While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed-form expression for the capacity of an arbitrary discrete memoryless channel. This paper describes an elementary technique based on Karush Kuhn Tucker (KKT) conditions to obtain (1) a good upper bound of a discrete memoryless channel having an invertible positive channel matrix and (2) a closed-form expression for the capacity if the channel matrix satisfies certain conditions related to its singular value and its Gershgorin disk.
This paper studies the capacity of a class of discrete memoryless interference channels where interference is defined analogous to that of Gaussian interference channel with one-sided weak interference. The sum-rate capacity of this class of channels is determined. As with the Gaussian case, the sum-rate capacity is achieved by letting the transceiver pair subject to interference communicate at a rate such that its message can be decoded at the unintended receiver using single user detection. It is also established that this class of discrete memoryless interference channels is equivalent in c…
The sum capacity of a class of discrete memoryless interference channels is determined. This class of channels is defined analogous to the Gaussian Z-interference channel with weak interference; as a result, the sum capacity is achieved by letting the transceiver pair subject to the interference communicates at a rate such that its message can be decoded at the unintended receiver using single user detection. Moreover, this class of discrete memoryless interference channels is equivalent in capacity region to certain discrete degraded interference channels. This allows the construction of a ca…
We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. The presented method requires $O(M^2 N \sqrt{\log N}/\varepsilon)$ to provide an estimate of the capacity to within $\varepsilon$, where $N$ and $M$ denote the input and output alphabet size; a single iteration has a complexity $O(M N)$. We also show how to approximately compute the capacity of memoryless channels having a bound…
In this paper, we give a distributed joint source channel coding scheme for arbitrary correlated sources for arbitrary point in the Slepian-Wolf rate region, and arbitrary link capacities using LDPC codes. We consider the Slepian-Wolf setting of two sources and one destination, with one of the sources derived from the other source by some correlation model known at the decoder. Distributed encoding and separate decoding is used for the two sources. We also give a distributed source coding scheme when the source correlation has memory to achieve any point in the Slepian-Wolf rate achievable reg…
We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In this way, we obtain single-letter characterizations of the entanglement-assisted classical capacities for both channel models. Moreover, we show that the entanglement-assisted classical capacity does exhibit no strong converse property for some compound quantum channels for the average as well as the maximal error criterion. A strong converse to the entangle…
We study the performance limits of state-dependent discrete memoryless channels with a discrete state available at both the encoder and the decoder. We establish the epsilon-capacity as well as necessary and sufficient conditions for the strong converse property for such channels when the sequence of channel states is not necessarily stationary, memoryless or ergodic. We then seek a finer characterization of these capacities in terms of second-order coding rates. The general results are supplemented by several examples including i.i.d. and Markov states and mixed channels.
We define the direct and reverse secret-key capacities of a memoryless quantum channel as the optimal rates that entanglement-based quantum key distribution protocols can reach by using a single forward classical communication (direct reconciliation) or a single feedback classical communication (reverse reconciliation). In particular, the reverse secret-key capacity can be positive for antidegradable channels, where no forward strategy is known to be secure. This property is explicitly shown in the continuous variable framework by considering arbitrary one-mode Gaussian channels.
Motivated by a greedy approach for generating {\it{information stable}} processes, we prove a universal maximum likelihood (ML) upper bound on the capacities of discrete information stable channels, including the binary erasure channel (BEC), the binary symmetric channel (BSC) and the binary deletion channel (BDC). The bound is derived leveraging a system of equations obtained via the Karush-Kuhn-Tucker conditions. Intriguingly, for some memoryless channels, e.g., the BEC and BSC, the resulting upper bounds are tight and equal to their capacities. For the BDC, the universal upper bound is rela…
Non-orthogonal communications play an important role in future communication architectures. In such scenarios, the received signal is corrupted by an interfering signal which is typically cyclostationary in continuous-time. If the period of interference is synchronized with the sampling period, the sampled interference is a discrete-time (DT) cyclostationary process. However, in the common interference scenario, the period of the interference is not necessarily synchronized with the sampling period. In such cases, the DT interference is an almost cyclostationary process. In this work we charac…
We determine the capacity of compound classical-quantum channels. As a consequence we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on the universal classical approximation of the quantum relative entropy which in turn rel…
In this paper, we characterize the capacity region for the two-user linear Gaussian compound Multiple Access Channel with common message (MACC) and with intersymbol interference (ISI) under an input power constraint. The region is obtained by converting the channel to its equivalent memoryless one by defining an n-block memoryless circular Gaussian compound MACC model and applying the discrete Fourier transform (DFT) to decompose the n-block channel into a set of independent parallel channels whose capacities can be found easily. Indeed, the capacity region of the original Gaussian compound MA…
