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Topic: Convolutional code

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Forward error correction

Viterbi algorithm

Code division multiplexing

Maximum likelihood

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Markov chain

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	Convolutional code - Wikipedia, the free encyclopedia
		Convolutional codes are often used to improve the performance of radio and satellite links.
		Such codes were used in the Pioneer program of the early 1970s to Jupiter and Saturn, but gave way to shorter, Viterbi-decoded codes, usually concatenated with large Reed-Solomon error correction codes that steepen the overall bit-error-rate curve and produce extremely low residual undetected error rates.
		Simple Viterbi-decoded convolutional codes are now giving way to turbo codes, a new class of iterated short convolutional codes that closely approach the theoretical limits imposed by Shannon's theorem with much less decoding complexity than the Viterbi algorithm on the long convolutional codes that would be required for the same performance.
	en.wikipedia.org /wiki/Convolutional_code (1132 words)

	A Tutorial on Convolutional Coding with Viterbi Decoding
		Convolutional encoding with Viterbi decoding is a FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by additive white gaussian noise (AWGN).
		Convolutional codes are usually described using two parameters: the code rate and the constraint length.
		The code rate, k/n, is expressed as a ratio of the number of bits into the convolutional encoder (k) to the number of channel symbols output by the convolutional encoder (n) in a given encoder cycle.
	pw1.netcom.com /~chip.f/viterbi/tutorial.html (2034 words)

	Convolutional Codes (Site not responding. Last check: 2007-10-21)
		The constraint length of the code is 2.
		Although we can also directly construct a code of rate 2/3 as we shall see later, the advantage of a punctured code is that the rates can be changed dynamically (through software) depending on the channel condition such as rain, etc. A fixed implementation, although easier, does not allow this flexibility.
		The coded sequence is 11 11 01 11 01 01 11.
	www.complextoreal.com /convo.htm (1936 words)

	Error-correcting code - Wikipedia, the free encyclopedia
		In information theory and coding, an error-correcting code or ECC is a code in which each data signal conforms to specific rules of construction so that departures from this construction in the received signal can generally be automatically detected and corrected.
		Note 3: The two main classes of error-correcting codes are block codes and convolutional codes.
		See also Hamming code and Reed-Solomon code; or, for state-of-the-art codes developed from 1993 to 2003, see sparse graph codes, specifically low-density parity-check codes, turbo codes, and digital fountain codes.
	en.wikipedia.org /wiki/Error-correcting_code (298 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		In systems using convolutional codes, the coding gain is typically maximized by increasing the constraint length of the code at the cost of implementing a more complex system in terms of latency, computation and memory area.
		It is well known, in channel coding theory, that the coding gain achieved through convolutional coding is related to the free distance of the code.
		The overall coding rate resulting from the BCC and repetition encoding is equal to 1/L. The parameter L will be referenced hereinafter as the redundancy factor and is a measure of the size of the code so obtained after repetition.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/71963.010927&ELEMENT_SET=DECL (2212 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		For telecommunication channels which are bandwidth-constrained and cannot tolerate the increase in bandwidth required by the convolutional code in Section 2, the Reed-Solomon code specified in Section 3 has the advantage of smaller bandwidth expansion and has the capability to indicate the presence of uncorrectable errors.
		Where a greater coding gain is needed than can be provided by the convolutional code or Reed-Solomon code alone, a concatenation of the convolutional code as the inner code with the Reed-Solomon code as the outer code may be used for improved performance.
		CODE RATE: The average ratio of the number of binary digits at the input of an encoder to the number of binary digits at its output.
	ssdoo.gsfc.nasa.gov /nost/wwwclassic/documents/text/CCSDS-101.0-B-4.txt (6910 words)

	United States Patent Application: 0020122502
		The apparatus according to claim 13, wherein the code word is a part of C that is a linear L.sub.t.times.n space-time code, wherein L.sub.t represents the number of transmit antennas, the constraint being.left brkt-bot.c.sub.1.sup.(s), c.sub.2.sup.(s),.
		The apparatus according to claim 25, wherein the code word is a part of C that is a linear L.sub.t.times.n space-time code, wherein L.sub.t represents the number of transmit antennas, the constraint being.left brkt-bot.c.sub.1.sup.(s), c.sub.2.sup.(s),.
		The apparatus according to claim 73, wherein the code word is a part of C that is a linear L.sub.t.times.n space-time code, wherein L.sub.t represents the number of transmit antennas, the constraint being.left brkt-bot.c.sub.1.sup.(s), c.sub.2.sup.(s),.
	www.ece.osu.edu /~helgamal/app2.html (10735 words)

	Convolutional Decoders for Amateur Packet Radio (Site not responding. Last check: 2007-10-21)
		Convolutional coding is one of the two major types of error control coding (the other is block coding, e.g., Golay, Reed-Solomon).
		Basically, all convolutional decoders work by generating local hypotheses about the originally transmitted data, running those hypotheses through a local copy of the encoder, and comparing the encoded results with the (noisy) encoded data that is actually received.
		He examined the assembler code generated by his compiler (Watcom) and discovered that by reordering the butterflies to place together those operating on the same pair of branch symbols, the compiler did a better job of allocating registers and keeping common subexpression results involving the branch metrics.
	people.qualcomm.com /karn/papers/cnc_coding.html (3057 words)

