For **code** **rate** 1/4; constraint length 4 and frame size 2000 was set. **Convolutional** encoding performed and random errors were added in the encoded data. Viterbi decoder was used for decoding the message and BER was calculated. In the Matlab **code** for selecting trellis all octal values from 0 to 17 cannot be taken because some values do not make connections at adder. The values of generator polynomials must be selected so that at least **one** connection should be between shift register and adder. For this value 17 was set fix and other values of a, b, c were taken from 1 to 17. For each combination of generator polynomial BER was calculated. For these combinations the results were stored in excel sheet and the final optimal results are given in Table 4.

Show more
communication system. To meet the new constraints of data **rate** or reliability, new coding schemes are currently being developed. Therefore, digital communication systems are in perpetual evolution and it is becoming very difficult to remain compatible with all standards used. A cognitive radio system seems to provide an interesting solution to this problem: the conception of an intelligent receiver able to adapt itself to a specific transmission context. This article presents a new algorithm dedicated to the blind recognition of **convolutional** encoders in the general k/n **rate** case. After a brief recall of **convolutional** **code** and dual **code** properties, a new iterative method dedicated to the blind estimation of **convolutional** encoders in a noisy context is developed. Finally, case studies are presented to illustrate the performances of our blind identification method.

Show more
At the receiver, the signal will be demodulated and decoded by Viterbi decoder in order to recover the original message. The bit error **rate** (BER) is calculated by comparing the decoded data with the original data. Then, CRC detector is used for detecting errors. At the receiving end, the additional bits are used to check if the message needs retransmission. If the receiver detects that there are errors in the received bit stream, the receiver asks the sender to retransmit the data. Negative acknowledgement (NACK) sends to the transmitter to request for retransmission of the previous data. The positive acknowledgment (ACK) sends where there are no errors being detected.

Show more
10 Read more

Fig 12 examines the performance of the punctured **convolutional** **code** with different rates. It appears that, for the punctured **convolutional** **code** with **rate** 2/3, the **rate** increases but the performance degrades. For the other curves, as the **rate** approximately remain constant its error correcting capability still fixed and its performance as the case of the original **convolutional** **code**, and its benefit is to save some decoding time and complexity by saving or removing only a small number of bits that out from the encoder. So, the punctured **convolutional** **code** adjusted to make a balance between its advantage and disadvantage, to have the same performance with less complexity. Finally, this technique can be adjusted according to the application requirements.

Show more
used to calculate the redundant bits and that for each data bit an additional redundant bit is added. Before the information bits are encoded, four bits are added at the end of the information bits. These bits are all set to zero and are used to reset the **convolutional** encoder to its initial state. Figure 2.1 shows the complete **convolutional** coding process for the full **rate** speech encoder. After the speech data passes through the parity encoder and the **convolutional** encoder, some of the bits have double protection, some have only a **convolutional** **code** protection, and some have no error protection. Good results were still obtained from this peculiar combination of error protection codes because the particular bits which were used for each type of error protection were carefully selected. Researchers discovered that some of the data bits produced by the full **rate** speech coder were much more important to perceptually good speech quality by testing many different digitally coded speech samples. The different bits have a particular role in the speech coding processing, and have different priority for various reasons. For example, any bit which comes from the most significant bit position of a number is clearly more important to the accuracy of the result than a bit from the least significant bit position.

