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This paper presents a lossless compression algorithm for the binary indices of the embedded algebraic vector quantizer (EAVQ) used by the AMR-WB (Extended Adaptive Multi-Rate Wide Band) codec. We present a statical study of the EAVQ indices for diverse audio types (speech, music, etc.) and we discuss the design of the lossless algorithm including the choice of different strategies. The proposed algorithm combines run length encoding (RLE) and context-based arithmetic encoding to reduce the bitrate of the EAVQ indices by about 10% at the expense of 1% rise in complexity of the codec. The proposed algorithm can increase the segmental signal to noise ratio of about 9% at low rates for speech signals and improve the subjective scores in noisy channels by about 0.5 on a five-point scale if combined with an additional protection layer.