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Bounds on the decoding complexity of punctured codes on graphs [article]

H. Pfister, I. Sason, R. Urbanke
2004 arXiv   pre-print
We also derive an information-theoretic lower bound on the decoding complexity of randomly punctured codes on graphs.  ...  The new bounded complexity result is achieved by puncturing bits, and allowing in this way a sufficient number of state nodes in the Tanner graph representing the codes.  ...  We also derive an information-theoretic lower bound on the decoding complexity of randomly punctured codes on graphs.  ... 
arXiv:cs/0409027v1 fatcat:br3jcuarrvdqphpdtlicrmdali

On Achievable Rates and Complexity of LDPC Codes for Parallel Channels: Information-Theoretic Bounds and Applications

Igal Sason, Gil Wiechman
2006 2006 IEEE International Symposium on Information Theory  
The paper presents bounds on the achievable rates and the decoding complexity of lowdensity parity-check (LDPC) codes.  ...  The bounds are applied to punctured LDPC codes. A diagram concludes our discussion by showing interconnections between the theorems in this paper and some previously reported results.  ...  Sason wishes to acknowledge Henry Pfister and Ruediger Urbanke for stimulating discussions on puncturing theorems during the preparation of the work in [5] . The work of I.  ... 
doi:10.1109/isit.2006.261700 dblp:conf/isit/SasonW06 fatcat:z76pye3v6zfwdlga7ddkl2kl5i

Performance versus Complexity Per Iteration for Low-Density Parity-Check Codes: An Information-Theoretic Approach [article]

Igal Sason, Gil Wiechman
2005 arXiv   pre-print
The paper is focused on the tradeoff between performance and decoding complexity per iteration for LDPC codes in terms of their gap (in rate) to capacity.  ...  The bounds are generalized for parallel channels, and are applied to ensembles of punctured LDPC codes where both intentional and random puncturing are addressed.  ...  Acknowledgment: The work was supported by the EU 6 th International Framework Programme via the NEWCOM Network of Excellence.  ... 
arXiv:cs/0512075v1 fatcat:7f4vqylixfc75fdxu73uy23hyq

On Achievable Rates and Complexity of LDPC Codes for Parallel Channels with Application to Puncturing [article]

Igal Sason, Gil Wiechman
2005 arXiv   pre-print
The paper relies on the latter bound for obtaining upper bounds on the achievable rates of ensembles of randomly and intentionally punctured LDPC codes over MBIOS channels.  ...  The paper also provides a lower bound on the decoding complexity (per iteration) of ensembles of LDPC codes under message-passing iterative decoding over parallel MBIOS channels; the bound is given in  ...  Sason wishes to acknowledge Henry Pfister and Ruediger Urbanke for stimulating discussions on puncturing theorems during the preparation of the work in [10] . The work of I.  ... 
arXiv:cs/0508072v1 fatcat:2kywszqu4nanxk32snf65jri24

On Achievable Rates and Complexity of LDPC Codes Over Parallel Channels: Bounds and Applications

Igal Sason, Gil Wiechman
2007 IEEE Transactions on Information Theory  
Upper bounds on the achievable rates under maximum-likelihood decoding, and lower bounds on the decoding complexity per iteration of ensembles of lowdensity parity-check (LDPC) codes are presented.  ...  The bounds are applied to ensembles of punctured LDPC codes where the puncturing patterns are either random or possess some structure.  ...  Sason wishes to acknowledge Henry Pfister and Ruediger Urbanke for stimulating discussions on puncturing theorems during the preparation of the work in [9] .  ... 
doi:10.1109/tit.2006.889462 fatcat:nyaqqeefojgpnlrve3gfmpunje

Bounds on the Number of Iterations for Turbo-Like Ensembles Over the Binary Erasure Channel

Igal Sason, Gil Wiechman
2009 IEEE Transactions on Information Theory  
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density  ...  The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity.  ...  Graphical Complexity of Codes Defined on Graphs As noted in Section 1, the decoding complexity of a graph-based code under iterative messagepassing decoding is closely related to its graphical complexity  ... 
doi:10.1109/tit.2009.2018342 fatcat:vijilrzggzc4zenk73yjeffgim

Bounds on the convergence speed of iterative message-passing decoders over the binary erasure channel

Igal Sason, Gil Wiechman
2008 2008 5th International Symposium on Turbo Codes and Related Topics  
Introduce new lower bounds on the number of iterations for the BEC where these bounds: Apply to various code ensembles defined on graphs (e.g., LDPC, RA, IRA, ARA) in the asymptotic case where n → ∞.  ...  For the BEC, the absolute reliability of the messages allows every edge in the graph to be used only once during the iterative decoding so the decoding complexity behaves like ln 1 ε .  ... 
doi:10.1109/turbocoding.2008.4658690 fatcat:mpzoxgkm4fgyvpn3dfphge7upy

Bounds on the Number of Iterations for Turbo-Like Ensembles over the Binary Erasure Channe [article]

Igal Sason, Gil Wiechman
2007 arXiv   pre-print
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density  ...  The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity.  ...  Graphical Complexity of Codes Defined on Graphs As noted in Section 1, the decoding complexity of a graph-based code under iterative messagepassing decoding is closely related to its graphical complexity  ... 
arXiv:0711.1056v1 fatcat:y5ox5ylq4jhprfwdgf346kiooq

