A wideband Rayleigh fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver (similar to pulse position modulation in IEEE Trans. Inf. Theory, vol. 46, no. 4, Apr. 2000 and IEEE Trans. Inf. Theory, vol. 52 no. 5, May 2006) is shown to achieve the capacity of this channel in the wideband limit. This strategy transmits energy only when the channel gain exceeds a threshold, hence only needs causal transmitter CSI. In the wideband limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI, which is proportional to the logarithm of the bandwidth. Similar threshold-based pulse position modulation is shown to achieve the capacity per unit cost of the dirty-tape channel (dirty paper channel with causal transmitter CSI and no receiver CSI), which equals its capacity per unit cost with full receiver CSI. Then, a general discrete channel with i.i.d. states is considered. Each input has an associated cost and a zero cost input “0” exists. The channel state is assumed to be known at the transmitter in a causal manner. Capacity per unit cost is found for this channel and a simple orthogonal code is shown to achieve this capacity. Later, a novel orthogonal coding scheme is proposed for the case of causal transmitter CSI and a condition for equivalence of capacity per unit cost for causal and noncausal transmitter CSI is derived.

The Rayleigh flat fading channel at low SNR is considered. With full channel state information (CSI) at the transmitter and receiver, its capacity is shown to be essentially SNR log(1SNR) nats/symbol, as SNR goes to zero. In fact, this rate can be achieved with a just one bit of CSI at the transmitter (per fading realization) and with no receiver CSI. The capacity for the case of noisy transmitter CSI is also found. Then a Rayleigh block fading channel of coherence interval T ≤ 1/ SNR is considered which has causal feedback and no a priori CSI. A training based scheme is proposed for such channels, which achieves a rate of SNR logT nats/symbol in the limit of small SNR and large T. Thus, when coherence interval T is of the order 1/SNR, without any a priori CSI at either end, the capacity with full CSI at both ends is achievable. For smaller values of T, a rate of SNR logT nats/symbol is shown to be achievable.

This paper investigates asymptotic (in blocklength) tradeoffs between rate and minimum distance, for codes that provide unequal error protection (UEP). Two notions of UEP are analyzed: bit-wise, where a subset of bits is special and needs more protection, and message-wise, where a subset of the message-set is special. Both notions are analyzed for two cases: binary, and large-alphabet. In message-wise UEP for the binary channel alphabet, it turns out that the special messages and ordinary messages can simultaneously achieve the Gilbert-Varshamov bound at their respective rates. Similar ¿successive refinement¿ of the Singleton bound is shown to hold for large non-binary alphabets. We also analyze the situation when there is only one special message. In bit-wise UEP, it is shown that when the ordinary bits are achieving the Singleton bound, even a single special bit cannot achieve any larger distance. For the binary case, an upper bound is provided on the protection of the single special bit. These coding theoretic limits in terms of Hamming distances are close analogues of the information theoretic limits in terms of error exponents.

An information-theoretic framework for unequal error protection is developed in terms of the exponential error bounds. The fundamental difference between thebit-wiseandmessage-wiseunequal error protection (UEP) is demonstrated, for fixed-length block codes on discrete memoryless channels (DMCs) without feedback. Effect of feedback is investigated via variable-length block codes. It is shown that, feedback results in a significant improvement in bothbit-wiseandmessage-wise UEPs(except the single message case for missed detection). The distinction between false-alarm and missed-detection formalizations formessage-wise UEPis also considered. All results presented are at rates close to capacity.

Various formulations are considered where some information is more important than other and needs better protection. Our information theoretic framework in terms of exponential error bounds provides some fundamental limits and optimal strategies for such problems of unequal error protection. Even for data-rates approaching the channel capacity, it shows how a crucial part of information can be protected with exponential reliability. Channels without feedback are analyzed first, which is useful later in analyzing channels with feedback. A new channel parameter, called the Red-Alert Exponent, is fundamentally important in such problems.

This paper is eligible for the student paper award. We formulate a broadcast problem, where based on their quality of observations, outputs at various receivers are represented on a graph (called "degradation graph"). If receiver Z is a physically degraded version of receiver Y, then node Z is a child of node Y in this graph. This generalization of the classical degraded broadcast channel provides a framework for various situations where at least some information should be available to receivers with partial (or noisier) observations. Upper and lower bounds are obtained on the capacity region. The upper bound is based on auxiliary variables, whose structure is described by the mirror image of the channel's degradation graph. As a special case of our problem, a packet broadcast network is considered.

A wireless network with fading and a single source-destination pair is considered. The information reaches the destination via multiple hops through a sequence of layers of single-antenna relays. At high signal-to-noise ratio (SNR), the simple amplify-and-forward strategy is shown to be optimal in terms of degrees of freedom, because it achieves the degrees of freedom equal to a point-to-point multiple-input multiple-output (MIMO) system. Hence, the lack of coordination in relay nodes does not reduce the achievable degrees of freedom. The performance of this amplify-and-forward strategy degrades with increasing network size. This phenomenon is analyzed by finding the tradeoffs between network size, rate, and diversity. A lower bound on the diversity-multiplexing tradeoff for concatenation of multiple random Gaussian matrices is obtained. Also, it is shown that achievable network size in the outage formulation (short codes) is a lot smaller than the ergodic formulation (long codes).

A wideband fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver is shown to achieve the capacity of this channel in the limit of large bandwidth. This code transmits energy only when the channel gain is large enough. In this limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI - a phenomenon also true for dirty paper coding. For Rayleigh fading, this capacity (per unit time) is proportional to the logarithm of the bandwidth. Our coding scheme is motivated from the Gel'fand-Pinsker and dirty paper coding. Nonetheless, our scheme requires only causal transmitter CSI (CSIT) in contrast with Gel'fand-Pinsker and dirty paper coding, which require non-causal CSIT. A general discrete channel with i.i.d. states is considered later. Each input has an associated cost and a zero cost input "0" exists. The channel state is known at the transmitter in a causal manner. Capacity per unit cost is found for this channel and a simple orthogonal code is shown to achieve it. Later, a novel orthogonal coding scheme is proposed for the case of causal CSIT and a condition for equal capacity per unit cost with causal and non-causal CSIT is derived