Asymptotically Optimal Decision Rules for Joint Detection and Source Coding

IEEE Trans. Inform. Theory

2014

Self Cite

Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list-size L. Two asymptotic regimes are considered, the fixed list-size regime, where L is fixed independently of the block length n, and exponential list size, where L grows exponentially with n. We first derive a general upper bound on the list-decoding average error probability, which is suitable for both regimes. This bound leads to more specific bounds in the two regimes. In the fixed list-size regime, the bound is related to known bounds and we establish its exponential tightness. In the exponential list-size regime, we establish the achievability of the well-known sphere packing lower bound. An immediate byproduct of our analysis in both regimes is the universality of the maximum mutual information list decoder in the error exponent sense. Finally, we consider expurgated bounds at low rates, both using Gallager's approach and Csiszár-Körner-Marton approach, which is equivalent for the optimal input assignment. The latter expurgated bound, which involves the notion of multi-information, is also modified to apply to continuous alphabet channels, and in particular, to the Gaussian memoryless channel, where the expression of the expurgated bound becomes quite explicit.Index Terms-List decoding, error exponent, random coding, sphere packing, expurgated exponent.

Section: Future Workmentioning

confidence: 75%

List Decoding—Random Coding Exponents and Expurgated Exponents

IEEE Trans. Inform. Theory

2014

Self Cite

“…This proof suggests an extension to a recent work [17] (see also [18]) concerning a decoder/detector that first has to decide whether the received channel output y really contains a transmitted message or it is simply pure noise (that is received when the transmitter is silent), and in the former case to decode the message in the ordinary way (L = 1).…”

Section: Future Workmentioning

confidence: 75%

List decoding - Random coding exponents and expurgated exponents

2014 IEEE International Symposium on Information Theory

2014

Self Cite

Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size L. Two asymptotic regimes are considered, the fixed list-size regime, where L is fixed independently of the block length n, and the exponential list-size, where L grows exponentially with n. We first derive a general upper bound on the list-decoding average error probability, which is suitable for both regimes. This bound leads to more specific bounds in the two regimes. In the fixed list-size regime, the bound is related to known bounds and we establish its exponential tightness. In the exponential list-size regime, we establish the achievability of the well known sphere packing lower bound. Relations to guessing exponents are also provided. An immediate byproduct of our analysis in both regimes is the universality of the maximum mutual information (MMI) list decoder in the error exponent sense. Finally, we consider expurgated bounds at low rates, both using Gallager's approach and the Csiszár-Körner-Marton approach, which is, in general better (at least for L = 1). The latter expurgated bound, which involves the notion of multi-information, is also modified to apply to continuous alphabet channels, and in particular, to the Gaussian memoryless channel, where the expression of the expurgated bound becomes quite explicit.Index Terms: List decoding, error exponent, random coding, sphere packing, expurgated exponent.

“…The main challenge in analyzing the random coding FA exponent, is that the likelihoods of both hypotheses, namely M m=1 W (Y|X m ) and M m=1 V (Y|X m ) are very correlated due to the fact the once the codewords are drawn, they are common for both likelihoods. This is significantly different from the situation in [10], in which the likelihood M m=1 W (Y|X m ) was compared to a likelihood Q 0 (Y), of a completely different distribution 9 . We first make the following observation.…”

Section: A Exact Random Coding Exponentsmentioning

confidence: 82%

“…This problem of joint detection/decoding belongs to a larger class of hypothesis testing problems, in which after performing the test, another task should be performed, depending on the chosen hypothesis. For example, in [7], [8], the problem of joint hypothesis testing and Bayesian estimation was considered, and in [9] the subsequent task is lossless source coding. A common theme for all the problems in this class, is that separately optimizing the detection and the task is sub-optimal, and so, joint optimization is beneficial.…”

mentioning

confidence: 99%

Channel Detection in Coded Communication

Weinberger

IEEE Trans. Inform. Theory

2017

Self Cite

We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to detect the set which contains the prevailing channel. We begin with the simplified case where each of the sets is a singleton. For any given code, we derive the optimum detection/decoding rule in the sense of the best trade-off among the probabilities of decoding error, false alarm, and misdetection, and also introduce sub-optimal detection/decoding rules which are simpler to implement. Then, various achievable bounds on the error exponents are derived, including the exact single-letter characterization of the random coding exponents for the optimal detector/decoder. We then extend the random coding analysis to general sets of channels, and show that there exists a universal detector/decoder which performs asymptotically as well as the optimal detector/decoder, when tuned to detect a channel from a specific pair of channels. The case of a pair of binary symmetric channels is discussed in detail.