### 2015

Olmos, Pablo M; Mitchell, David G M; Costello, Daniel J

Analyzing the Finite-Length Performance of Generalized LDPC Codes Inproceedings

In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 2683–2687, IEEE, Hong Kong, 2015, ISBN: 978-1-4673-7704-1.

Abstract | Links | BibTeX | Tags: BEC, binary codes, binary erasure channel, Block codes, Codes on graphs, Decoding, Differential equations, error probability, finite-length generalized LDPC block codes, finite-length performance analysis, generalized LDPC codes, generalized peeling decoder, GLDPC block codes, graph degree distribution, graph theory, Iterative decoding, parity check codes, protographs

@inproceedings{Olmos2015b,

title = {Analyzing the Finite-Length Performance of Generalized LDPC Codes},

author = {Pablo M Olmos and David G M Mitchell and Daniel J Costello},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7282943},

doi = {10.1109/ISIT.2015.7282943},

isbn = {978-1-4673-7704-1},

year = {2015},

date = {2015-06-01},

booktitle = {2015 IEEE International Symposium on Information Theory (ISIT)},

pages = {2683--2687},

publisher = {IEEE},

address = {Hong Kong},

abstract = {In this paper, we analyze the performance of finite-length generalized LDPC (GLDPC) block codes constructed from protographs when transmission takes place over the binary erasure channel (BEC). A generalized peeling decoder is proposed and we derive a system of differential equations that gives the expected evolution of the graph degree distribution during decoding. We then show that the finite-length performance of a GLDPC code can be estimated by means of a simple scaling law, where a single scaling parameter represents the finite-length properties of the code. We also show that, as we consider stronger component codes, both the asymptotic threshold and the finite-length scaling parameter are improved.},

keywords = {BEC, binary codes, binary erasure channel, Block codes, Codes on graphs, Decoding, Differential equations, error probability, finite-length generalized LDPC block codes, finite-length performance analysis, generalized LDPC codes, generalized peeling decoder, GLDPC block codes, graph degree distribution, graph theory, Iterative decoding, parity check codes, protographs},

pubstate = {published},

tppubtype = {inproceedings}

}

Vazquez-Vilar, Gonzalo; Martinez, Alfonso; i Fabregas, Albert Guillen

A derivation of the Cost-Constrained Sphere-Packing Exponent Inproceedings

In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 929–933, IEEE, Hong Kong, 2015, ISBN: 978-1-4673-7704-1.

Links | BibTeX | Tags: Channel Coding, channel-coding cost-constrained sphere-packing exp, continuous channel, continuous memoryless channel, cost constraint, error probability, hypothesis testing, Lead, Memoryless systems, Optimization, per-codeword cost constraint, reliability function, spherepacking exponent, Testing

@inproceedings{Vazquez-Vilar2015,

title = {A derivation of the Cost-Constrained Sphere-Packing Exponent},

author = {Gonzalo Vazquez-Vilar and Alfonso Martinez and Albert Guillen i Fabregas},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7282591},

doi = {10.1109/ISIT.2015.7282591},

isbn = {978-1-4673-7704-1},

year = {2015},

date = {2015-06-01},

booktitle = {2015 IEEE International Symposium on Information Theory (ISIT)},

pages = {929--933},

publisher = {IEEE},

address = {Hong Kong},

keywords = {Channel Coding, channel-coding cost-constrained sphere-packing exp, continuous channel, continuous memoryless channel, cost constraint, error probability, hypothesis testing, Lead, Memoryless systems, Optimization, per-codeword cost constraint, reliability function, spherepacking exponent, Testing},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2014

Olmos, Pablo M; Mitchell, David G M; Truhachev, Dimitri; Costello, Daniel J

Improving the Finite-Length Performance of Long SC-LDPC Code Chains by Connecting Consecutive Chains Inproceedings

In: 8th IEEE International Symposium on Turbo Codes &amp; Iterative Information Processing, pp. 72–76, IEEE, Bremen, 2014.

