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We propose a novel packetization and variable bitrate compression scheme for DSR source coding, based on the Group of Pictures concept from video coding. The proposed algorithm simultaneously packetizes and further compresses source coded features using the high interframe correlation of speech, and is compatible with a variety of VQ-based DSR source coders. The algorithm approximates vector quantizers as Markov Chains, and empirically trains the corresponding probability parameters. Feature frames are then compressed as I-frames, P-frames, or B-frames, using Huffman tables. The proposed scheme can perform lossless compression, but is also robust to lossy compression through VQ pruning or frame puncturing. To illustrate its effectiveness, we applied the proposed algorithm to the ETSI DSR source coder. The algorithm provided compression rates of up to 31.60% with negligible recognition accuracy degradation, and rates of up to 71.15% with performance degradation under 1.0%.