# Performance evaluation of concatenated kernel codes

VIT University

^{1}01 Mar 2017-pp 1-4

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.

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TL;DR: An example of concatenated kernel code and its trellis is constructed to demonstrate the importance of defined code andIts computation.

Abstract: Concatenated codes introduced by Forney in 1966 received wide attention due to their extensive usage in space missions. Thereafter, many concatenated codes were constructed on the similar lines and...

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##### References

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01 Jan 1948

TL;DR: The Mathematical Theory of Communication (MTOC) as discussed by the authors was originally published as a paper on communication theory more than fifty years ago and has since gone through four hardcover and sixteen paperback printings.

Abstract: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

10,215 citations

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TL;DR: The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.

Abstract: The probability of error in decoding an optimal convolutional code transmitted over a memoryless channel is bounded from above and below as a function of the constraint length of the code. For all but pathological channels the bounds are asymptotically (exponentially) tight for rates above R_{0} , the computational cutoff rate of sequential decoding. As a function of constraint length the performance of optimal convolutional codes is shown to be superior to that of block codes of the same length, the relative improvement increasing with rate. The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.

6,804 citations

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6,667 citations

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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

### "Performance evaluation of concatena..." refers background in this paper

...Concatenated Code met both the objectives [5] of, communicating with the rate R less than the channel capacity C (R < C) (Shannon model [6]) and correcting the errors that occur during the transmission within the limit of decoding failure (Hamming model [7])....

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TL;DR: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered and an optimal decoding algorithm is derived.

Abstract: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. The decoding of linear block and convolutional codes to minimize symbol error probability is shown to be a special case of this problem. An optimal decoding algorithm is derived.

4,830 citations

### "Performance evaluation of concatena..." refers methods in this paper

...Grpah decoder like Maximum likelihood Viterbi decoder [12] and Bahl, Cocke, Jelinek and Raviv (or BCJR in short) [13] etc....

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