A novel joint source-channel (JSC) coding scheme that combines transform source coding with polar channel codes is proposed with performance gains at low SNRs in terms of bandwidth and energy efficiency. Binary wavelet transform source coding is first applied to decompose the binary source data into a set of components with uneven distributions, particularly, components that are zero with high probability. Normally, a polar code of rate K/N appends N − K redundant bits to the message which can decrease the throughput and introduce an extra energy consumption. By exploiting the binary wavelet transform, the proposed scheme transforms the original signal to the polar code without adding redundant zeros. Hence, the resulting JSC code is of rate one. Since no floating-point arithmetic is required and all operations are performed in GF(2), complexity is vastly reduced which can eventually alleviate the total hardware cost as well as the energy consumption.