Variations on a Theme by Schalkwijk and Kailath

Gallager, Robert G
Nakiboğlu, Barış
Schalkwijk and Kailath (1966) developed a class of block codes for Gaussian channels with ideal feedback for which the probability of decoding error decreases as a second-order exponent in block length for rates below capacity. This well-known but surprising result is explained and simply derived here in terms of a result by Elias (1956) concerning the minimum mean-square distortion achievable in transmitting a single Gaussian random variable over multiple uses of the same Gaussian channel. A simple modification of the Schalkwijk-Kailath scheme is then shown to have an error probability that decreases with an exponential order which is linearly increasing with block length. In the infinite bandwidth limit, this scheme produces zero error probability using bounded expected energy at all rates below capacity. A lower bound on error probability for the finite bandwidth case is then derived in which the error probability decreases with an exponential order which is linearly increasing in block length at the same rate as the upper bound.


Errors-and-Erasures Decoding for Block Codes With Feedback
Nakiboğlu, Barış (2012-01-01)
Inner and outer bounds are derived on the optimal performance of fixed-length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First, an inner bound is derived using a two-phase encoding scheme with communication and control phases together with the optimal decoding rule for the given encoding scheme, among decoding rules that can be represented in terms of pairwise comparisons between the messages. Then, an outer bound is derived using a generalization of the stra...
Upper bounds to error probability with feedback
Nakiboğlu, Barış (2010-01-22)
A new analysis technique is suggested for bounding the error probability of fixed length block codes with feedback on discrete memoryless channels from above. Error analysis is inspired by Gal lager's error analysis for block codes without feedback. Using Burnashev-Zigangirov-D'yachkov encoding scheme analysis recovers previously known best results on binary symmetric channels and improves up on the previously known best results on k-ary symmetric channels and binary input channels.
Upper Bounds to Error Probability with Feedback
Nakiboğlu, Barış (2009-08-18)
A new technique is proposed for upper bounding the error probability of fixed length block codes with feedback. Error analysis is inspired by Gal lager's error analysis for block codes without feedback. Zigangirov-D'yachkov (Z-D) encoding scheme is analyzed with the technique on binary input channels and k-ary symmetric channels. A strict improvement is obtained for k-ary symmetric channels.
Effect of water-filling method on the PAPR for OFDM and MIMO systems
Vural, Mehmet; Akta, Tugcan; Yılmaz, Ali Özgür (2007-06-13)
In this paper, the peak-to-average power ratio (PAPR) problem for orthogonal frequency division multiplexing (OFDM) is investigated. The variations in the nature of the problem along with the utilization of water-filling technique are observed and the corresponding cumulative distribution function for PAPR is determined. In addition to OFDM analysis, another analysis is carried out for the comparison of water-filling technique and an equal power distribution algorithm in case of a multiple input multiple ou...
A simplified MAP channel estimator for OFDM systems under Rayleigh fading
ÇÜRÜK, SELVA; Tanık, Yalçın (2010-06-01)
This paper presents a simplified Maximum A Posteriori (SMAP) channel estimator to be used in orthogonal frequency division multiplexing (OFDM) systems under the Rayleigh fading assumption for the subchannels, using a parametric correlation model and assuming that the channel is frequency selective and slowly time varying. Expressions for the mean-square error (MSE) of estimations are derived to evaluate the performance of the estimator. The relation between the correlation of subchannels taps and error vari...
Citation Formats
R. G. Gallager and B. Nakiboğlu, “Variations on a Theme by Schalkwijk and Kailath,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 6–17, 2010, Accessed: 00, 2020. [Online]. Available: