Theory and practice of error control codes
01 Sep 1986-Vol. 74, Iss: 9, pp 1293-1294
TL;DR: This chapter discusses algorithmics and modular computations, Theory of Codes and Cryptography (3), and the theory and practice of error control codes (3).
Abstract: algorithmics and modular computations, Theory of Codes and Cryptography (3).From an analytical 1. RE Blahut. Theory and practice of error control codes. eecs.uottawa.ca/∼yongacog/courses/coding/ (3) R.E. Blahut,Theory and Practice of Error Control Codes, Addison Wesley, 1983. QA 268. Cached. Download as a PDF 457, Theory and Practice of Error Control CodesBlahut 1984 (Show Context). Citation Context..ontinued fractions.
Citations
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TL;DR: The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R< I( W) there exists a sequence of polar codes {Cfrn;nges1} such that Cfrn has block-length N=2n, rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate.
Abstract: A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W) of any given binary-input discrete memoryless channel (B-DMC) W. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a second set of N binary-input channels {WN(i)1 les i les N} such that, as N becomes large, the fraction of indices i for which I(WN(i)) is near 1 approaches I(W) and the fraction for which I(WN(i)) is near 0 approaches 1-I(W). The polarized channels {WN(i)} are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R< I(W) there exists a sequence of polar codes {Cfrn;nges1} such that Cfrn has block-length N=2n , rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N logN) for each.
3,554 citations
19 Oct 2003
TL;DR: The design and implementation of SplitStream are presented and experimental results show that SplitStream distributes the forwarding load among all peers and can accommodate peers with different bandwidth capacities while imposing low overhead for forest construction and maintenance.
Abstract: In tree-based multicast systems, a relatively small number of interior nodes carry the load of forwarding multicast messages. This works well when the interior nodes are highly-available, dedicated infrastructure routers but it poses a problem for application-level multicast in peer-to-peer systems. SplitStream addresses this problem by striping the content across a forest of interior-node-disjoint multicast trees that distributes the forwarding load among all participating peers. For example, it is possible to construct efficient SplitStream forests in which each peer contributes only as much forwarding bandwidth as it receives. Furthermore, with appropriate content encodings, SplitStream is highly robust to failures because a node failure causes the loss of a single stripe on average. We present the design and implementation of SplitStream and show experimental results obtained on an Internet testbed and via large-scale network simulation. The results show that SplitStream distributes the forwarding load among all peers and can accommodate peers with different bandwidth capacities while imposing low overhead for forest construction and maintenance.
1,535 citations
Cites background from "Theory and practice of error contro..."
...Instead of relying on a multicast infrastructure in the network (which is not widely available), the participating hosts route and distribute multicast messages using only unicast network services....
[...]
TL;DR: A simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs is introduced and a simple criterion involving the fractions of nodes of different degrees on both sides of the graph is obtained which is necessary and sufficient for the decoding process to finish successfully with high probability.
Abstract: We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability. By carefully designing these graphs we can construct for any given rate R and any given real number /spl epsiv/ a family of linear codes of rate R which can be encoded in time proportional to ln(1//spl epsiv/) times their block length n. Furthermore, a codeword can be recovered with high probability from a portion of its entries of length (1+/spl epsiv/)Rn or more. The recovery algorithm also runs in time proportional to n ln(1//spl epsiv/). Our algorithms have been implemented and work well in practice; various implementation issues are discussed.
1,341 citations
10 Sep 2007
TL;DR: New protocols for the IP protection problem on FPGAs are proposed and the first construction of a PUF intrinsic to current FPGA based on SRAM memory randomness present on current FFPAs is provided.
Abstract: In recent years, IP protection of FPGA hardware designs has become a requirement for many IP vendors. In [34], Simpson and Schaumont proposed a fundamentally different approach to IP protection on FPGAs based on the use of Physical Unclonable Functions (PUFs). Their work only assumes the existence of a PUF on the FPGAs without actually proposing a PUF construction. In this paper, we propose new protocols for the IP protection problem on FPGAs and provide the first construction of a PUF intrinsic to current FPGAs based on SRAM memory randomness present on current FPGAs. We analyze SRAM-based PUF statistical properties and investigate the trade offs that can be made when implementing a fuzzy extractor.
1,235 citations
TL;DR: This work proves sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case and shows how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels.
Abstract: The authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we show that they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case. In particular, we show how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinite-length signals with finite local rate of innovation, we show local sampling and reconstruction based on spline kernels. The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and error-correction coding. This leads to standard computational procedures for solving the sampling problem, which we show through experimental results. Applications of these new sampling results can be found in signal processing, communications systems, and biological systems.