Show more
Lin et al [7] employs the combination of both FEC and ARQ systems in order to attain an excellent reliability as exhibited by ARQ system and high throughput as also exhibited by FEC systems. With the HARQ bringing together these two properties of FEC and ARQ, the shortcomings experienced when either of the codes is used independently are overcome. Unlike ARQ system which discards signals that were previously received due to the presence of error, HARQ is rather suggested to improve the performance of the signal by adding all the received signals together so as to decode the message transmitted. The main aim of **Convolutional** **Code** (CC) is to make available an efficient and reliable error correcting capability over an impairment channel, in the presence of a physically implementable decoder, to complement the success of J. A. Viterbi as proposed in 1967 [8], when he developed a decoding algorithm for **convolutional** codes. Though the Viterbi algorithm was relatively simple, it still met the criteria of exhibiting behaviour almost like that of a Maximum Likelihood Decoding (MLD) in practical decoders [9]. This Viterbi algorithm invention opened doors for new developments in **convolutional** codes as more factual research and advancement followed suit since then, which links **convolutional** coding with Viterbi decoding. Three types of CC exists which are Automatic Repeat request (ARQ), Forward Error Correction (FEC), and Hybrid Automatic Repeat ReQuest (HARQ).

Show more
11 Read more

For example, the proposed power saving AM scheme employing two modulation techniques (QPSK and 16-Q- AM) is depicted in Figure 4. This scheme assumes port- able reception (i.e. v=3km/hr, thus channel is quasi- stationary over the period of **one** super frame). Hence, an adaptation **rate** of super frame is adopted. Furthermore, 1/2 **rate** **convolutional** **code** is employed in order to main- tain reliable performance in bad SNR conditions. Each transmitted super frame is arranged such that higher mo- dulation symbols (in this example 16-QAM symbols) are transmitted first followed by lower modulation symbols (in this example QPSK symbols). The selected bits are chosen according to the pre-defined selection patterns summarized in Table 6. Assume the receiver decides that the 16-QAM is sufficient to meet the target BER. Then, the receiver will receive 136 instead of 272 OFDM sym- bols. This translates into a power saving of 50% compa- red to the worst case of receiving the whole super frame. 3.2.3. Power Saving Potential

Show more
15 Read more

According to Shannon’s theorem, bit error **rate** (BER) performance is typically improved by choosing longer and more complex codes [1]. But with the increase in block length, decoding complexity increases exponentially. Since then efforts have been made for designing good codes that approach the near channel capacity limitation with moderate complexity. Forney in 1966 first introduced the idea of concatenated codes [2]. As per Forney, concatenation is a method of building long codes out of shorter ones in order to resolve the problem of decoding complexity by breaking the required computation into manageable segments according to the divide and conquer strategy. In 1989, concatenation of multiple **convolutional** codes was introduced [3], and was used with Soft Output Viterbi Algorithm (SOVA). A recent landmark development in channel coding is Turbo codes, in particularly Parallel Concatenated **Convolutional** Codes (PCCC), by Berrou, et.al. in 1993 with simple iterative decoding technique based on the Maximum A Posteriori (MAP) algorithm with Soft-In Soft-Out [4]. It was shown that the performance of Turbo **code**, in terms of Bit Error **Rate** (BER), is very close to Shannon’s limit. The concatenation of **convolutional** codes was examined further in which turbo **code** namely Serially Concatenated **Convolutional** **Code** (SCCC) was introduced & it was shown that SCCC has better performance than PCCC [5]. An iterative decoding approach to SCCC’s was introduced in [6]. The iterative decoding method provides a significant increase in performance over a single iteration and in some cases approaches the theoretical limit. Through iterative decoding scheme, performance in terms of BER is enhanced, but at the expense of complexity of the system. However, the **convolutional** codes suffered from the problem of burst errors [7] & Reed Solomon codes suffered from problem of random errors [8]. To compensate this problem, a new concatenated scheme was proposed in which a concatenation of a Reed-Solomon (RS) **code** and a Recursive systematic **convolutional** **code** (RSC) codes was used & it was shown that RS-RSC concatenated codes have good performance than RSC itself [9].

