A. S. Barbulescu and S. S. Pietrobon, \Terminating the trellis of turbo-codes in the same state," Electr. Lett., vol. 31, pp. 22-23, 5th Jan. 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the same time. For short sequence lengths and encoders with a small number of 18 k U U k k k S S o k Figure 2.2: Turbo code encoder structure. 19 memory M , specially designed interleavers can guarantee both encoder states to be terminated to the all zero state. For example, in [12], the sequence length is 420 bits and the memory is 2. However, such design may not be easily extended to long sequence lengths and encoders with large memory. Therefore, the second encoder state is usually not terminated. 2.3 Turbo Code Decoder and Iterative Decoding Before introducing the ....

A. S. Barbulescu and S. S. Pietrobon, \Terminating the trellis of turbo-codes in the same state," Electr. Lett., vol. 31, pp. 22-23, 5th Jan. 1995.

....encoders It is also possible to terminate both component en coders in their zero states. At least two different ways of achieving this has been reported in the liter ature: By imposing interleaver restrictions, the second encoder can be forced to end up in the same state as the first encoder [6, 7]. It is then sufficient to append tail bits according to ter mination Class II in order to terminate both encoders in their zero states. By identifying specific, interleaver dependent, input positions it is possible to force the component encoders to their zero states indepen dently of each ....

A. S. Barbulescu and S. S. Pietrobon, "Terminat- ing the trellis of turbo-codes in the same state," Electronics Letters, vol. 31, pp. 22-23, Jan. 1995.

....coefficient of a linear curve. For a block interleaver, the angular coefficient is the interleaver depth. Henceforth, we will refer to both and as linear interleavers. Note that many of the interleavers with simple constructions that have been proposed in the literature fall in this category [27] [28]. The interleaver in [28] is a variation of the helical interleaver in [29] and has the interesting property that it terminates the trellis of the lower component code to the same state as the top component code. For an interleaver , since by definition , the following congruence is always ....

....For a block interleaver, the angular coefficient is the interleaver depth. Henceforth, we will refer to both and as linear interleavers. Note that many of the interleavers with simple constructions that have been proposed in the literature fall in this category [27] 28] The interleaver in [28] is a variation of the helical interleaver in [29] and has the interesting property that it terminates the trellis of the lower component code to the same state as the top component code. For an interleaver , since by definition , the following congruence is always solvable in with a unique ....

A. Barbulescu and S. Pietrobon, "Terminating the trellis of turbo codes in the same state," Electron. Lett., vol. 31, no. 1, pp. 22--23, Jan. 1995.

....in [19] Thus, 28) V. SIMULATION RESULTS For all simulations, the component encoders are rate recursive systematic convolutional encoders with memory four and octal generators . The packet size is 1760 information bits and the number of decoder iterations is five. A helical interleaver [20] is used to guarantee trellis termination. The SNR of the full band thermal noise is set to 20 dB. Cases with memory are simulated using 20, 80, and 160 bits per hop (BPH) Fig. 2 shows the plot of minimum needed to achieve a packet error rate (PER) of for a given . As would be expected, the ....

A. Barbulescu and S. Pietrobon, "Terminating the trellis of turbo codes in the same state," Electron. Lett., vol. 31, pp. 22--23, Nov.

....bits. We assume, though, that the parity bits in the tail region are transmitted for both encoders. The problem of terminating the parallel encoders in a Turbo code is that the interleaver causes the two trellises to finish in a different state, and hence different tail sequences are required. Barbulescu and Pietrobon [1995] propose a restriction on the interleaver pattern which forces the two trellises to end in the same state. This allows the use of a single tail sequence for both encoders. This type of interleaver is called a simile interleaver. 2.3.7 Interleaver Design While the effect of the interleaver on ....

....parity bit in the interleaved sequence is not punctured. It is stated that this gives a uniform distribution of the correcting capability of the codes, and results in better Turbo code performance. This design was further improved when the block helical simile interleaver was proposed [Barbulescu Pietrobon, 1995], which combines the odd even property with the possibility of using the same tail for interleaved and non interleaved trellises. Recently, a mathematical model of interleavers has been proposed by Andrews et al. 1997] who also used this to guide the generation of new interleavers for Turbo ....

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BARBULESCU, SORIN ADRIAN, & PIETROBON, STEVEN SILVIO. 1995. Terminating the Trellis of Turbo-Codes in the Same State. Electronics Letters, 31(1), 22--23.

....to the double terminating property and the assumption must be false. We denote the set of interleavers with the double terminating property as the class of double terminating interleavers . For the special case of scramblers with a period p = 1, we obtain the simile interleavers of [2]. One sub type of these are the helical interleavers presented in [2] There exist rectangular double terminating interleavers. Generally, for rectangular m Thetan interleavers, the transpositions are defined as follows: i i = i modn) Delta m i div n. For rectangular interleavers ....

