Source–Channel Diversity for Parallel Channels

J.N. Laneman, E. Martinian, G.W. Wornell, J.G. Apostolopoulos
2005 IEEE Transactions on Information Theory  
We consider transmitting a source across a pair of independent, non-ergodic channels with random states (e.g., slow fading channels) so as to minimize the average distortion. The general problem is unsolved. Hence, we focus on comparing two commonly used source and channel encoding systems which correspond to exploiting diversity either at the physical layer through parallel channel coding or This work has been presented in part at DRAFT SUBMITTED TO IEEE TRANS. ON INFORM. THEORY the mutual
more » ... rmation in a Taylor series for high signal-to-noise ratio. See Section IV-A for details. May 11, 2005 DRAFT SUBMITTED TO IEEE TRANS. ON INFORM. THEORY 6 Cover develop an achievable rate region for two descriptions in [28], and this region is shown to be optimal for the Gaussian source, with mean-square distortion, by Ozarow [44]. Specialized results for the binary symmetric source, with Hamming distortion, are developed by Berger & Zhang [24], [26], [45] and Ahlswede [27]. Zamir [23] develops high-rate bounds for memoryless sources. Most recently, work by Venkatarami et. al [3], [21] provides achievable rate regions for many descriptions that generalize the results in [26], [28]. Important special cases of the MD coding problem have also been examined, including successive refinement, or layered coding, [1], [46] and certain symmetric cases [2], [20]. Some practical approaches to MD coding include MD scalar quantization, dithered MD lattice quantization, and MD transform coding. Vaishampayan [25] pioneered the former, Frank-Dayan and Zamir considered the use of dither [7], and Wang, Orchard, Vaishampayan, and Reibman [22] and later Goyal & Kovacevic [16] studied the latter. See [17] for a thorough review of both approaches. Recently, the design of MD video coders has received considerable attention [4], [8]-[10], [13], [19] All of the classical work on MD coding utilizes an "on-off" model for the channels or networks under consideration, without imposing strict delay constraints. More specifically, source codes are designed assuming that each description is completely available (error-free) at the receiver, or otherwise completely lost. Furthermore, the likelihood of these events occurring is independent of the choice of source coding rates. Under such conditions, it is not surprising that MD coding outperforms SD coding; however, for many practical channel and network environments, these conditions do not hold. For example, in delay constrained situations, suitable for real-time or interactive communication, descriptions may have to be encoded as multiple packets, each of which might be received or lost individually. Furthermore, congestion and outage conditions often depend heavily upon the transmission rate. Thus, it is important to consider MD coding over more practical channel models, as well as to fairly compare performance with SD coding. Some scattered work is appearing in this area. Ephremides et. al [11] examine MD coding over a parallel queue channel, compare to SD coding, and show that MD coding offers significant advantages under high traffic (congestion) situations. This essentially results because the MD packets are more compact than SD packets, and indicates the importance of considering the influence of rate on congestion. Coward et. al [6], [15] examine MD coding over several channel models, including memoryless symbol-erasure and symbol-error channels, as well as block fading channels. For strict delay constraints, they show that MD outperforms SD; for longer delay constraints, allowing for more sophisticated channel coding, they show that SD outperforms MD. Thus, the impact of delay constraints are important. This paper examines fading conditions similar to those in [6], [15], but considers a wider variety of channel coding and decoding May 11, 2005 DRAFT
doi:10.1109/tit.2005.855578 fatcat:yp7ukp4bvfdrhj3qo5dqrqhaae