The capacity of a network in which a multiple access channel (MAC) generates interference to a single-user channel is studied. An achievable rate region based on superposition coding and joint decoding is established for the discrete case. If the interference is very strong, the capacity region is obtained for both the discrete memoryless channel and the Gaussian channel. For the strong interference case, the capacity region is established for the discrete memoryless channel; for the Gaussian case, we attain a line segment on the boundary of the capacity region. Moreover, the capacity region f…
This paper employs equal-image-size source partitioning techniques to derive the capacities of the general discrete memoryless wiretap channel (DM-WTC) under four different secrecy criteria. These criteria respectively specify requirements on the expected values and tail probabilities of the differences, in absolute value and in exponent, between the joint probability of the secret message and the eavesdropper's observation and the corresponding probability if they were independent. Some of these criteria reduce back to the standard leakage and variation distance constraints that have been pre…
We investigate if feedback can increase the capacity of an energy harvesting communication channel where a transmitter powered by an exogenous energy arrival process and equipped with a finite battery communicates to a receiver over a memoryless channel. For a simple special case where the energy arrival process is deterministic and the channel is a BEC, we explicitly compute the feed-forward and feedback capacities and show that feedback can strictly increase the capacity of this channel. Building on this example, we also show that feedback can increase the capacity when the energy arrivals a…
Several non-asymptotic formulas are established in channel resolvability and identification capacity, and they are applied to wire-tap channel. By using these formulas, the $ε$ capacities of the above three problems are considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a channel. As a result, we solve an open problem proposed in Han & Verdu and Han. Moreover, we obtain lower bounds of the exponents of error probability and the wire-tapper's information in wire-tap channel.
Finite blocklength and second-order (dispersion) results are presented for the arbitrarily-varying channel (AVC), a classical model wherein an adversary can transmit arbitrary signals into the channel. A novel finite blocklength achievability bound is presented, roughly analogous to the random coding union bound for non-adversarial channels. This finite blocklength bound, along with a known converse bound, is used to derive bounds on the dispersion of discrete memoryless AVCs without shared randomness, and with cost constraints on the input and the state. These bounds are tight for many channe…
This paper considers the memoryless input-constrained binary erasure channel (BEC). The channel input constraint is the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s in the input sequence be separated by at least $d$ $0$s. We consider a scenario where there is causal, noiseless feedback from the decoder. We demonstrate a simple, labelling-based, zero-error feedback coding scheme, which we prove to be feedback capacity-achieving, and, as a by-product, obtain an explicit characterization of the feedback capacity. Our proof is based on showing th…
The fundamental limits of communication over state-dependent discrete memoryless channels with noiseless feedback are studied, under the assumption that the communicating parties are allowed to use variable-length coding schemes. Various cases are analyzed, with the employed coding schemes having either bounded or unbounded codeword lengths, and with state information revealed to the encoder and/or decoder in a strictly causal, causal, or non-causal manner. In each of these settings, necessary and sufficient conditions for positivity of the zero-error capacity are obtained and it is shown that…
We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the {\em topological entropy} of the chan…
The upper bound on the capacity of a 3-node discrete memoryless relay channel is considered, where a source X wants to send information to destination Y with the help of a relay Z. Y and Z are independent given X, and the link from Z to Y is lossless with rate $R_0$. A new inequality is introduced to upper-bound the capacity when the encoding rate is beyond the capacities of both individual links XY and XZ. It is based on generalization of the blowing-up lemma, linking conditional entropy to decoding error, and channel simulation, to the case with side information. The achieved upper-bound is …
We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an …
No information transmission through quantum channels above capacity
National Taiwan University（国立台湾大学）；National Center for Theoretical Sciences, Taiwan（台湾理论科学中心）；Hon Hai (Foxconn) Quantum Computing Center, Taiwan（台湾鸿海（富士康）量子计算中心）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
In this paper, we formally define and analyze the class of noisy permutation channels. The noisy permutation channel model constitutes a standard discrete memoryless channel (DMC) followed by an independent random permutation that reorders the output codeword of the DMC. While coding theoretic aspects of this model have been studied extensively, particularly in the context of reliable communication in network settings where packets undergo transpositions, and closely related models of DNA based storage systems have also been analyzed recently, we initiate an information theoretic study of this…
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the deterministic capacity does have discontinuity points, whil…
