Multiple description coding (MDC) is one of the widely used mechanisms to combat packet-loss in non-feedback systems. However, the number of descriptions in the existing MDC schemes is very small (typically 2). With the number of descriptions increasing, the coding complexity increases drastically and many decoders would be required. In this paper, the compressive sensing (CS) principles are studied and an alternative coding paradigm with a number of descriptions is proposed based upon CS for high packet loss transmission. Two-dimentional discrete wavelet transform (DWT) is applied for sparse representation. Unlike the typical wavelet coders (e.g., JPEG 2000), DWT coefficients here are not directly encoded, but re-sampled towards equal importance of information instead. At the decoder side, by fully exploiting the intra-scale and inter-scale correlation of multiscale DWT, two different CS recovery algorithms are developed for the low-frequency subband and high-frequency subbands, respectively. The recovery quality only depends on the number of received CS measurements (not on which of the measurements that are received). Experimental results show that the proposed CS-based codec is much more robust against lossy channels, while achieving higher rate-distortion (R-D) performance compared with conventional wavelet-based MDC methods and relevant existing CS-based coding schemes.