1,206 citations
Cites background from "Theory and practice of error contro..."
...In error-correction coding, it is called the error locator polynomial [1]....
[...]
...Take a Poisson process, which generates Diracs with independent and identically distributed (i.i.d.) interarrival times, the distribution being exponential with probability density function ....
[...]
References
More filters
TL;DR: The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R< I( W) there exists a sequence of polar codes {Cfrn;nges1} such that Cfrn has block-length N=2n, rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate.
Abstract: A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W) of any given binary-input discrete memoryless channel (B-DMC) W. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a second set of N binary-input channels {WN(i)1 les i les N} such that, as N becomes large, the fraction of indices i for which I(WN(i)) is near 1 approaches I(W) and the fraction for which I(WN(i)) is near 0 approaches 1-I(W). The polarized channels {WN(i)} are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R< I(W) there exists a sequence of polar codes {Cfrn;nges1} such that Cfrn has block-length N=2n , rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N logN) for each.
3,554 citations
Book•
01 Jan 1983
TL;DR: To understand the theoretical framework upon which error-control codes are built and then Algebraic Codes for Data Transmission by Richard E. Blahut, needed, several examples to illustrate the performance of the approximation scheme in practice are needed.
Abstract: To understand the theoretical framework upon which error-control codes are built and then Algebraic Codes for Data Transmission By Richard E. Blahut. Hamid Jafarkhani, “Space-Time Coding: Theory and Practice”, Cambridge. Textbook, Richard E. Blahut, Algebraic Codes for Data Transmission. Bibliography Peter Sweeney, Error Control Coding: From Theory to Practice Juergen. 2Automatic Control Laboratory, ETH Zurich, Switzerland several examples to illustrate the performance of the approximation scheme in practice. Information theory says that there exists operational quantities called channel (9) Richard E. Blahut, “Computation of channel capacity and rate-distortion functions,” IEEE.
1,973 citations
19 Oct 2003
TL;DR: The design and implementation of SplitStream are presented and experimental results show that SplitStream distributes the forwarding load among all peers and can accommodate peers with different bandwidth capacities while imposing low overhead for forest construction and maintenance.
Abstract: In tree-based multicast systems, a relatively small number of interior nodes carry the load of forwarding multicast messages. This works well when the interior nodes are highly-available, dedicated infrastructure routers but it poses a problem for application-level multicast in peer-to-peer systems. SplitStream addresses this problem by striping the content across a forest of interior-node-disjoint multicast trees that distributes the forwarding load among all participating peers. For example, it is possible to construct efficient SplitStream forests in which each peer contributes only as much forwarding bandwidth as it receives. Furthermore, with appropriate content encodings, SplitStream is highly robust to failures because a node failure causes the loss of a single stripe on average. We present the design and implementation of SplitStream and show experimental results obtained on an Internet testbed and via large-scale network simulation. The results show that SplitStream distributes the forwarding load among all peers and can accommodate peers with different bandwidth capacities while imposing low overhead for forest construction and maintenance.
1,535 citations
TL;DR: A simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs is introduced and a simple criterion involving the fractions of nodes of different degrees on both sides of the graph is obtained which is necessary and sufficient for the decoding process to finish successfully with high probability.
Abstract: We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability. By carefully designing these graphs we can construct for any given rate R and any given real number /spl epsiv/ a family of linear codes of rate R which can be encoded in time proportional to ln(1//spl epsiv/) times their block length n. Furthermore, a codeword can be recovered with high probability from a portion of its entries of length (1+/spl epsiv/)Rn or more. The recovery algorithm also runs in time proportional to n ln(1//spl epsiv/). Our algorithms have been implemented and work well in practice; various implementation issues are discussed.
1,341 citations
10 Sep 2007
TL;DR: New protocols for the IP protection problem on FPGAs are proposed and the first construction of a PUF intrinsic to current FPGA based on SRAM memory randomness present on current FFPAs is provided.
Abstract: In recent years, IP protection of FPGA hardware designs has become a requirement for many IP vendors. In [34], Simpson and Schaumont proposed a fundamentally different approach to IP protection on FPGAs based on the use of Physical Unclonable Functions (PUFs). Their work only assumes the existence of a PUF on the FPGAs without actually proposing a PUF construction. In this paper, we propose new protocols for the IP protection problem on FPGAs and provide the first construction of a PUF intrinsic to current FPGAs based on SRAM memory randomness present on current FPGAs. We analyze SRAM-based PUF statistical properties and investigate the trade offs that can be made when implementing a fuzzy extractor.
1,235 citations