Near-Lossless Compression of Two Independent Binary Sources with One Encoder

In this paper, we consider the near-lossless compression of two distinct but independent binary random sources <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$V$</tex>, both of which are asymmetrical independent and identically distributed (i.i.d.) sources. In particular, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$V$</tex> is assumed to be sparser than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex>. We show that, to efficiently compress <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$V$</tex>, explicit source coding (compression) for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$V$</tex> (the sparser one) is not required. The basic idea is to encode <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex> with an error-correction code and then superimpose <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$V$</tex> on the codeword. Hence, only one encoder-decoder pair (EDP) suffices to compress two sources. Theoretical analysis shows that the proposed coding scheme is entropy-approaching in terms of bit-error rate (BER) of both sources, and numerical results verify our analysis. Furthermore, we analyze the complexity of compression using the block Markov superposition transmission-repetition (BMST-R) codes to discuss the advantage of the proposed scheme. Simulation results demonstrate that the proposed scheme compresses the two sources simultaneously in a more compact way but causes no performance degradation.