....false. We denote the set of interleavers with the double terminating property as the class of double terminating interleavers . For the special case of scramblers with a period p = 1, we obtain the simile interleavers of [2] One sub type of these are the helical interleavers presented in [2]. There exist rectangular double terminating interleavers. Generally, for rectangular m Thetan interleavers, the transpositions are defined as follows: i i = i modn) Delta m i div n. For rectangular interleavers belonging to the class of double terminating interleavers, we have hence the ....

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A. Barbulescu and S. Pietrobon. Terminating the trellis of turbo-codes in the same state. Electronics Letters, pages 22--23, 1995.

....fflf Gamma1; 1g and then puts out three streams: the information bits d k , the parity bits p 1;k of the first component encoder with input d k , and the parity bits p 2;k of the second component encoder with interleaved d k as input. A helical interleaver is used to guarantee trellis termination [5]. BPSK modulation is considered with coherent demodulation and BFSK modulation is considered with noncoherent demodulation. The resultant signal is frequency hopped. The hopping patterns of the FH SS system are modeled as sequences of independent random variables uniformly distributed over the ....

A. Barbulescu and S. Pietrobon, "Terminating the trellis of turbo codes in the same state," Electronics Letters, vol. 31, Nov. 1995. 5

....using two constituent codes. As in the original work by Berrou et al. [2] the constituent codes considered in this paper are recursive systematic convolutional codes. The turbo encoder is formed by concatenating the constituent codes in parallel and then separating the codes by an interleaver [5]. The encoder takes as input the data sequence d k fflf Gamma1; 1g and then outputs three streams: the information bits d k , the parity bits p 1;k of the first component encoder with input d k , and the parity bits p 2;k of the second component encoder with interleaved d k as input. BPSK ....

A. Barbulescu and S. Pietrobon, "Terminating the trellis of turbo codes in the same state," Electronics Letters, vol. 31, Nov. 1995. 5

....reasons, it will be assumed in the remainder of the paper that the first encoder is forced to return to the all zero state and that the final state of the second encoder is unknown. Special interleaver structures that result in both encoders returning to the all zero state are discussed in [31] [32], 34] 35] and [36] 2.1 Performance Bounds In order to make clear the distinction between Turbo codes and convolutional codes, it is useful to consider these codes as block codes. To this end, the input sequences are restricted to length N , where N corresponds to the size of the interleaver ....

A. S. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbo-codes in the same state", Electronics Letters, Vol. 31, No. 1, pp. 22--23, January 5, 1995. 24

....intervals BOTH RSCs will be back in the all zero state. The paper by Blackert et al. 16] gives conditions on the interleaver which guarantee this possible. For this dissertation, we will assume all interleavers are chosen with this property. Other inquiries into interleaver design are given in [10, 11]. This will make more clear the prevailing notion that turbo codes can be thought of as large block codes. We can represent each N block of output from the RSC as follows using Proposition 2.2.4. For 0 we have: 0 B B B B B y N y N 1 . y N N 1 1 C C C C C A = 0 B B B B ....

....to do by hand) reveals that this code has d 8 = 8. Example 7.2.7 For = 4 and F 13 , choose = 7. Then the following matrices de ne our code: A = 2 6 4 7 0 0 0 0 10 0 0 0 0 5 0 0 0 0 9 3 7 5 ; A 0 = 2 6 4 11 0 0 0 0 12 0 0 0 0 6 0 0 0 0 3 3 7 5 ; B = 2 6 4 1 1 1 1 3 7 5 ; C = [ 11 2 6 6 ] ; D = 1 ] Again, a computer veri cation yields that d 11 = 10. Remark 7.2.8 It should be noted that for each of the example codes above, the full conjecture holds true, not just for when = 3 1. In fact, for smaller the bound is not tight. In particular, for the example when = 4, it can ....

A.S. Barbulescu and S.S. Pietrobon. Terminating the trellis of turbo-codes in the same state. Electronics Letters, 31(1):22-23, 1995.

....of the 2 M possible states, there does exist an M bit code that will drive each encoder to the all zero state. Unfortunately, at each point in time, the state of each component encoder is generally different due to the existence of the interleaver. To solve this problem, a helical interleaver [13] is considered. In short, a helical interleaver forces both encoders to end in the same state, thus allowing a sequence of M bits to terminate both trellises. The modulation considered is binary frequency shift keying (BFSK) The resultant signal is frequency hopped. The hopping patterns of the ....

A. Barbulescu and S. Pietrobon, "Terminating the trellis of turbo codes in the same state," Electronics Letters, vol. 31, Nov. 1995.

....Interleaver Interleaver Encoder Encoder Encoder 1 2 M 1 2 M d p 1 p 2 p M . Figure 2. 1: Block Diagram of the Turbo Encoder If M = 2 and the constituent codes are constraint length K convolutional codes, a helical interleaver can be used to guarantee trellis termination [27]. The helical interleaver (also described in the Appendix) essentially constrains the trellises of both component codes to end in the same state, allowing a K Gamma 1 bit tail to drive both codes to the all zeros state. In general, the constituent codes are recursive systematic convolutional ....

