The multiple description coding of an independent and identically distributed Gaussian source over bit error channels is considered. A novel practical multiple description coding scheme is proposed based on scalar embedded quantizers and rateless codes. A peer-to-peer network model is studied where users can receive different number of descriptions and an arbitrary large number of descriptions can be created and transmitted between peers. For this network model convex system optimization problems are defined and solved. The proposed scheme can be regarded as an efficient implementation of "channel optimized quantization", where the index assignment is obtained via a low-complexity linear function. The scheme is shown to be robust to bit errors and to achieve higher reconstruction signal-to-noise ratios when compared to previously reported designs.
I. INTRODUCTIONIn the Multiple Description (MD) coding problem, a block of source symbols is encoded into several coded blocks referred to as "descriptions", such that any subset of these descriptions can be used to reconstruct the source with certain distortion. In the most general case, MD is yet an open problem in information theory, with the exception of the two-description Gaussian-quadratic case [1]. Achievable information theoretic schemes for the general case [1], [2], and practical MD schemes for multimedia applications such as image [3], video [4], audio [5] have been proposed.An immediate application of MD coding for multimedia communications is represented by peer-to-peer (P2P) networks. In conventional systems, compressed sources are stored in one or several servers. Clients download the desired source from a server. However, due to the potentially very large number of requests, servers must employ costly high-speed connections and back-up redundancy techniques to avoid delays and system failures. In contrast, in P2P networks, the information is exchanged among a large number of peer terminals. By spreading information throughout the P2P network, none of the peer terminals must be particularly reliable or be connected with particularly high-speed links. Indeed, each user will "grab" the desired source scattered into many pieces among the peers, and reconstruct it by combining the pieces. To fight against "peer going down" events or packet losses, MD coding can be used. Though, this application requires a very flexible, simple, simultaneous, independent MD encoding by different source nodes [6]. The design should work with any number of descriptions and in order to avoid extra communication, each node should locally create a description but still a receiver should be able to seamlessly combine these descriptions. As will be seen in Section III-B1, the novel scheme proposed in this paper based on rateless codes has these properties.Existing explicit MD coding constructions can be grouped into two classes: schemes based on signal processing methods such as MD scalar quantizers (MDSQ) [7], vector