Low-redundancy bit interleaving

We consider joint source-channel coding with bandwidth expansion, in a quadratic-Gaussian setting. We seek a scheme that will have favorable delay and robustness characteristics: it should be scalar (working on a single source sample), and closely follow the optimal curve of signal-to-distortion ratio (SDR) versus signal-to-noise ratio (SNR), asymptotically as the SNR grows. A natural candidate is bit interleaving, which was already proposed by Shannon in the context of bandwidth compression; however, in the case of expansion it suffers from severe noise amplification. A scheme proposed by Teherzadeh and Khandani introduces fixed bits in order to combat noise amplification, and has a multiplicative gap that is exponential the square root of the SNR from the ideal SDR-SNR curve. We propose an improved scheme that allocates the fixed bits in a source-dependent manner. This approach reduces the number of fixed bits needed, and thus has lower redundancy; we show that the multiplicative gap from the ideal curve is only linear in the SNR.