S.Dolinar,and D. Divsalar, Weight distribution of turbo codes using random and nonrandom permutations. JPL, TDA Progress. Rep. 42-122, Aug. 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a picture and count accordingly. 7 S random permutation In our construction of the turbo graph (Figure 3) we use a random permutation, i.e. the one toone connections of nodes from the two chains are chosen randomly by a random permutation. In this section we look at the S random permutation [8]. This is a semirandom permutation that achieves some nonrandom design objective but still retains some degree of randomness to prevent too much regularity. Formally, the S random permutation is a random permutation function f( on the sequence 1; 2; n such that 8i; j :j i j j S = j ....

....of length k 8 it is not clear what (if any) restrictions the S random construction places on such cycles. We simulated S random graphs and counted cycles in the same manner as described in Section 6, except that the random permutation was now carried out in the S random fashion as described in [8]. The results in Table 1 show that changing the value of S does not appear to change the nature of the cycle distribution. The S random distributions of course have zero probability for k 8, but for k 8 the results from both types of permutation appear qualitatively similar, with a relatively ....

S. Dolinar and D. Divsalar (1995), Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations. TDA Progress Report 42-121 (August 1995), Jet Propulsion Laboratory, Pasadena, California.

....to this form of analysis. For example, for the case of a turbo code with more than two constituent encoders, one can generalize the notion of candidate loop labeling and count accordingly. As another example, we applied the same techniques of counting loops to turbo codes with S random permutation [6]. In both simulation and analysis the S random construction is shown to eliminate very short loops and for larger loops results in only a small systematic decrease in the probability of such loops [7] For other codes with similar iterative decoding algorithms to turbo codes, the same techniques ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," Tech. Rep., Jet Propulsion Laboratory, Pasadena, CA, Aug 1995.

....have to start by sending the receiver the current interleaving pattern. Consequently, we have to choose a specific interleaver in such a case. It is possible to design the interleaver so as to break up as many of the low weight error sequences as possible. The S random interleaver introduced in [59] does just that. It is defined as follows: Each randomly selected integer is compared to the S previously selected integers. If the current selection is equal to any of the S previous selections within a distance of S, the current selection is rejected. It is however also concluded in [59] that ....

....in [59] does just that. It is defined as follows: Each randomly selected integer is compared to the S previously selected integers. If the current selection is equal to any of the S previous selections within a distance of S, the current selection is rejected. It is however also concluded in [59] that if the interleaver is designed to break up, for example the weight 2 patterns, the regularity introduced to do this actually enhances the probability of bad sequences of weight 4 and over. Usually, choosing an S N produces an interleaver within reasonable time. However, for a ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," JPL TDA Progress Report 42-122, Jet Propulsion Laboratory, Pasadena, CA, USA, pp. 56-65, August 1995.

....phase and develops a linear objective function which is solved using the Hungarian method [19] These interleavers result in BER performance superior to that of a random interleaver. A good review of other non random and semi random interleavers was performed by S. Dolinar and D. Divsalar in [20]. Specifically, the authors consider a non random interleaver which ensures that the minimum distance due to weight two input sequences grows roughly as 2N , where N is the block length. They also introduce a semi random interleaver, which they called S random. This interleaver is designed by ....

S. Dolinar and D. Divsalar, "Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations", The Telecommunications and Data Ac- quisition Progress Report 42-122, April-June 1995.

....code (RSCC) of rate R c to obtain the sequence j of N c = N b R c coded bits. The parity bits from the coded sequence are punctured at a rate 1:K, i.e. every (K 1) parity bit is removed to obtain N p punctured coded bits. This sequence is then interleaved using an S rand interleaver [10] and interspersed with pilot bits with frequency 1:P to give N p P 1 total bits. Using pilot bits rather than whole symbols is a slightly more flexible approach than direct PSAM, as for turbo equalization we do not need entire pilot symbols, which will be discussed in section 4. Finally, this ....

S. Dolinar and D. Divsalar, "Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations," tech. rep., TDA Progress Report 42122, Aug. 1995.

....the consecutive input bits by at least M in the interleaver output. In this respect, block interleavers are better than random interleavers. But it is also important to avoid systematic patterns in the interleaver. Existing interleaver designs for turbo codes are also applicable to our setup [7] [8], 22] For simplicity, however, we will use random interleavers in our simulations. IV. TURBO DECODING Exhaustive search over all possible input sequences certainly offers exact ML detection for our joint coded precoded transmissions. Presence of the interleaver # 1 , in between the EC code and ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," NASA JPL TDA Progress Report, vol. 42-122, Aug. 1995; downloadable from

....on these tail bits and, hence, individual tail sequences are required for each component en coder. The performance of a specific trellis termination method is dependent on the particular interleaver used in the Turbo encoder. This dependency is the result of interleaver edge effects [2]. This paper de scribes interleaver edge effects for the case of uniform interleaving [4] It is demonstrated how the choice of different termination methods influences the per formance for Turbo codes with different interleaver lengths and different number of memory elements in the component ....

....a method to derive the CWEF for various trellis termination methods is presented. 2.1. Interleaver edge effects Interleaver edge effects refer to the implications on the distance spectrum resulting from the block partitioning of the input sequence, as the result of a limited length interleaver [2]. Due to this trunca tion, low weight parity words can be generated even though the encoder input sequences do not force the encoders back to the zero states. In terms of weight enumerating functions, this means that we require knowledge not only of the number of trellis paths that lead to the ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations." TDA progress report 42-122, Jet propulsion Lab., Pasadena, CA, August 1995.

....D and feedforward generator polynomial 1 D D D , both in octal) The trellis of the upper encoder is terminated with 3 tail bits, while the trellis of the lower encoder is left open. The data frame consists of 1247 data bits and 3 tail bits. The turbo encoder uses a bit random interleaver, with [26]. Puncturing is used to increase the overall code rate to 1 2. In particular, the even indexed parity bits from the upper encoder and odd indexed parity bits from the lower encoder are deleted prior to transmission. The channel interleaver has a depth of 50 and is implemented with a 50 by 50 ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations,", JPL TDA Progress Rep., vol. 42, Aug. 15, 1995.

....which estimates the data and code bits. The SCCC encoder comprises of two rate recursive systematic convolutional (RSC) encoders. The information bits are rst encoded by the outer r = RSC encoder. The systematic and parity bits generated by the outer encoder are fed to a spread interleaver ( [7]. In our model, however, the spread interleaver is structured such that it outputs all the systematic bits appearing at the output of the outer encoder before it outputs the encoder s parity bits. The interleaved bits are then fed to the inner RSC encoder. The interleaver structure helps to ....

S. Dolinar and D. Divsalar, \Weight distributions for turbo codes using random and nonrandom permutations," JPL TDA Progress Report, vol. 42-122, pp. 56-65, Aug. 15 1995.

....encoder. A 3 bit tail is used to terminate the trellis of the upper RSC encoder and is appended to the 925 bit CRC code word. The resulting 928 bit sequence is encoded first by the upper encoder. Next, the sequence of data, CRC, and tail are interleaved by a 928 bit S random interleaver with S=#9[5]andencodedbythe lower encoder (a separate tail is not computed for the lower encoder) The overall output of the turbo encoder consists of 2784 code bits. Since the payload of an AUX# packet contains a # byte payload header and 29 bytes of payload data [#] the entire turbo code word can be ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations, " JPL TDA Progress Report, vol. 42, pp. 56---65, Aug. #5th #995.

....write read pattern along rows columns allows the memory access operations of this interleaver to make use of cycle counters to activate both word (row) lines and bit (column) lines, thereby eliminating the necessity to perform memory address decoding. More sophisticated interleaver designs [8], 9] yield improved error rate performance, but result in increased implementation complexity. Therefore, the implementation of the described basic interleaver provides a lower limit on complexity. III. MAP DECODER A MAP decoder implements the BCJR [2] algorithm. It is used to obtain the a ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," JPL, TDA Progress Rep., Aug. 1995.

....but still achieves good coding gains [9] For short interleavers, say of length less than , the results in [10] 11] indicate that there are some block, and thus deterministic, interleavers of specific sizes and interleaver depths that produce more favorable results than random interleavers. In [12], a class of nonrandom permutations is presented but found to give poor performance; we show that they are in a sense equivalent to block interleavers and thus perform poorly if long block lengths are used. We also show that for short block lengths, they are as good as block interleavers if a ....

....are in a sense equivalent to block interleavers and thus perform poorly if long block lengths are used. We also show that for short block lengths, they are as good as block interleavers if a suitable interleaver depth is chosen. Further, we give a single description of both interleavers in [10] [12] and determine their important design parameters. Finally, we show that the cycle length of the feedback polynomial of the component code has a great impact on the BER performance of a turbo code using block interleavers by constructing a surprisingly good nonrandom turbo code of length based on a ....

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S. Dolinar and D. Divsalar, "Weight distribution of turbo codes using random and nonrandom permutations," JPL, TDA Progr. Rep. 42-122, Aug. 1995.

....complexity grows only linearly with the interleaver length. Designing the interleaver = 1 ; K ) of length K of a Turbo code serves to increase the code s minimum distance min and hence to lower the error oor of the Word and Bit Error Rates (WER BER) An ecient method was presented in [1]. Examinations show that for so designed interleavers, the codeword at min is mainly caused by a combination of an input word u (1) of the rst component encoder (identical to the Turbo encoder input u) and a second component input word u (2) as shown in Fig. 1. In this example, 1001 ....

.... The s random interleaver does not avoid that the four 1 s in the two error patterns of u (1) are mapped crosswise to two error patterns in u (2) since the two 1 s belonging to each error pattern in u (1) are spread to distant positions in u (2) and hence the spreading condition of [1] is satis ed. However, this unlucky mapping of positions can be avoided and min can be increased by modifying the interleaver design algorithm. Figure 1: Unlucky mapping of positions The proposed algorithm incorporates the s random method of [1] and hence, it successively determines 1 to K . ....

[Article contains additional citation context not shown here]

S. Dolinar and D. Divsalar, \Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations", JPL{ TDA Progress Report, pp. 56-65, 1995.

....that with perfect channel estimation, the fully interleaved channel has at least 3 dB more energy efficiency at BER=10 5 over that of correlated Rayleigh fading with BT=0.01 and even more over correlated fading with BT=0.001. A spread random interleaver will be used for channel interleaving [7]. As for the outer code, we follow the UMTS turbo code standard [8] Each recursive constituent code is a rate convolutional code with generator polynomial (1, 13 15) Both trellises are terminated with independent tails. The design of our turbo interleaver also follows the UMTS standard, which ....

S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," JPL TDA Progress Report, vol. 42, pp. 56-65, Aug. 15 1995.

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S.Dolinar,and D. Divsalar, Weight distribution of turbo codes using random and nonrandom permutations. JPL, TDA Progress. Rep. 42-122, Aug. 1995.

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S. Dolinar and D. Divsalar, \Weight distributions for turbo codes using random and nonrandom permutations," Tech. Rep., Jet Propulsion Laboratory, Pasadena, CA, Aug 1995.

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S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," JPL, TDA Progress Report 42-122, Aug. 1995.

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S. Dolinar and D. Divsalar, "Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations," JPL, TDA Progress Report, vol. 42-122, Aug. 1995.

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S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations", TDA Progress Rep. 42-122, Jet Propulsion Lab., Pasadena, CA, USA, Aug. 15, 1995, pp. 56-65. 62

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S. Dolinar and D. Divsalar, "Weight distribution for turbo codes using random and nonrandom permutations," JPL progress report 42-122, pp. 56-65, Aug. 1995.

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S. Dolinar and D. Divsalar. (1995, Aug.) Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations, NASA JPL TDA Progress Report. [Online]Available: http://tmo.jpl.nasa.gov/tmo/

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S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," TDA Progress Report, vol. 42122, pp. 56--65, April-June 1995.

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S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," TDA Progress Report, vol. 42122, pp. 56--65, April-June 1995.

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S. Dolinar and D. Divsalar, "Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations," JPL, TDA Progress Report, vol. 42-122, Aug. 1995.

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S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," TDA Progress Report 42-122, pp. 56-65, August 1995.

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