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Linear prediction (LP) is a powerful technique for efficient source-system model based representation of signals, such as speech, and video, with useful applications including compression, and recognition. This has been found to be particularly true when vector quantization is used to code the linear predictor coefficients. Recently, signal processing in multiple nonorthogonal domains has been reported that further enhances the efficiency of signal representation. In this contribution, a novel LP model based coding technique is presented where the advantages of multiple nonorthogonal domain representations of the LP coefficients and the prediction residuals are exploited in conjunction with vector quantization to yield considerable LP coding enhancement. The proposed signal coding technique is applied to one of the most commonly used signals, namely, speech. The resulting performance improvement is clearly demonstrated in terms of reconstruction quality for the same bit rate compared to the existing single domain vector quantization techniques.