution optimization of PCC scheme

• In TFi+1, the received coded symbols at each user have been generated from k + si information symbols using Ω(x) as the degree distribution

• si information symbols of each user are already known at the other user in TFi+1, all edges connected to the known symbols can be removed from the bipartite graph at users

• To generate a coded symbol of degree d+l, d+l information symbols are selected uniformly at random from k + si information symbols

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Degree distribution optimization of PCC scheme

• The probability that this coded symbol is connected to l known information symbols and d unknown information symbols is

• The probability that this coded symbol has a degree d+l is d+l when l varies from 0 to si

• The probability that a coded symbol has degree d, after removing all the edges connected to the known information symbols, can be calculated as follows

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Degree distribution optimization of PCC scheme

• Since each user tries to decode the other user message from the received coded symbols in TFi+1 and the previous time frames, the number of coded symbols in TFi+1 will be N(i+1) = (i+1)N(1-e)

• The probability that a coded symbol is of degree d in TFi+1

which arises from the fact that a specific coded symbol is received in TFj with probability N(1- e) / N(i+1) and it is of degree d with probability

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Degree distribution optimization of PCC scheme

• Insert (4) into (5)

• If the degree distribution of coded symbols is Ω(x), the probability that an information symbol is not recovered after l iterations is pl = where

• In PCC scheme, the degree distribution of coded symbols in TFi is at each user.

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Degree distribution optimization of PCC scheme

• The probability that an information symbol is not recovered after l iterations, denoted by pl

where • si can be calculated as k(1-pl) when l and k go

to infinity.

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Fig. 4. Ratio of recovered intermediate symbols in different time frames

The fraction of recovered information symbols in each TF for the case that N = 100, k = 1000 and

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Degree distribution optimization of PCC scheme

• Let Pi and Qi denote the i-th part of U1 and U2

• The length of Pi is the same as the length of Qi and it equals to si - si-1

• When the destination already knows si information symbols of each user, it removes all edges connected to these symbols.

• The degree distribution of coded symbols will be

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Degree distribution optimization of PCC scheme

• To ensure that the destination can decode the remaining information symbols, the following condition needs to be satisfied

for x [0, 1-δ] and some constant ri, c and δ• To find the optimum degree distribution, (9) needs to

be satisfied for all i’s. Therefore, the optimization problem can be summarized as follows

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• For given si’s, the objective function and all constraints are linear in terms of Ω(x) and ri, so the optimization problem can be solved by means of linear programming.

• Several optimized degree distributions

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Simulation Results• Settings

– Assume that the transmitter has no knowledge of channel state information of any channel, either inter-user channel or the user to the destination channel.

– N = 1000– k = 10000

• No-cooperation scheme– Each user only generates coded symbols from its own information symbols and

transmits them to the destination without any cooperation with the other user. • Perfect-cooperation scheme

– Assume that each user knows perfectly the other user’s message before its transmission.

– Each user generates coded symbols from both users’ information symbols and sends them to the destination.

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Similar to the relay channel scenario, because information symbols of U2 are only sent by U1.

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Conclusions

• The PCC scheme effectively combines advantages of rateless codes with coded cooperation techniques to increase overall system throughput with no additional complexity compared to existing schemes.

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References• [13] W. Chen and W. Chen, “A new rateless coded cooperation scheme

for multiple access channels,” in Proceedings. IEEE International Conference on Communications (ICC), pp. 1 –5, June. 2011.

• [14] M. Shirvanimoghaddam, Y. Li, and B. Vucetic, “Distributed rateless coding with cooperative sources,” in Proceedings. IEEE International Symposum on Information Theory (ISIT), July 2012.

• [15] S. Kim and S. Lee, “Improved intermediate performance of rateless codes,” in Proceedings. 11th International Conference on Advanced Communication Technology (ICACT), vol. 03, pp. 1682 –1686, Feb. 2009.

• [16] A. Talari and N. Rahnavard, “Rateless codes with optimum intermediate performance,” in Proceedings. IEEE Global Telecommunications Conference (GLOBECOM), Dec. 2009.