	On Woven Convolutional Codes
		This thesis is devoted to woven convolutional codes, a construction where the constituent codes are woven together in a manner that resembles the structure of a fabric.
		Lower bounds on the active distances and the free distance are derived for the ensemble of periodically time-varying cascaded convolutional codes.
		In the constructions convolutional codes are woven together in a manner that resembles the structure of a fabric.
	www.it.lth.se /stefanh/Thesis/Thesis.html (1728 words)

	Channel coding aims at improving transmission quality when the signal encounters disturbances (noise, interference, ...
		Fire Code: this code is dedicated to the detection and correction of 'bursty' errors, i.e., errors that occur in a short time interval.
		The convolutional sequences ere obtained by applying an 'exclusive or' operation to the sequence and delayed versions of it, after addition of fixed bits at both ends of the original sequence.
		A Fire code is a conventional linear binary block code, i.e., it consists in transmitting, in addition to the information bits, k a number or redundant bits computed by exclusive-or manipulations on the information bits.
	www.tml.tkk.fi /Studies/Tik-110.300/1999/Wireless/channel_1.html (1816 words)

	Ensemble Analysis of Iteratively Decodable Convolutional - Zigangirov and Lentmaier (Site not responding. Last check: 2007-10-21)
		Convolutional codes are often used as component codes in schemes for iterative decoding, such as turbo codes (parallel concatenated convolutional codes), serially concatenated convolutional codes, or self-concatenated convolutional codes.
		Often the convolutional components of turbo-like codes are terminated, resulting in an overall block code of relatively large length.
		On the other hand, convolutional turbo codes can be described by sparse parity-check matrices and considered as a variant of LDPC convolutional codes with convolutional component codes.
	www.nd.edu /~cam/ima/EAIDCC_zigangirov_lentmaier.htm (556 words)

	High-rate Turbo Codes: Design and Efficient Decoding
		Channel coding provides the desired reliability by adding structured redundancy to the transmitted information, which can be used at the receiver side to correct some of the errors introduced by the channel.
		With the advent of concatenated codes with interleavers (or turbo-like codes), hard-in hard-out and soft-in hard-out decoding algorithms must be replaced by SISO symbol decoding algorithms to be embedded into the iterative decoding strategies adopted for those codes.
		To search for good high-rate (n; n-1) convolutional codes, The basic idea is to build an overall convolutional encoder composed of two constituent encoders: a block encoder associated to the parallel edges, and a low-to-moderate rate convolutional encoder that defines the dynamical part of the trellis.
	www.iua.upf.es /activitats/semirec/TurboCodes (1638 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		By coding M bits in parallel with a first (outer) encoder and N bits in parallel with a second (inner) encoder, the overall coding delays for the concatenated encoder can be significantly reduced.
		At the appropriate time, N code bits are retrieved from the memory and coded in parallel in accordance with a second coding scheme to generate coded data.
		Convolutional encoder 500 includes an encoder state machine 510 that implements the state machine defined in Table 2 and a data phase output generator 520 that generates the encoder outputs defined in Table 2.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=03/26137.030327&ELEMENT_SET=DECL (9775 words)

	PPI no. 3, 2002
		Due to memory and delay constraints in practical coding schemes, convolutional codes often are either terminated or decoded by a window decoder.
		When a window decoder is used, the convolutional code sequence is not terminated; instead, the window decoder estimates information digits after receiving a finite number of noise-corrupted code symbols, thereby keeping the decoding delay short.
		An exact characterization of the error-correcting capability of window decoded convolutional codes is given by using active distances of convolutional codes.
	www.ee.umd.edu /~abarg/ppi/contents/3-02-abstracts.html (516 words)

	Convolutional Coding / Decoding (Site not responding. Last check: 2007-10-21)
		Convolutional coding consists in transmitting the results of convolutions of the source sequence using different convolution formulas.
		Convolutional decoding can be performed using a Viterbi algorithm [2].
		Its complexity increases exponentially with the constraint length K. The GSM convolutional coding rate per data flow is 378 bits each 20 ms, i.e.: 18.9 kb/s.
	www.tns.lcs.mit.edu /~turletti/gsm-overview/node9.html (247 words)

	Using the Libraries (Using the Communications Blockset)
		Thus the constraint length of the code is 7.
		The code generator is a 1-by-2 matrix of octal numbers because the encoder has one input and two outputs.
		Notice that while the message data entering the Convolutional Encoder block is a scalar bit stream, the encoded data leaving the block is a stream of binary vectors of length 2.
	www.weizmann.ac.il /matlab/toolbox/commblks/usersguide/tutor140.html (1406 words)

	Iterative Decoding of a Serially Concatenated Convolutional Code (SCCC) - Demo (Using the Communications Blockset)
		The encoding portion of the demo uses a Convolutional Encoder block to encode a data frame, a Random Interleaver block to shuffle the bits in the code words, and another Convolutional Encoder block to encode the interleaved bits.
		In general, the purpose of interleaving is to protect code words from burst errors in a noisy channel.
		In each iteration, the decoding portion of the demo decodes the inner convolutional code, deinterleaves the result, and decodes the outer convolutional code.
	www.weizmann.ac.il /matlab/toolbox/commblks/usersguide/examp16a.html (968 words)