Capacity-Achieving Ensembles for the Binary Erasure Channel With Bounded Complexity

H.D. Pfister, I. Sason, R. Urbanke
2005 IEEE Transactions on Information Theory  
We also derive an information-theoretic lower bound on the decoding complexity of randomly punctured codes on graphs.  ...  The new bounded complexity result is achieved by puncturing bits, and allowing in this way a sufficient number of state nodes in the Tanner graph representing the codes.  ...  They are grateful to the two anonymous reviewers for their constructive feedback on an earlier version of this paper, and for providing their reviews in a very short time.  ... 
doi:10.1109/tit.2005.850079 fatcat:vkjvt4yrjrbnnogb46ojvywjnu

Decoding Complexity of Irregular LDGM-LDPC Codes Over the BISOM Channels [article]

Manik Raina, Predrag Spasojevic
2010 arXiv   pre-print
A lower-bound on the average degree of the check-nodes of the irregular LDGM-LDPC codes is obtained. The bound does not depend on the decoder used at the receiver.  ...  The measure of complexity is the average-degree (per information-bit) of the check-nodes for the factor-graph of the code.  ...  DISCUSSION This paper obtains lower-bounds on the complexity of the decoding-complexity of irregular LDGM-LDPC codes.  ... 
arXiv:1003.2454v3 fatcat:jufgucdz2nfwnf7cy356khcuq4

Low complexity rate compatible puncturing patterns design for LDPC codes

Fulvio Babich, Matteo Noschese, Alessandro Soranzo, Francesca Vatta
2017 2017 25th International Conference on Software, Telecommunications and Computer Networks (SoftCOM)  
Moreover, through puncturing, allowing the adaption of the coding rate to different channel conditions with a single encoder/decoder pair, adaptability and flexibility can be obtained at a low computational  ...  We address a new design criterion for the puncturing patterns using a simplified analysis of the decoding belief propagation algorithm, i.e., considering a Gaussian approximation for message densities  ...  A low complexity performance assessment of the puncturing patterns was presented and formally justified, thanks to the work in [11] and to the bounds on thresholds found in [24] .  ... 
doi:10.23919/softcom.2017.8115558 dblp:conf/softcom/BabichNSV17 fatcat:gcrqksli6beulpezebdo63myyq

Low Complexity Rate Compatible Puncturing Patterns Design for LDPC Codes

Fulvio Babich, Matteo Noschese, Alessandro Soranzo, Francesca Vatta
2018 Journal of Communications Software and Systems  
Moreover, through puncturing, allowing the adaption of the coding rate to different channel conditions with a single encoder/decoder pair, adaptability and flexibility can be obtained at a low computational  ...  We address a new design criterion for the puncturing patterns using a simplified analysis of the decoding belief propagation algorithm, i.e., considering a Gaussian approximation for message densities  ...  A low complexity performance assessment of the puncturing patterns was presented and formally justified, thanks to the work in [11] and to the bounds on thresholds found in [24] .  ... 
doi:10.24138/jcomss.v14i4.639 fatcat:5rj4ngtz6jfc3pexqrronkgwwy

Results on Punctured Low-Density Parity-Check Codes and Improved Iterative Decoding Techniques

Hossein Pishro-Nik, Faramarz Fekri
2007 IEEE Transactions on Information Theory  
Specifically, this implies that rates arbitrarily close to one are achievable via puncturing. Bounds on the performance of punctured LDPC codes are also presented.  ...  Based on the above observations, a method is proposed to design good punctured LDPC codes over a broad range of rates.  ...  The authors are also grateful to Rudiger Urbanke, the Associate Editor, for handling the review.  ... 
doi:10.1109/tit.2006.889701 fatcat:jrfawlmiuvdkdnor6ee5i4xjlu

Accumulate-Repeat-Accumulate Codes: Systematic Codes Achieving the Binary Erasure Channel Capacity with Bounded Complexity [article]

Henry D. Pfister, Igal Sason
2005 arXiv   pre-print
The results here improve on the tradeoff between performance and complexity provided by the first capacity-achieving ensembles of irregular repeat-accumulate (IRA) codes with bounded complexity per information  ...  The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with bounded complexity per information bit.  ...  The work of I. Sason was also supported by the Taub and Shalom Foundations.  ... 
arXiv:cs/0509044v1 fatcat:nfk7tz6h2ne2xk54olgr7ajdl4

Lower bounds on the graphical complexity of finite-length LDPC codes

Igal Sason
2009 2009 IEEE International Symposium on Information Theory  
This paper considers information-theoretic lower bounds on the graphical complexity of finite-length LDPC codes.  ...  The lower bounds on the graphical complexity are compared to some explicit LDPC codes (or code ensembles), showing that these bounds are informative for considering the fundamental tradeoff which exists  ...  lower bounds on the graphical complexity of finite-length LDPC codes.  ... 
doi:10.1109/isit.2009.5205822 dblp:conf/isit/Sason09a fatcat:7iktzmxjyffitjmjz7zs6mo5ti
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