TY - GEN
T1 - Channel dispersion and moderate deviations limits for memoryless channels
AU - Polyanskiy, Yury
AU - Verdu, Sergio
PY - 2010/12/1
Y1 - 2010/12/1
N2 - Recently, Altug and Wagner [1] posed a question regarding the optimal behavior of the probability of error when channel coding rate converges to the capacity sufficiently slowly. They gave a sufficient condition for the discrete memoryless channel (DMC) to satisfy a moderate deviation property (MDP) with the constant equal to the channel dispersion. Their sufficient condition excludes some practically interesting channels, such as the binary erasure channel and the Z-channel. We extend their result in two directions. First, we show that a DMC satisfies MDP if and only if its channel dispersion is nonzero. Second, we prove that the AWGN channel also satisfies MDP with a constant equal to the channel dispersion. While the methods used by Altug and Wagner are based on the method of types and other DMC-specific ideas, our proofs (in both achievability and converse parts) rely on the tools from our recent work [2] on finite-blocklength regime that are equally applicable to non-discrete channels and channels with memory.
AB - Recently, Altug and Wagner [1] posed a question regarding the optimal behavior of the probability of error when channel coding rate converges to the capacity sufficiently slowly. They gave a sufficient condition for the discrete memoryless channel (DMC) to satisfy a moderate deviation property (MDP) with the constant equal to the channel dispersion. Their sufficient condition excludes some practically interesting channels, such as the binary erasure channel and the Z-channel. We extend their result in two directions. First, we show that a DMC satisfies MDP if and only if its channel dispersion is nonzero. Second, we prove that the AWGN channel also satisfies MDP with a constant equal to the channel dispersion. While the methods used by Altug and Wagner are based on the method of types and other DMC-specific ideas, our proofs (in both achievability and converse parts) rely on the tools from our recent work [2] on finite-blocklength regime that are equally applicable to non-discrete channels and channels with memory.
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U2 - 10.1109/ALLERTON.2010.5707068
DO - 10.1109/ALLERTON.2010.5707068
M3 - Conference contribution
AN - SCOPUS:79952422103
SN - 9781424482146
T3 - 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
SP - 1334
EP - 1339
BT - 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
T2 - 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
Y2 - 29 September 2010 through 1 October 2010
ER -