Construction of Binary and Nonbinary LDPC-like Codes from Kernel Codes
01 Jan 2016-pp 459-466
TL;DR: A new method of constructing binary and nonbinary LDPC-like codes from Kernel codes defined over groups is discussed and constructed, and it is shown that constructions of binary andnonbinaryLDPC- like codes are particular cases of this proposed method.
Abstract: Low Density Parity Check (LDPC) codes have been of great interest to researchers due to its low complexity in encoding as well as decoding. Since the introduction of Turbo codes in 1993, importance of LDPC codes has been widely explored. Various techniques have been introduced for encoding and decoding of low density parity check codes based on algebraic structures, codes on graphs, etc. In this paper, a new method of constructing binary and nonbinary LDPC-like codes from Kernel codes defined over groups is discussed. Also, we show that constructions of binary and nonbinary LDPC-like codes are particular cases of our proposed method.
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TL;DR: Error correction coding is extensively used to achieve reliability in digital communication especially in Physical Layer and construction of concatenated kernel code defined over algebraic structure group is discussed.
3 citations
01 Mar 2017
TL;DR: It is observed that the concatenatedkernel codes with random selection of groups perform better than kernel codes withrandom selection of homomorphisms with coding gain.
Abstract: Concatenated codes proposed by Forney are used extensively in digital communication. In this paper, concatenated kernel codes, a class of group codes is constructed with inner code and outer code. Binary and non — binary variants of concatenated kernel code is discussed with example. Constructed concatenated kernel code is represented over trellis. Minimal trellis representation is given for the concatenated kernel code and its state complexity profile is discussed. Performance evaluation of concatenated kernel code is derived in terms of BER. It is observed that the concatenated kernel codes with random selection of groups perform better than kernel codes with random selection of homomorphisms with coding gain.
1 citations
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...More zero homomorphisms can be defined to obtain sparse codes [15]....
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References
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TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.
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01 Jan 1963TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Abstract: A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.
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Proceedings Article•
01 Jan 1993
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23 May 1993
TL;DR: In this article, a new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed.
Abstract: A new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed. The turbo-code encoder is built using a parallel concatenation of two recursive systematic convolutional codes, and the associated decoder, using a feedback decoding rule, is implemented as P pipelined identical elementary decoders. >
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TL;DR: The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result.
Abstract: The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result. This problem of “doing things right” on a large scale is not essentially new; in a telephone central office, for example, a very large number of operations are performed while the errors leading to wrong numbers are kept well under control, though they have not been completely eliminated. This has been achieved, in part, through the use of self-checking circuits. The occasional failure that escapes routine checking is still detected by the customer and will, if it persists, result in customer complaint, while if it is transient it will produce only occasional wrong numbers. At the same time the rest of the central office functions satisfactorily. In a digital computer, on the other hand, a single failure usually means the complete failure, in the sense that if it is detected no more computing can be done until the failure is located and corrected, while if it escapes detection then it invalidates all subsequent operations of the machine. Put in other words, in a telephone central office there are a number of parallel paths which are more or less independent of each other; in a digital machine there is usually a single long path which passes through the same piece of equipment many, many times before the answer is obtained.
5,408 citations