Abstract | Links | BibTeX | Tags: Decoding, Error analysis, error probability, Information processing, parity check codes, Turbo codes

@inproceedings{Olmos2014,

title = {Improving the Finite-Length Performance of Long SC-LDPC Code Chains by Connecting Consecutive Chains},

author = {Pablo M Olmos and David G M Mitchell and Dimitri Truhachev and Daniel J Costello},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6955088},

year = {2014},

date = {2014-01-01},

booktitle = {8th IEEE International Symposium on Turbo Codes &amp; Iterative Information Processing},

pages = {72--76},

publisher = {IEEE},

address = {Bremen},

abstract = {We propose a novel encoding/transmission scheme called continuous chain (CC) transmission that is able to improve the finite-length performance of a system using long spatially coupled low-density parity-check (SC-LDPC) code chains. First, we show that the decoding of SC-LDPC code chains is more reliable for shorter chain lengths, i.e., the scaling between block error rate and gap to threshold is more favorable for shorter chains. This motivates the use of CC transmission in which, instead of transmitting a sequence of independent codewords from a long SC-LDPC chain, we connect multiple chains in a layered format, where encoding, transmission, and decoding are now performed in a continuous fashion. Finally, we show that CC transmission can be implemented with only a small increase in decoding complexity or delay with respect to a system employing a single SC-LDPC code chain for transmission},

keywords = {Decoding, Error analysis, error probability, Information processing, parity check codes, Turbo codes},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2013

Yang, Wei; Durisi, Giuseppe; Koch, Tobias; Polyanskiy, Yury

Quasi-Static SIMO Fading Channels at Finite Blocklength Inproceedings

In: 2013 IEEE International Symposium on Information Theory, pp. 1531–1535, IEEE, Istanbul, 2013, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: achievability bounds, AWGN channel, AWGN channels, channel capacity, channel dispersion, channel gains, Dispersion, error probability, error statistics, Fading, fading channels, fading realizations, fast convergence, finite blocklength, maximal achievable rate, numerical evaluation, outage capacity, quasistatic SIMO fading channels, Random variables, Receivers, SIMO Rician channel, single-input multiple-output, Transmitters, zero dispersion

@inproceedings{Yang2013a,

title = {Quasi-Static SIMO Fading Channels at Finite Blocklength},

author = {Wei Yang and Giuseppe Durisi and Tobias Koch and Yury Polyanskiy},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6620483},

issn = {2157-8095},

year = {2013},

date = {2013-01-01},

booktitle = {2013 IEEE International Symposium on Information Theory},

pages = {1531--1535},

publisher = {IEEE},

address = {Istanbul},

abstract = {We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases. In the example of a particular 1×2 SIMO Rician channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity.},

keywords = {achievability bounds, AWGN channel, AWGN channels, channel capacity, channel dispersion, channel gains, Dispersion, error probability, error statistics, Fading, fading channels, fading realizations, fast convergence, finite blocklength, maximal achievable rate, numerical evaluation, outage capacity, quasistatic SIMO fading channels, Random variables, Receivers, SIMO Rician channel, single-input multiple-output, Transmitters, zero dispersion},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2012

Olmos, Pablo M; Perez-Cruz, Fernando; Salamanca, Luis; Murillo-Fuentes, Juan Jose

Finite-Length Analysis of the TEP Decoder for LDPC Ensembles over the BEC Inproceedings

In: 2012 IEEE International Symposium on Information Theory Proceedings, pp. 2346–2350, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: Approximation methods, BEC, binary codes, binary erasure channel, Decoding, Error analysis, error probability, finite-length analysis, LDPC ensembles, low-density parity check ensembles, parity check codes, TEP decoder, Trajectory, tree-expectation propagation algorithm, waterfall region

@inproceedings{Olmos2012a,

title = {Finite-Length Analysis of the TEP Decoder for LDPC Ensembles over the BEC},

author = {Pablo M Olmos and Fernando Perez-Cruz and Luis Salamanca and Juan Jose Murillo-Fuentes},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6283932},

issn = {2157-8095},

year = {2012},

date = {2012-01-01},

booktitle = {2012 IEEE International Symposium on Information Theory Proceedings},

pages = {2346--2350},

publisher = {IEEE},

address = {Cambridge, MA},

abstract = {In this work, we analyze the finite-length performance of low-density parity check (LDPC) ensembles decoded over the binary erasure channel (BEC) using the tree-expectation propagation (TEP) algorithm. In a previous paper, we showed that the TEP improves the BP performance for decoding regular and irregular short LDPC codes, but the perspective was mainly empirical. In this work, given the degree-distribution of an LDPC ensemble, we explain and predict the range of code lengths for which the TEP improves the BP solution. In addition, for LDPC ensembles that present a single critical point, we propose a scaling law to accurately predict the performance in the waterfall region. These results are of critical importance to design practical LDPC codes for the TEP decoder.},