....of noncoherent reception is presented. For these simulations, the component encoders are rate 1 2 recursive systematic convolutional encoders with memory 4 and octal generators (37; 21) The packet size is 1760 information bits and the number of decoder iterations is 5. A helical interleaver [27] is used to guarantee trellis termination (see Appendix) The SNR of the full band thermal noise is set to 20 dB. Cases with memory are simulated using 20, 80, and 160 bits per hop (BPH) Figure 3.4 shows the plot of minimum E b =N J needed to achieve a packet error rate (PER) of 10 Gamma3 as a ....

[Article contains additional citation context not shown here]

A. Barbulescu and S. Pietrobon, "Terminating the Trellis of Turbo Codes in the Same State," Electronics Letters, vol. 31, Nov. 1995.

....literature. For the fully interleaved channel, we have plotted simulation data for various rate 1=3 turbo schemes in Fig. 1 3. For the fully interleaved channel, we are considering input frames of length k = 420, 5,000 and 50,000 bits. The k = 420 scheme uses the helical interleaver discussed in [7] which has been shown to be very effective on the AWGN channels (d min = 22) The k = 5; 000 and k = 50; 000 bit frames use randomly generated interleavers without any optimization. In all cases, simulations use 8 decoding iterations for k = 420, 18 iterations for k = 5; 000 and 20 iterations for ....

A. S. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbo-codes in the same state," Electronics Letters, vol. 31, pp. 22--23, Jan. 1995.

....(e.g. 1] For the fully interleaved channel, we have plotted simulation data for rate 1=3 turbo schemes with different block sizes in Figures 1 and 2. Here, we are considering input frames of length k = 420, 5000 and 50000 bits. The k = 420 scheme uses the helical interleaver discussed in [7] which has been shown to be very effective on the AWGN channels (d min = 22) The k = 5000 and k = 50000 bit frames use randomly generated interleavers without any optimization. With SI, one observes that for k = 50000, the performance of these codes is within 1:3 dB of the capacity limit. Without ....

A. S. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbo-codes in the same state," Electronics Letters, vol. 31, pp. 22--23, Jan. 1995.

....were done using the optimum metric rather than the simplified metric shown previously [13] In all cases, a single turbo interleaver is used with the interleaver fixed for all simulated frames. For K = 420, a helical interleaver is used which has been shown to be effective on the AWGN channel [14]. For block sizes greater that 1000, it has been observed that randomly generated interleavers generally perform better than deterministic interleaver designs [15] Therefore, for K = 5000 and K = 50000, the fixed interleaver is generated randomly and used without optimization. With SI, it can be ....

A. S. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbo-codes in the same state," Electronics Letters, vol. 31, pp. 22--23, Jan. 1995.

....reasons, it will be assumed in the remainder of the paper that the first encoder is forced to return to the all zero state and that the final state of the second encoder is unknown. Special interleaver structures that result in both encoders returning to the all zero state are discussed in [31] [32], 34] 35] and [36] 2.1 Performance Bounds In order to make clear the distinction between Turbo codes and convolutional codes, it is useful to consider these codes as block codes. To this end, the input sequences are restricted to length N , where N corresponds to the size of the interleaver ....

A. S. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbocodes in the same state", Electronics Letters, Vol. 31, No. 1, pp. 22--23, January 5, 1995.

....bits, the original and the interleaved one) the state of both encoders of the turbo code are to be the same. This allows only 18 one tail to be appended to the information bits, which drives both encoders to the same zero state. This is why we called it a simile type of interleaver [42]. The idea behind the simile interleaver is that the whole block of N information bits can be divided in # 1 sequences, where # is the memory length of the code. For # = 2, we get: Sequence 0 = d k k mod ## 1) 0 Sequence 1 = d k k mod ## 1) 1 Sequence 2 = d k k mod ## 1) ....

S. A. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbo codes in the same state," Electron. Lett., vol. 31, No. 1, pp. 22--23, Jan. 1995.

....the convolutional code. To achieve this, a complicated method based on inserting certain bits in pre determined positions was presented in [47] We explain in this section a simple interleaver design for rate half turbo codes which allows both encoders of a turbo encoder to end in the same state [48]. This method is more bandwidth efficient and will improve the performance of turbo codes when the MAP decoding algorithm is used. Until now, the main purpose of the interleaver was to increase the minimum distance of the turbo code such that after the correction in one dimension the remaining ....

S. A. Barbulescu and S. S. Pietrobon, "Terminating the trellis of turbo codes in the same state," Electron. Lett., vol. 31, No. 1, pp. 22--23, Jan. 1995.

No context found.

A.S. Barbulescu and S.S. Pietrobon, "Terminating the trellis of Turbo codes in the same state," Electronic Letters, vol. 31, pp. 22-23, January 5 1995.

No context found.

A.S. Barbulescu and S.S. Peitrobon, "Terminating the trellis of Turbo codes in the same state," Electronic Letters, vol. 31, pp. 22-23, January 1995.

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