Binary Symmetric Broadcast Channel Research Articles

The Arbitrarily Varying Broadcast Channel With Causal Side Information at the Encoder

In this paper, we study the arbitrarily varying broadcast channel (AVBC) when the state information is available at the transmitter in a causal manner. We establish the inner and outer bounds on both the random code capacity region and the deterministic code capacity region with degraded message sets. The capacity region is then determined for a class of channels satisfying a condition on the mutual information between the strategy variables and the channel outputs. As an example, we consider the arbitrarily varying binary symmetric broadcast channel. We show the cases where the condition holds and, hence, the capacity region is determined and other cases where there is a gap between the bounds. This gap shows that the minimax theorem does not hold for rate regions.

Common-Message Broadcast Channels With Feedback in the Nonasymptotic Regime: Stop Feedback

We investigate the maximum coding rate for a given average blocklength and error probability over a K-user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiy et al. (2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e., zero dispersion. In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message K-user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.

Common-Message Broadcast Channels With Feedback in the Nonasymptotic Regime: Full Feedback

We investigate the maximum coding rate for a given average blocklength and error probability over a $K$ -user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiy et al. (2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e., zero dispersion . In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message $K$ -user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.

Exact Random Coding Exponents and Universal Decoders for the Asymmetric Broadcast Channel

This paper contains two main contributions concerning the asymmetric broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both users. These universal decoders are certain variants of the maximum mutual information universal decoder, and they achieve the corresponding random coding exponents of optimal decoding. In addition, we introduce some lower bounds, which involve optimizations over very few parameters, unlike the original, exact exponents, which involve minimizations over auxiliary probability distributions. Numerical results for the binary symmetric broadcast channel show improvements over previously derived error exponents for the same model.

Multi-destination aggregation with binary symmetric broadcast channel based coding in 802.11 WLANs

In this paper we consider the potential benefits of adopting a binary symmetric broadcast channel paradigm for multi-destination aggregation in 802.11 WLANs, as opposed to a more conventional packet erasure channel paradigm. We propose two approaches for multi-destination aggregation, i.e. superposition coding and a simpler time-sharing coding. Theoretical and simulation results for both unicast and multicast traffic demonstrate that increases in network throughput of more than 100% are possible over a wide range of network conditions and that the much simpler time-sharing scheme yields most of these gains and have minimal loss of performance. Importantly, these performance gains are achieved exclusively through software rather than hardware changes.

Coding Schemes With Rate-Limited Feedback That Improve Over the No Feedback Capacity for a Large Class of Broadcast Channels

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the no feedback capacity region for a large class of channels, including the class of strictly essentially less-noisy BCs that we introduce in this paper. Examples of strictly essentially less-noisy BCs are the binary symmetric BC or the binary erasure BC with unequal crossover or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feedback quantization messages about their receive signals. In the first scheme, the transmitter simply relays the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme, the transmitter first reconstructs and processes the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme also applies to memoryless BCs without feedback but with strictly causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information.

Optimal Encoding for Discrete Degraded Broadcast Channels

Consider a memoryless degraded broadcast channel (DBC) in which the channel output is a single-letter function of the channel input and the channel noise. As examples, for the Gaussian broadcast channel (BC), this single-letter function is real scalar addition and for the binary-symmetric BC, this single-letter function is modulo-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. This paper also 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.

A Simple Characterization of Strategic Behaviors in Broadcast Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this letter, we consider the problem of resource allocation between two competing users sharing a binary symmetric broadcast channel. We model the interaction between autonomous selfish users in the resource allocation and analyze their strategic behavior in manipulating the allocation outcome. We analytically show that users will improve their performance (i.e., gain higher allocated rates) if they have more information about the strategy of the competing user. </para>

Capacity results for the discrete memoryless network

A discrete memoryless network (DMN) is a memoryless multiterminal channel with discrete inputs and outputs. A sequence of inner bounds to the DMN capacity region is derived by using code trees. Capacity expressions are given for three classes of DMNs: (1) a single-letter expression for a class with a common output, (2) a two-letter expression for a binary-symmetric broadcast channel (BC) with partial feedback, and (3) a finite-letter expression for push-to-talk DMNs. The first result is a consequence of a new capacity outer bound for common output DMNs. The third result demonstrates that the common practice of using a time-sharing random variable does not include all time-sharing possibilities, namely, time sharing of channels. Several techniques for improving the bounds are developed: (1) causally conditioned entropy and directed information simplify the inner bounds, (2) code trellises serve as simple code trees, (3) superposition coding and binning with code trees improves rates. Numerical computations show that the last technique enlarges the best known rate regions for a multiple-access channel (MAC) and a BC, both with feedback. In addition to the rate bounds, a sequence of inner bounds to the DMN reliability function is derived. A numerical example for a two-way channel illustrates the behavior of the error exponents.

Coding for the binary symmetric broadcast channel with two receivers

Block coding for the binary symmetric broadcast channel with two receivers is investigated. A graph-theoretic approach to the construction of a class of block codes with unequal error protection for two different sets of messages is presented. A code in this class is a direct sum of two component codes; each set of messages is encoded based on one component code. The codes in this class are easy to implement. Decoding of these codes is presented, and lower bounds on the achievable rates of these codes are derived. The bounds are tighter than the Katsman's bounds.