keywords = {Approximation methods, BEC, binary codes, binary erasure channel, Decoding, Error analysis, error probability, finite-length analysis, LDPC ensembles, low-density parity check ensembles, parity check codes, TEP decoder, Trajectory, tree-expectation propagation algorithm, waterfall region},

pubstate = {published},

tppubtype = {inproceedings}

}

Campo, Adria Tauste; Vazquez-Vilar, Gonzalo; i Fàbregas, Albert Guillen; Koch, Tobias; Martinez, Alfonso

Random Coding Bounds that Attain the Joint Source-Channel Exponent Inproceedings

In: 2012 46th Annual Conference on Information Sciences and Systems (CISS), pp. 1–5, IEEE, Princeton, 2012, ISBN: 978-1-4673-3140-1.

Abstract | Links | BibTeX | Tags: code construction, combined source-channel coding, Csiszár error exponent, Ducts, error probability, error statistics, Gallager exponent, joint source-channel coding, joint source-channel exponent, random codes, random-coding upper bound, Yttrium

@inproceedings{Campo2012,

title = {Random Coding Bounds that Attain the Joint Source-Channel Exponent},

author = {Adria Tauste Campo and Gonzalo Vazquez-Vilar and Albert Guillen i Fàbregas and Tobias Koch and Alfonso Martinez},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6310910},

isbn = {978-1-4673-3140-1},

year = {2012},

date = {2012-01-01},

booktitle = {2012 46th Annual Conference on Information Sciences and Systems (CISS)},

pages = {1--5},

publisher = {IEEE},

address = {Princeton},

abstract = {This paper presents a random-coding upper bound on the average error probability of joint source-channel coding that attains Csiszár's error exponent. The bound is based on a code construction for which source messages are assigned to disjoint subsets (classes), and codewords are generated according to a distribution that depends on the class of the source message. For a single class, the bound recovers Gallager's exponent; identifying the classes with source type classes, it recovers Csiszár's exponent. Moreover, it is shown that as a two appropriately designed classes are sufficient to attain Csiszár's exponent.},

keywords = {code construction, combined source-channel coding, Csiszár error exponent, Ducts, error probability, error statistics, Gallager exponent, joint source-channel coding, joint source-channel exponent, random codes, random-coding upper bound, Yttrium},

pubstate = {published},

tppubtype = {inproceedings}

}

Campo, Adria Tauste; Vazquez-Vilar, Gonzalo; i Fabregas, Albert Guillen; Koch, Tobias; Martinez, Alfonso

Achieving Csiszár's Source-Channel Coding Exponent with Product Distributions Inproceedings

In: 2012 IEEE International Symposium on Information Theory Proceedings, pp. 1548–1552, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: average probability of error, Channel Coding, code construction, codewords, Csiszár's source-channel coding, Decoding, Encoding, error probability, error statistics, Joints, Manganese, product distributions, random codes, random-coding upper bound, source coding, source messages, Upper bound

@inproceedings{Campo2012a,

title = {Achieving Csiszár's Source-Channel Coding Exponent with Product Distributions},

author = {Adria Tauste Campo and Gonzalo Vazquez-Vilar and Albert Guillen i Fabregas and Tobias Koch and Alfonso Martinez},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6283524},

issn = {2157-8095},

year = {2012},

date = {2012-01-01},

booktitle = {2012 IEEE International Symposium on Information Theory Proceedings},

pages = {1548--1552},

publisher = {IEEE},

address = {Cambridge, MA},

abstract = {We derive a random-coding upper bound on the average probability of error of joint source-channel coding that recovers Csiszár's error exponent when used with product distributions over the channel inputs. Our proof technique for the error probability analysis employs a code construction for which source messages are assigned to subsets and codewords are generated with a distribution that depends on the subset.},

keywords = {average probability of error, Channel Coding, code construction, codewords, Csiszár's source-channel coding, Decoding, Encoding, error probability, error statistics, Joints, Manganese, product distributions, random codes, random-coding upper bound, source coding, source messages, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2011

