Consider communication over a channel whose probabilistic model is completely unknown vector-wise and is not assumed to be stationary. Communication over such channels is challenging because knowing the past does not indicate anything about the future. The existence of reliable feedback and common randomness is assumed. In a previous paper, it was shown that the Shannon capacity cannot be attained, in general, if the channel is not known. An alternative notion of capacity was defined, as the maximum rate of reliable communication by any block-coding system used over consecutive blocks. This rate was shown to be achievable for the modulo-additive channel with an individual, unknown noise sequence, and not achievable for some channels with memory. In this paper, this capacity is shown to be achievable for general channel models possibly including memory, as long as this memory fades with time. In other words, there exists a system with feedback and common randomness that, without knowledge of the channel, asymptotically performs as well as any block code, which may be designed knowing the channel. For channels in which memory does not fade with time, a weaker type of capacity is shown to be achievable.

Is it a good idea to use the frequency of events in the past, as a guide to their frequency in the future (as we all do anyway)? In this paper the question is attacked from the perspective of universal prediction of individual sequences. It is shown that there is a universal sequential probability assignment, such that for a large class loss functions (optimization goals), the predictor minimizing the expected loss under this probability, is a good universal predictor. The proposed probability assignment is based on randomly dithering the empirical frequencies of states in the past, and it is easy to show that randomization is essential. This yields a very simple universal prediction scheme which is similar to Follow-the-Perturbed-Leader (FPL) and works for a large class of loss functions, as well as a partial justification for using probabilistic assumptions.

Consider the problem of universally communicating over an arbitrarily varying channel, i.e., a channel comprised of an unknown, arbitrary sequence of memoryless channels. It is shown that there is a communication system using feedback and common randomness that asymptotically attains, with high probability, the capacity of the time-averaged channel, universally for every sequence of channels. This attainable rate is optimal under certain conditions. While no prior knowledge of the channel sequence is assumed, the capacity of the time-averaged channel meets or exceeds the traditional arbitrarily varying channel (AVC) capacity for every memoryless AVC defined over the same alphabets, and therefore, the system universally attains the random code AVC capacity, without knowledge of the AVC parameters. The presented system combines rateless coding with a universal prediction scheme for the input “prior” distribution, from which the codebook is randomly drawn. Because at each point in time, the future of the channel sequence is unknown to the communicators, the adaptation of the input behavior, by universally predicting the prior, plays a major role in the result.

Which communication rates can be attained over a channel whose output is an unknown (possibly stochastic) function of the input that may vary arbitrarily in time with no a priori model? Following the spirit of the finite-state compressibility of a sequence, defined by Lempel and Ziv, a “capacity” is defined for such a channel as the highest rate achievable by a designer knowing the particular relation that indeed exists between the input and output for all times, yet is constrained to use a fixed finite-length block communication scheme without feedback, i.e., use the same encoder and decoder over each block. In the case of the modulo additive channel, where the output sequence is obtained by modulo addition of an unknown individual sequence to the input sequence, this capacity is upper bounded by a function of the finite state compressibility of the noise sequence. A universal communication scheme with feedback that attains this capacity universally, without prior knowledge of the noise sequence, is presented.

Consider communication over a channel whose probabilistic model is completely unknown vector-wise and is not assumed to be stationary. Communication over such channels is challenging because knowing the past does not indicate anything about the future. The existence of reliable feedback and common randomness is assumed. In a previous paper it was shown that the Shannon capacity cannot be attained, in general, if the channel is not known. An alternative notion of “capacity” was defined, as the maximum rate of reliable communication by any block-coding system used over consecutive blocks. This rate was shown to be achievable for the modulo-additive channel with an individual, unknown noise sequence, and not achievable for some channels with memory. In this paper this “capacity” is shown to be achievable for general channel models possibly including memory, as long as this memory fades with time. In other words, there exists a system with feedback and common randomness that, without knowledge of the channel, asymptotically performs as well as any block-coding system, which may be designed knowing the channel. For non-fading memory channels a weaker type of “capacity” is shown to be achievable.

We consider the problem of communicating over an unknown and arbitrarily varying channel, using feedback. This paper focuses on the problem of determining the input behavior, or more specifically, a prior which is used to randomly generate a codebook. We pose the problem of setting the prior as a sequential universal prediction problem using information theoretic abstractions of the communication channel. For the case where the channel is block-wise constant, we show it is possible to asymptotically approach the best rate that can be attained by any system using a fixed prior. For the case where the channel may change on each symbol, we combine a rateless coding scheme with a prior predictor and asymptotically approach the capacity of the average channel universally for every sequence of channels.

Which communication rates can be attained over a channel whose output is an unknown (possibly stochastic) function of the input that may vary arbitrarily in time with no a-priori model? Following the spirit of the finite-state compressibility of a sequence defined by Lempel and Ziv, we define a “capacity” for such a channel as the highest rate achievable by a designer knowing the particular relation that indeed exists between the input and output for all times, yet is constrained to use a fixed finite-length block communication scheme (i.e., use the same scheme over each block). In the case of the binary modulo additive channel, where the output sequence is obtained by modulo addition of an unknown individual sequence to the input sequence, this capacity is upper bounded by 1 - ρ where ρ is the finite state compressibility of the noise sequence. We present a communication scheme with feedback that attains this rate universally without prior knowledge of the noise sequence.

A communication problem in considered, where no mathematical model is specified for the channel. The achievable rates are determined as a function of the channel input and output sequences known a-posteriori, without assuming any a-priori relation between them. For discrete channels the empirical mutual information between the input and output sequences is shown to be achievable, while for continuous channels the achievable rate is based on the empirical correlation between the sequences. A rate-adaptive scheme employing feedback which achieves these rates asymptotically with a guaranteed reliability, without prior knowledge of the channel behavior, is presented.

We consider the problem of communicating over a multiple-input multiple-output (MIMO) real valued channel for which no mathematical model is specified, and achievable rates are given as a function of the channel input and output sequences known a-posteriori. This paper extends previous results regarding individual channels by presenting a rate function for the MIMO individual channel, and showing its achievability in a fixed transmission rate communication scenario.

In order to meet the constantly increasing demand for ubiquitous, mobile access to the internet, next-generation mobile broadband communications systems based on OFDMA, such as IEEE 802.16 m, require a significant performance increase over previous generation systems, such as IEEE 802.16e-2005, particularly in cell-edge and average spectral efficiency. In this paper, we address the downlink adaptive frequency reuse (AFR) and multi-user MIMO (MU-MIMO) techniques which are considered to be the most promising candidates for meeting the requirements on cell-edge and average spectral efficiency of next-generation mobile broadband systems.

We consider the problem of communicating over a channel for which no mathematical model is specified. We present achievable rates as a function of the channel input and output sequences known a-posteriori for discrete and continuous channels. Furthermore we present a rate-adaptive scheme employing feedback which achieves these rates asymptotically without prior knowledge of the channel behavior.

We consider a real-valued additive channel with an individual unknown noise sequence. We present a simple sequential communication scheme based on the celebrated Schalkwijk-Kailath scheme, which varies the transmit power according to the power of the sequence, so that asymptotically the relation between the SNR and the rate matches the Gaussian channel capacity R ¿ 1/2 log(1 + SNR) for almost every noise sequence.