6 research outputs found
Arimoto channel coding converse and Rényi divergence
Abstract-Arimoto [1] proved a non-asymptotic upper bound on the probability of successful decoding achievable by any code on a given discrete memoryless channel. In this paper we present a simple derivation of the Arimoto converse based on the dataprocessing inequality for Rényi divergence. The method has two benefits. First, it generalizes to codes with feedback and gives the simplest proof of the strong converse for the DMC with feedback. Second, it demonstrates that the sphere-packing bound is strictly tighter than Arimoto converse for all channels, blocklengths and rates, since in fact we derive the latter from the former. Finally, we prove similar results for other (non-Rényi) divergence measures
The Sphere Packing Bound for DSPCs with Feedback a la Augustin
Establishing the sphere packing bound for block codes on the discrete
stationary product channels with feedback ---which are commonly called the
discrete memoryless channels with feedback--- was considered to be an open
problem until recently, notwithstanding the proof sketch provided by Augustin
in 1978. A complete proof following Augustin's proof sketch is presented, to
demonstrate its adequacy and to draw attention to two novel ideas it employs.
These novel ideas (i.e., the Augustin's averaging and the use of subblocks) are
likely to be applicable in other communication problems for establishing
impossibility results.Comment: 12 pages, 2 figure
The Sphere Packing Bound via Augustin's Method
A sphere packing bound (SPB) with a prefactor that is polynomial in the block
length is established for codes on a length product channel
assuming that the maximum order Renyi capacity among the component
channels, i.e. , is . The
reliability function of the discrete stationary product channels with feedback
is bounded from above by the sphere packing exponent. Both results are proved
by first establishing a non-asymptotic SPB. The latter result continues to hold
under a milder stationarity hypothesis.Comment: 30 pages. An error in the statement of Lemma 2 is corrected. The
change is inconsequential for the rest of the pape
Sphere-packing bound for block-codes with feedback and finite memory
A lower bound bound is established on the error probability of fixed-length block-coding systems with finite memory feedback, which can be described in terms of a time dependent finite state machine. It is shown that the reliability function of such coding systems over discrete memoryless channels is upper-bounded by the sphere-packing exponent