Olmos, Pablo M; Urbanke, Rudiger

Scaling Behavior of Convolutional LDPC Ensembles over the BEC Inproceedings

In: 2011 IEEE International Symposium on Information Theory Proceedings, pp. 1816–1820, IEEE, Saint Petersburg, 2011, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: BEC, binary codes, binary erasure channel, Bit error rate, convolutional codes, convolutional LDPC ensembles, coupled sparse graph codes, Couplings, Decoding, error probability, Iterative decoding, parity check codes, scaling behavior

@inproceedings{Olmos2011,

title = {Scaling Behavior of Convolutional LDPC Ensembles over the BEC},

author = {Pablo M Olmos and Rudiger Urbanke},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6033863},

issn = {2157-8095},

year = {2011},

date = {2011-01-01},

booktitle = {2011 IEEE International Symposium on Information Theory Proceedings},

pages = {1816--1820},

publisher = {IEEE},

address = {Saint Petersburg},

abstract = {We study the scaling behavior of coupled sparse graph codes over the binary erasure channel. In particular, let 2L+1 be the length of the coupled chain, let M be the number of variables in each of the 2L+1 local copies, let ℓ be the number of iterations, let Pb denote the bit error probability, and let ∈ denote the channel parameter. We are interested in how these quantities scale when we let the blocklength (2L + 1)M tend to infinity. Based on empirical evidence we show that the threshold saturation phenomenon is rather stable with respect to the scaling of the various parameters and we formulate some general rules of thumb which can serve as a guide for the design of coding systems based on coupled graphs.},

keywords = {BEC, binary codes, binary erasure channel, Bit error rate, convolutional codes, convolutional LDPC ensembles, coupled sparse graph codes, Couplings, Decoding, error probability, Iterative decoding, parity check codes, scaling behavior},

pubstate = {published},

tppubtype = {inproceedings}

}

Goparaju, S; Calderbank, A R; Carson, W R; Rodrigues, Miguel R D; Perez-Cruz, Fernando

When to Add Another Dimension when Communicating over MIMO Channels Inproceedings

In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3100–3103, IEEE, Prague, 2011, ISSN: 1520-6149.

Abstract | Links | BibTeX | Tags: divide and conquer approach, divide and conquer methods, error probability, error rate, error statistics, Gaussian channels, Lattices, Manganese, MIMO, MIMO channel, MIMO communication, multiple input multiple output Gaussian channel, Mutual information, optimal power allocation, power allocation, power constraint, receive filter, Resource management, Signal to noise ratio, signal-to-noise ratio, transmit filter, Upper bound

@inproceedings{Goparaju2011,

title = {When to Add Another Dimension when Communicating over MIMO Channels},

author = {S Goparaju and A R Calderbank and W R Carson and Miguel R D Rodrigues and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5946351},

issn = {1520-6149},

year = {2011},

date = {2011-01-01},

booktitle = {2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},

pages = {3100--3103},

publisher = {IEEE},

address = {Prague},

abstract = {This paper introduces a divide and conquer approach to the design of transmit and receive filters for communication over a Multiple Input Multiple Output (MIMO) Gaussian channel subject to an average power constraint. It involves conversion to a set of parallel scalar channels, possibly with very different gains, followed by coding per sub-channel (i.e. over time) rather than coding across sub-channels (i.e. over time and space). The loss in performance is negligible at high signal-to-noise ratio (SNR) and not significant at medium SNR. The advantages are reduction in signal processing complexity and greater insight into the SNR thresholds at which a channel is first allocated power. This insight is a consequence of formulating the optimal power allocation in terms of an upper bound on error rate that is determined by parameters of the input lattice such as the minimum distance and kissing number. The resulting thresholds are given explicitly in terms of these lattice parameters. By contrast, when the optimization problem is phrased in terms of maximizing mutual information, the solution is mercury waterfilling, and the thresholds are implicit.},

keywords = {divide and conquer approach, divide and conquer methods, error probability, error rate, error statistics, Gaussian channels, Lattices, Manganese, MIMO, MIMO channel, MIMO communication, multiple input multiple output Gaussian channel, Mutual information, optimal power allocation, power allocation, power constraint, receive filter, Resource management, Signal to noise ratio, signal-to-noise ratio, transmit filter, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}