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Capacity per Unit Cost

Description

Gallager [1] studied the capacity regions of energy limited channels as in wideband and multi-access communication. He showed that reliable communication over such channels is fundamentally limited by a normalized rate, the capacity per unit energy. Verdu's capacity per unit cost [2] generalizes this concept to channels with arbitrary per-symbol cost functions. Since then, capacity per unit cost has been used to analyze a variety of communication scenarios in research literature.

The student will understand the concept and motivation of capacity per unit cost, and will be able to discuss the differences to Shannon's capacity result. The student will identify and review scenarios in literature where capacity per unit cost has been applied. Finally, the student will choose one of these applications and discuss in more detail how capacity per unit cost relates to this problem and how it helped in solving it.

References:

[1] R. G. Gallager, “Energy limited channels: Coding, multiaccess, and spread spectrum,” Tech. Rep. LIDS-P-1714, Nov. 1987.

[2] S. Verdú, “On channel capacity per unit cost,” IEEE Trans. Inf. Theory, vol. 36, no. 5, pp. 1019–1030, Sep. 1990.

Prerequisites

Supervisor:

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Decoding for High-Throughput Applications

Description

Implementation and analysis of decoding algorithms for high-throughput applications.

Supervisor:

Student

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Protograph-based LDPC Code Design for Finite Number of Iterations

Description

Low-density parity-check (LDPC) codes are usually designed using an extrinsic information transfer (EXIT) analysis to compute the asymptotic iterative decoding threshold for a given code ensemble. The iterative decoding threshold over an additive white Gaussian noise (AWGN) channel is thereby defined as the minimum signal-to-noise ratio (SNR) for which the a posteriori mutual information converges to one as the number of decoding iterations goes to infinity.

For practical applications, however, decoding is often performed using only a small number of iterations. Mulholland et al. investigated a code design for protograph-based LDPC codes where the protograph-based EXIT (PEXIT) analysis [1] is run for the targeted number of decoding iterations only [2]. They showed that for the binary erasure channel (BEC), the obtained iteration-constrained threshold does not match the bit error rate (BER) threshold of finite-length codes.

In this thesis, the student will understand and reproduce the results from [2], apply these tools to the AWGN channel, and compare them to code design tools developed at the institute.

[1] G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Nov. 2007, pp. 3250–3254.

[2] I. P. Mulholland, E. Paolini, and M. F. Flanagan, “Design of protograph-based LDPC code ensembles with fast convergence properties,” in Proc. Int. ITG Conf. Syst. Commun. Coding (SCC), Feb. 2017, pp. 1–6.

Prerequisites

Supervisor:

Student