	Citebase - On the weight distribution of convolutional codes
		Detailed information about the weight distribution of a convolutional code is given by the adjacency matrix of the state diagram associated with a controller canonical form of the code.
		Moreover, it will be proven that codes with the same adjacency matrix have the same dimension and the same Forney indices and finally that for one-dimensional binary convolutional codes the adjacency matrix determines the code uniquely up to monomial equivalence.
		Convolutional codes and their performance in communication systems.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:cs/0501016 (362 words)

	[No title]
		The PN code we have been referring to is the pseudo-random noise sequence that is a random series of 1’s and —1’s.
		Convolutional Codes (CC) Overview CC is an error detection and correction method [3].
		A convolutional code is a sequence of encoded symbols, which is generated by passing the information sequentially through a binary shift register [1][3].
	www.utdallas.edu /~torlak/wireless/projects/ninaq.doc (3538 words)

	Using the Communications Toolbox (Communications Toolbox)
		The functions for encoding and decoding convolutional codes are
		code = convenc(ones(100,1),t); % Encode a string of ones.
		The first command converts a polynomial description of a feedforward convolutional encoder to the corresponding trellis description.
	www.eecs.umich.edu /dco/faq/matlab-6.5/help/toolbox/comm/tutor131.html (355 words)

	APP Decoder (Communications Blockset)
		The APP Decoder block performs a posteriori probability (APP) decoding of a convolutional code.
		The input L(u) represents the sequence of log-likelihoods of encoder input bits, while the input L(c) represents the sequence of log-likelihoods of code bits.
		To define the convolutional encoder that produced the coded input, use the Trellis structure parameter.
	www-rohan.sdsu.edu /doc/matlab/toolbox/commblks/ref/appdecoder.html (672 words)

	Constructions of Convolutional Codes with Large Free Distance by Roxana Smarandache
		This motivates the search for convolutional codes with a specified rate and degree (or constraint length) that have maximum free distance.
		The convolutional codes attaining this bound will be called MDS convolutional codes since they naturally generalize MDS block codes.
		Convolutional codes from quasi-cyclic codes: A link between the theories of block and convolutional codes.
	www.ima.umn.edu /biology/wkshp_abstracts/smarandache1.html (223 words)

	CCSDS Meetings - Fall 2000 - Panel 1B Information (Site not responding. Last check: 2007-10-21)
		Additional codes with lower overhead can be obtained by taking our basic r=1/2 convolutional code and puncturing (deleting selected bits) in the output.
		It was agreed to retain the current r=1/2 code as currently described including the G2 inverter (to help with existing implementations) and add a new section to define the new punctured codes without the G2 inverter.
		Also, the r=3/4 punctured convolutional code now being standardzed seems promising for use with the multidimensional trellis coded 8-PSK proposed by Ribes in P1E, providing it is verified to be rotationally invariant.
	ssdoo.gsfc.nasa.gov /nost/wwwclassic/meetings/2000fall/p1a_report_extract.html (1004 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Parity Equation of the Constiturnt Systematic Convolutional Code: The parity equation have both the numerator and denominator.
		Setting the numerator to 1 corresponse to a non-recursive systematic convolutional code.
		The followings are examples of the parity equation of constituent 1/2 rate convolutional code Ex1) Recursive Systematic Convolutional encoder 1+D+D^2+D^3 17 (1, -----------) = (1, --) in octal format 1+D^3 11 Ex2) Non-Recursive Systematic Convolutional encoder 1+D^2 (1, -----) = (1, 7) in octal format 1 -.
	www.eccpage.com /tcds_readme.txt (485 words)

	Parallel concatenated tail-biting convolutional code and decoder therefor (US5721745) (Site not responding. Last check: 2007-10-21)
		Method for a maximum likelihood decoding of a convolutional code with decision weighting, and corresponding decoder
		Error-correction coding method with at least two systematic convolutional codings in parallel, corresponding iterative decoding method, decoding module and decoder
		"Illuminating the Structure of Code and Decoder of Parallel Concatenated Recursive Systematic (Turbo) Codes," P. Robertson, 1994 IEEE Globecom Conference, pp.
	www.delphion.com /details?pn=US05721745__ (558 words)

	[No title]
		CONVOLUTIONAL CODES A convolutional encoder transforms k — input bits into n — output bits using SHIFT-registers and XOR’s Example: k = 1, n = 2 + + c1 binary input I output c2 Every time instant 1 input digit is shifted into the shift register and two outputs are produced.
		The encoder is denoted in octal notation as (1,7) and is said to have constraint length (memory) (= 2.
		Homework: determine the free distance for the code (1,7) Definition: Non-catastrophic Starting from any given non-zero physical encoder state, it should be impossible to generate an all zero output sequence.
	www.exp-math.uni-essen.de /~vinck/channel-coding/6-convcodes.doc (496 words)

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