TY - JOUR

T1 - A Single-Letter Upper Bound on the Mismatch Capacity via Multicast Transmission

AU - Somekh-Baruch, Anelia

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2022/5/1

Y1 - 2022/5/1

N2 - We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric q. Our bound is obtained by considering a multicast transmission over a two-user broadcast channel with decoding metrics q and ρ at the receivers, referred to as (q,ρ) -surely degraded. This channel has the property that the intersection event of correct q -decoding of receiver 1 and erroneous ρ -decoding of receiver 2 has zero probability for any fixed-composition codebook of a certain composition P. Our bound holds in the strong converse sense of an exponential decay of the probability of correct decoding at rates above the bound. Further, we refine the proof and present a bound that is tighter than that of any choice of ρ . Several examples that demonstrate the strict improvement of our bound compared to previous results are analyzed. Finally, we detect equivalence classes of isomorphic channel-metric pairs (W,q) that share the same mismatch capacity. We prove that if the class contains a matched pair, then our bound is tight and the mismatch capacity of the entire class is fully characterized and is equal to the LM rate, which is achievable by random coding, and may be strictly lower that the matched capacity.

AB - We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric q. Our bound is obtained by considering a multicast transmission over a two-user broadcast channel with decoding metrics q and ρ at the receivers, referred to as (q,ρ) -surely degraded. This channel has the property that the intersection event of correct q -decoding of receiver 1 and erroneous ρ -decoding of receiver 2 has zero probability for any fixed-composition codebook of a certain composition P. Our bound holds in the strong converse sense of an exponential decay of the probability of correct decoding at rates above the bound. Further, we refine the proof and present a bound that is tighter than that of any choice of ρ . Several examples that demonstrate the strict improvement of our bound compared to previous results are analyzed. Finally, we detect equivalence classes of isomorphic channel-metric pairs (W,q) that share the same mismatch capacity. We prove that if the class contains a matched pair, then our bound is tight and the mismatch capacity of the entire class is fully characterized and is equal to the LM rate, which is achievable by random coding, and may be strictly lower that the matched capacity.

KW - Channel coding

KW - Mismatch capacity

KW - Mismatched decoding

UR - http://www.scopus.com/inward/record.url?scp=85123680138&partnerID=8YFLogxK

U2 - 10.1109/TIT.2022.3146308

DO - 10.1109/TIT.2022.3146308

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AN - SCOPUS:85123680138

SN - 0018-9448

VL - 68

SP - 2801

EP - 2812

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -