P. Elias, "Error-free coding," IRE Trans. Inform. Theory, vol. IT-4, Sept., 1954, 29-37.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....byte errors that may cause the RS ECC decoder to fail. Due to the high decoding complexity of turbo codes, current research focuses on lower complexity solutions that are easily implementable in hardware. Iterative decoding of turbo product codes (TPC) also referred to as block turbo codes (BTC) [10] [13] and low density parity check codes in particular [5] 9] seem to be potential solutions. An LDPC code exhibits similar performance to that of a turbo code, yet with considerably less decoding complexity (about 1=10 that of a turbo decoder) A randomly constructed LDPC code has quadratic ....

....of the system is prohibitively complex, the practical, yet e ective way, is to use turbo equalization to iterate soft outputs between the outer decoder and the equalizer, and then feed the hard decision decoding to the RS ECC code. 2. 1 Introduction to TPC SPC Codes A turbo product code [10] is composed of a multi dimensional array of codewords from linear block codes like Hamming codes, BCH codes and parity check codes (see Fig. for the code structure) A 2 dimensional turbo product code, C, formed from component codes C i (n i ; k i ; d i ; G i ) i = 1; 2; has parameters (n 1 ....

P. Elias, \Error-free coding," IRE Trans. Inform. Theory, vol. IT-4, pp. 29-37, Sept., 1954.

....Conclusions and future work are discussed in Section 9. 2 Background on TPC SPC Codes Since the motivation for the proposed product accumulate codes stems from TPC SPC codes, it is desirable to first discuss TPC SPC codes. 2. 1 TPC SPC Code Structure and Properties A turbo product code (TPC) [6] is composed of a multi dimensional array of codewords from linear block codes, such as parity check codes, Hamming codes and BCH codes. Particularly of interest is the simplest type of TPC codes, namely, single parity check turbo product codes (TPC SPC) due to their simplicity and high rate. An ....

P. Elias, "Error-free coding," IRE Trans. Inform. Theory, pp. 29-37, Sept., 1954.

....convolutional codes, having Markov properties. The error performance described by these bounds can be reached by applying maximum likelihood decoding on these codes, which is much too complex to use for codes with practically interesting sizes. Iterative decoding methods, first introduced by Elias [6], have attracted great interest during resent years when applied to turbo codes [5] Since the complexity of iterative decoding practically does not depend on the memory of the code, it can be used for decoding very long codes, and very good performance can be achieved even for transmission close ....

P. Elias, "Error-free coding", IRE Transactions on Information Theory, vol. PGIT-4, pp. 29-37, Sept. 1954.

....of HPCs, and compare our bounds to simulations using iterative (turbo) decoding. Section VI concludes the paper. The Appendix provides a proof of one of our formulas for the multiplicity of d min codewords. II. Product Codes with Hyper Diagonal Parity Product codes, introduced by Elias in 1954 [7], are concatenations of two or more block codes arranged in an array. Consider two systematic linear block codes C 1 and C 2 with parameters (n 1 ; k 1 ; d 1 ) and (n 2 ; k 2 ; d 2 ) where n i ; k i ; d i , i = 1; 2) denote codeword length, number of information bits, and minimum Hamming ....

P. Elias, \Error-free coding," IRE Trans. Inform. Theory, vol. IT-4, pp. 29-37,1 1954.

....SPC product codes is introduced. This structure involves interleaving between the encoding of each dimension. Weight distribution analysis is used to explain the extremely good performance results for this class of codes. 1 Background Product codes, or iterated codes, were introduced by Elias [1] in 1954 and represent the first method capable of achieving error free coding with a non zero code rate (as the number of dimensions increases to infinity) A product code can be constructed in the following way [6] The data to be transmitted is arranged in a hypercube of dimension d with the ....

P. Elias, "Error free coding," IRE Trans. Inform. Theory, Vol. 4, pp. 29--37, Sept. 1954.

....strategy which in an iterative process can approach the performance of the MLDA. Encoding techniques used in conjunction with iterative decoding combine different codes in such a way that each of them can be decoded independently. We include in this category product block codes [2], concatenated codes [3] multilevel codes [4, 5, 6] and, most importantly, turbo codes [7] The common feature of all these techniques is that decoding can be done sequentially, using one decoder at a time (i.e. after one code is decoded another decoder is used for the next code, and so on) ....

P. Elias, "Error--free coding," IRE Transactions on Information Theory, PGIT--4, pp. 29--37, Sep. 1954.

....to a point where decoding becomes physically unrealizable. Thus, the research in coding theory has seen many proposals aiming at constructing powerful codes with large equivalent block lengths structured so as to permit breaking the ML decoding into simpler partial decoding steps. Iterated codes [1], product codes and their extension [2] concatenated codes [3] and their generalized version [4] large constraint length convolutional codes with suboptimal decoding strategies like sequential decoding are non exhaustive examples of these attempts, and some of them have been successfully ....

P. Elias. "Error-free coding". IEEE Transactions on Information Theory, PGIT4: 29--37, September 1954.

....thesis outline, and a summary of the original contributions. 1.1 Fundamentals The encoding techniques used in iterative decoding are those coding techniques which combine different codes in such a way that each of them can be decoded independently. We include in this category product block codes [1], concatenated codes [2] multilevel codes [3] and, most importantly, turbo codes [4] The common feature of all these techniques is that decoding can be done sequentially, using one decoder at a time (i.e. after one code is decoded another decoder is used for the next code, and so on) This is ....

P. Elias, "Error--free coding," IRE Transactions on Information Theory, PGIT--4, pp. 29--37, Sep. 1954.

No context found.

P. Elias, "Error-free coding," IRE Trans. Inform. Theory, vol. IT-4, Sept., 1954, 29-37.

No context found.

P. Elias, "Error-free coding," IRE Trans. Inform. Theory, vol. PGIT-4, pp. 29--37, Sept. 1954.

No context found.

P. Elias, "Error-Free Coding," IRE Transactions on Information Theory, PGIT - 4, Sept., 1954, pp. 29-37.

No context found.

P. Elias, "Error free coding," IRE Trans. Inf. Theory, Vol. 4, pp. 29--37, Sept. 1954. 12

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC