Partial Reed Solomon Codes for Erasure Channels

In this paper, we introduce a new family of linear block codes, which we refer to as Partial Reed Solomon (PRS) Codes. These codes are specifically designed and optimized for real-time multimedia communication over packet-based erasure channels. Based on the constraints and flexibilities of real time applications, we define a performance measure, message throughput ( m τ ), which is suitable for these applications. This measure differentiates the notion of optimum codes for the target multimedia applications as compared to performance measures that are used for non-realtime data. Based on the proposed measure, we combine the advantages of lowering the density of a code for near capacity performance with the high decoding efficiency of Reed Solomon (RS) codes, in order to design optimum PRS codes. Then, we demonstrate, through an example of a Binary Erasure Channel (BEC), that at near-capacity coding rates, appropriate design of a PRS code can outperform an RS-code. We extend this analysis and optimization for a general BEC over a wide range of channel conditions. Moreover, as compared with RS codes, the proposed PRS codes provide a significantly improved graceful degradation when the number of losses exceeds the number of parity symbols within the code block. This is a highly desirable feature for realtime multimedia applications.