Capacity Bounds and Sum Rate Capacities of a Class of Discrete Memoryless Interference Channels

Abstract

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 capacity region to certain degraded interference channels. This allows the construction of capacity outer-bounds using the capacity regions of associated degraded broadcast channels. The same technique is then used to determine the sum-rate capacity of discrete memoryless interference channels with mixed interference as defined in the paper. The obtained capacity bounds and sum-rate capacities are used to resolve the capacities of several new discrete memoryless interference channels.

Code Design for Discrete Memoryless Interference Channels

“…where q = P (X 2 = 1) and h(.) is the binary entropy function, and verify that for P (X 1 = 0) < 0.71 the condition in (26) holds, i.e., the example becomes an instance of the weak interference channel by the definition in [17,Eq. (23)].…”

“…Z 1 and Z 2 are the noise samples at receiver 1 and 2 drawn from a Bernoulli distribution with parameters 1 = 0.21 and 2 = 0.25, respectively. This model does not satisfy the Markov chain condition for weak interference definition [17], however, we can simplify the mutual information condition I(…”

“…(23)]. Therefore, motivated by the results of [17], we utilize the simple coding scheme of sending the messages of both users as private and compute a subregion of the overall HK ARR. The achievable HK subregion is plotted for the considered example in Fig.…”

“…Z 1 and Z 2 are independent noise samples at receiver 1 and 2 drawn from a Bernoulli distribution with parameters 1 and 2 , respectively. This model satisfies the Markov chain condition for weak interference [17,Definition 2], namely, X 2 − (X 1 , Y 2 ) − Y 1 , hence the sum rate capacity result [17,Th. 1] holds, and it can be achieved by treating interference as noise and using only private messages.…”

“…In this scheme, each user splits its data into private and public messages, which are decoded at the intended receivers and both receivers, respectively. More recently, [17] derives the sum rate capacity of a DMIC with one-sided weak interference, and shows that in order to achieve this sum rate both users should transmit their information as private messages only, i.e., the receivers should decode their desired messages while treating the interference as noise.…”