On Error Exponents of Encoder-Assisted Communication Systems

We consider a point–to–point communication system, where in addition to the encoder and decoder, there is helper that observes non–causally realization of noise vector provides (lossy) rate– $ {R}_{{ \text { h}}}$ description it ( h}}} < \infty $ ). In continuation Lapidoth Marti (2020), who derived capacity this model, here our focus on error exponents. both continuous–alphabet, additive white Gaussian channels finite–alphabet, modulo–additive channels, for each one them, we study cases fixed–rate variable–rate descriptions by helper. Our main finding that, as long channel–coding rate, R, below helper–rate, , achievable exponent unlimited (i.e., can be made arbitrarily large), some cases, even strictly infinite probability zero). However, range coding rates notation="LaTeX">$( h}}}, h}}}+ {C}_{0})$ C 0 being ordinary channel (without help), best finite positive, although certain gap between upper bound (converse bound) lower (achievability) highest exponent. This means model encoder–assisted essentially equivalent noisy also parallel noiseless bit–pipe . extend scope multiple access (MAC) characterize rate sub–region, or infinite.