2022/05/14 by Ran Tamir, Neri Merhav, Tamir, Ran +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Cooperative Communication and Network Coding #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.2205.07140
openalex publication_date 2022/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive various error exponents for communication channels with random states, which are available non-causally at the encoder only. For both the finite-alphabet Gel'fand-Pinsker channel and its Gaussian counterpart, the dirty-paper channel, we derive random coding exponents, error exponents of the typical random codes (TRCs), and error exponents of expurgated codes. For the two channel models, we analyze some sub-optimal bin-index decoders, which turn out to be asymptotically optimal, at least for the random coding error exponent. For the dirty-paper channel, we show explicitly via a numerical example, that both the error exponent of the TRC and the expurgated exponent strictly improve upon the random coding exponent, at relatively low coding rates, which is a known fact for discrete memoryless channels without random states. We also show that at rates below capacity, the optimal values of the dirty-paper design parameter α in the random coding sense and in the TRC exponent sense are different from one another, and they are both different from the optimal α that is required for attaining the channel capacity. For the Gel'fand-Pinsker channel, we allow for a variable-rate random binning code construction, and prove that the previously proposed maximum penalized mutual information decoder is asymptotically optimal within a given class of decoders, at least for the random coding error exponent.