Navigation

by

Computing the Meta-Converse Bound: A Saddlepoint Approximation of Hypothesis Testing

Gonzalo Vazquez Vilar (Universidad Carlos III de Madrid)

Abstract:
In channel coding, binary hypothesis testing has been instrumental in the derivation of several lower bounds to the error probability, one prominent example the meta-converse bound. In this talk, we propose a saddlepoint approximation to the error probability of a binary hypothesis test with certain parameters. This approximation is then used to efficiently compute the metaconverse bound for moderate block-lengths in several cases of interest. The resulting expression can be numerically optimized when operating far from capacity, e.g., when the pay-load is small in a machine-to-machine transmission. Joint work with: Albert Guillén i Fàbregas (ICREA, Universitat Pompeu Fabra, University of Cambridge)

https://iot2017.mit.edu/vazquez-vilar/

by

The Meta-Converse and Perfect Codes

Albert Guillén i Fàbregas (ICREA and Universitat Pompeu Fabra)

Abstract:
The decoding process in the point-to-point communication problem is an instance of Bayesian M-ary hypothesis testing. This talk will illustrate how the error probability of an arbitrary code can be expressed as a function of a non-Bayesian binary hypothesis test, proving the tightness of the so-called meta-converse bound. Furthermore, for symmetric channels, the error probability of the best code is shown to coincide with that of a binary hypothesis test with certain parameters. The points in which they coincide, are precisely the points at which perfect or quasi-perfect codes exist.

https://iot2017.mit.edu/guillen-i-fabregas/

by

An Exact Spectrum Formula for the Maximum Size of Finite Length Block Codes

Vincent Tan (National University of Singapore)

Abstract:
An exact information spectrum-type formula for the maximum size of finite length block codes subject to a minimum pairwise distance constraint is presented. This formula can be applied to codes for a broad class of distance measures. As revealed by the formula, the largest code size is fully characterized by the information spectrum of the distance between two independent and identically distributed (i.i.d.) random codewords drawn from an optimal distribution. A new family of lower bounds to the maximal code size is thus established, and the well-known Gilbert-Varshamov (GV) lower bound is a special case of this family. By duality, an explicit expression for the largest minimum distance of finite length block codes of a fixed code size is also obtained. Under an arbitrary uniformly bounded symmetric distance measure, the asymptotic largest code rate (in the block length n) attainable for a sequence of (n,M,n\delta)-codes is given exactly by the maximum large deviation rate function of the normalized distance between two i.i.d. random codewords. The exact information spectrum-type formula also yields bounds on the second-order terms in the asymptotic expansion of the optimum finite length rate for block codes with a fixed normalized minimum distance. This is joint work with Ling-Hua Chang, Carol Wang, Po-Ning Chen, and Yunghsiang S. Han and can be found at 1706.04709.

https://iot2017.mit.edu/tan/

by

Advances in Random Access Protocols for Satellite Communications

Gianluigi Liva (German Aerospace Center)

Abstract:
This talk provides a survey of recent developments in the area of random access protocols, with emphasis on satellite communications. A class of modern random access protocols (coded slotted Aloha) for collision channels is presented, showing how the theory of codes on graphs can be applied to analyze the performance. The limitations coming from the adoption of a collision model are briefly discussed. An example of a modified coded Aloha protocol, capable of improving the efficiency over actual (satellite) wireless links, is finally illustrated.

https://iot2017.mit.edu/liva/

by

Low Rate LDPC Codes

Dariush Divsalar (NASA JPL)

Abstract:
We design, construct, and show the performance of both binary and non-binary low rate LDPC codes. Construction of codes with rates as low as 1/50 is discussed. These codes include short block codes as short as n=256 bits. We show the importance of having degree 1 nodes in the structure of low rate codes. Performance of these codes with different rates and block sizes will be compared based on PPV Normalized Rate for BIAWGN channel in finite block regime at a given code word error rate.

https://iot2017.mit.edu/divsalar/