Optimal Transmission Strategy and Capacity Region for Broadcast Z Channels

Xie, Bike; Griot, M.; Casado, A.I.V.; Wesel, Richard D.

doi:10.1109/itw.2007.4313106

Cited by 5 publications

(9 citation statements)

References 5 publications

(10 reference statements)

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“…Following the lower bound on given in Theorem 13, we obtain In order to find , we note that the Z-channel with crossover probability is the cascade of two Z-channels with crossover probabilities and (see also [37] and is attained at and . So, again, the "last" layer is silent.…”

Section: Examplesmentioning

confidence: 99%

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Variable-Rate Channel Capacity

Verdú

Shamai

2010

IEEE Trans. Inform. Theory

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Abstract-This paper introduces the notions of variable-to-fixed and fixed-to-variable channel capacity, without feedback. For channels that satisfy the strong converse, these notions coincide with the conventional Shannon capacity. For channels that do not behave ergodically, the conventional fixed-rate Shannon capacity only depends on least-favorable channel conditions, while the variable-rate capacity notions are able to capture the whole range of channel states and their likelihood, even in the absence of any side information about channel state at the transmitter. Particular emphasis is placed on memoryless channels that are governed by finitely valued states. We show that (single-user) variable-to-fixed channel capacity is intimately connected to the capacity region of broadcast channels with degraded message sets, and we give an expression for the fixed-to-variable capacity.

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Section: Examplesmentioning

confidence: 99%

“…If a layer is associated with channel realization , we let ; otherwise . Furthermore, denote the number of active layers up to and including state (214) Let stand for the effective crossover probability of a Z-channel with crossover and all undetected layers (215) The incremental rate decoded at level is [37] (216)…”

Section: Examplesmentioning

confidence: 99%

Variable-Rate Channel Capacity

Verdú

Shamai

2010

IEEE Trans. Inform. Theory

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“…As an example, the NE scheme for a two-receiver Gaussian BC has as each transmitted symbol the real addition of two real symbols from independent codebooks. The NE scheme is known to achieve the boundary of the capacity region for several BCs including Gaussian BCs [6], binary-symmetric BCs [2] [7] [8] [9], discrete additive DBCs [10] and two-receiver broadcast Z channels [11] [12].…”

Section: A Backgroundmentioning

confidence: 99%

Optimal Encoding for Discrete Degraded Broadcast Channels

Xie

Courtade

Wesel

2013

IEEE Trans. Inform. Theory

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Consider a memoryless degraded broadcast channel (DBC) in which the channel output is a singleletter function of the channel input and the channel noise. As examples, for the Gaussian broadcast channel (BC) this single-letter function is regular Euclidian addition and for the binary-symmetric BC this single-letter function is Galois-Field-two addition. This paper identifies several classes of discrete memoryless DBCs for which a relatively simple encoding scheme, which we call natural encoding, achieves capacity. Natural Encoding (NE) combines symbols from independent codebooks (one for each receiver) using the same single-letter function that adds distortion to the channel. The alphabet size of each NE codebook is bounded by that of the channel input.Inspired by Witsenhausen and Wyner, this paper defines the conditional entropy bound function F * , studies its properties, and applies them to show that NE achieves the boundary of the capacity region for the multi-receiver broadcast Z channel. Then, this paper defines the input-symmetric DBC, introduces permutation encoding for the input-symmetric DBC, and proves its optimality. Because it is a special case of permutation encoding, NE is capacity achieving for the two-receiver group-operation DBC. Combining the broadcast Z channel and group-operation DBC results yields a proof that NE is also optimal for the discrete multiplication DBC. Along the way, the paper also provides explicit parametric expressions for the two-receiver binary-symmetric DBC and broadcast Z channel. 2 Degraded broadcast channel, natural encoding, broadcast Z channel, input-symmetric, group-operation degraded broadcast channel, discrete multiplication degraded broadcast channel, Gaussian broadcast channel, binary-symmetric broadcast channel. F * (q, s). Section III uses duality to evaluate F * (q, s) and provides an approach to characterizing optimal transmission strategies for the discrete DBC based on this evaluation. As an example, Section III-B uses the duality-based computation of F * (q, s) to provide an explicit parametric expression for the capacity region of the two-receiver binary-symmetric BC. Section IV proves the optimality of the NE scheme for broadcast Z channels with more than two receivers. Section V defines the IS-DBC, introduces the permutation encoding approach, and proves its optimality for IS-DBCs. Section VI studies the discrete multiplication DBC and shows that NE achieves the boundary of the capacity region for the discrete multiplication DBC. Section VII delivers the conclusions. D. NotationDenote X → Y as a discrete memoryless channel with channel input X and output Y .is the channel input, and Y (i) (i = 1, · · · , K) is the i-th least-degraded output. For simplicity of notation, we also denote X → Y → Z as a two-receiver DBC where Y is the less-degraded output and Z is the more-degraded output. Since the capacity region of a statistically-degraded BC without feedback is equivalent to that of the corresponding physically-degraded BC with the same marginal transitio...

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“…Natural encoders are known to achieve the capacity region boundary of the broadcast Gaussian channel [4], the broadcast binary-symmetric channel [2] [5], and discrete additive DBCs [6]. Recently, natural encoding has also been shown to achieve the capacity region of the two-user broadcast Z channel [7].…”

Section: Introductionmentioning

confidence: 99%

Optimal natural encoding scheme for discrete multiplicative degraded broadcast channels

Wesel

Xie

2009

2009 IEEE International Symposium on Information Theory

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Abstract-Certain degraded broadcast channels (DBCs) have the property that the boundary of the capacity region can be achieved by an encoder that combines independent codebooks (one for each receiver) using the same singleletter function that adds distortion to the channel. We call this the natural encoder for the DBC. Natural encoders are known to achieve the capacity region boundary of the broadcast Gaussian channel, and the broadcast binary-symmetric channel. Recently, they have also been shown to achieve the capacity region of the broadcast Z channel. This paper shows that natural encoding achieves the capacity region boundary for discrete multiplicative DBCs. The optimality of the natural encoder also leads to a relatively simple expression for the capacity region for discrete multiplicative DBCs.Index Terms-Conditional entropy bound, degraded broadcast channel, discrete multiplicative degraded broadcast channel, natural encoding

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Optimal Transmission Strategy and Capacity Region for Broadcast Z Channels

Cited by 5 publications

References 5 publications

Variable-Rate Channel Capacity

Variable-Rate Channel Capacity

Optimal Encoding for Discrete Degraded Broadcast Channels

Optimal natural encoding scheme for discrete multiplicative degraded broadcast channels

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