Show more
The security in channel encoder can be improved by puncturing and trellis pruning. The constituent encoders are randomly punctured to produce codes of higher **rate** and poor performance for specific channel conditions. In addition with secret trellis pruning which increases performance allows legitimate users to experience a low bit error **rate**. In that the key defines how pruning is applied on the trellis of a mother **convolutional** **code**, this results into a secret pruned trellis that legitimate users are using to perform decoding , in contrast to the eaves dropper that employed the full mother trellis diagram. The minimum pruning **rate** guaranteeing the desired reliability levels. However, security requirements may impose various constraints on , as pruning is performed in a secret fashion. The complexity of cryptanalytic attack depend on , which needs to be large enough to allow for adequate security. The EXIT chart has been presented as an engineering tool for the design of iterative decoding schemes. we have presented the extrinsic information transfer characteristics based on mutual information to describe the flow of extrinsic information through the soft in/soft out constituent decoders.

Show more
1553nm and optical detector APD having gain 1000, efficiency 0.85, and shape of pulse is Gaussian. The performance of OIDMA system may be upgraded by selecting the proper inter-leaver mechanism. In the system, random inter-leaver and tree inter-leaver are used. Random inter-leaver is simple in generation and it requires a lot of memory. In figure 5 the graph is plotted for bit error **rate** versus number of users having **convolutional** **code** **rate** (1,3) O-IDMA using random and tree inter- leaver with spreading length 16 and data length 512.In figure 6the graph is plotted for bit error **rate** versus number of users having **convolutional** **code** **rate** (1,3) O- IDMA using random and tree inter-leaver with spreading length 16 and data length 1024. In Figure-7 the graph is plotted for bit error **rate** versus number of users having **convolutional** **code** **rate** (1,3) O-IDMA using random and tree inter-leaver with spreading length 32 and data length 512. In Figure-8 the graph is plotted for bit error **rate** versus number of users having **convolutional** **code** **rate** (1,3) O-IDMA using random and tree inter-leaver with spreading length 32 and data length 1024.

Show more
Convolution codes offer an alternative to block codes for transmission over a noisy channel. Convolution coding can be applied to a continuous input stream (which cannot be done with block codes), as well as blocks of data. The overall block diagram of this paper is shown in the fig. 1. The message bits are generated and they are sent to the crypto system and then the decoded output is obtained. The type of crypto system used is Convolution Encoder and Viterbi Decoder. The **Convolutional** encoder encodes the message and then the encoded bits are generated. The bits which are encoded are again sent to the Viterbi Decoder and then the A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream but here we are using this viterbi decoder for decoding of continuous bit stream that has been encoded using Forward error correction based on a Convolution **code**. various type of decoders are used for decoding of **Convolutional** **code** but viterbi decoder is the best way to decode **Convolutional** **code** and it will give the error free original input at the receiver compared to other decoders.

Show more
11 Read more

CPC is a new coding method in which the information bits are placed into two dimensions (2D) matrix. The rows and the columns are encoded separately by using recursive systematic **convolutional** encoders. Each row of the matrix is encoded using a **convolutional** **code**, the same recursive systematic **convolutional** **code** is used to encode each row. Once all rows have been encoded, the matrix is sent, if desired, to an interleaver. Our original data matrix dimensions are (n × k), and the encoded data matrix dimensions will be (2n × k). The coded rows matrix is then recoded by column using the same or diﬀerent recursive systematic **convolutional** encoder. CPC uses a recursive systematic **convolutional** **code** with **rate** 1/2 and generator polynomials (1, 5/7) octal to encode each row and column. Hence, the overall **code** **rate** is 1/4.

Show more
Figure 5 is a performance comparison between the **convolutional** codes and BCH codes for the implant- to-body surface channel with random errors. It is clear that the higher the SNR, the lower the BER. From Fig- ure 5, we can see that, while SNR > 10dB, **convolutional** **code** shows lower BER than BCH **code**, as **convolutional** **code** has higher ability to correct random errors while BCH **code** is super for burst errors correction. Figure 5 also indicates that conv.(2,1,7) shows the best BER per- formance among the list. It must be noted, that if the data **rate** is sensitive, BCH (63,51) **code** must be chosen. Oth- erwise, **convolutional** **code** is preferred.

Show more
By substituting I delays for each delay (or storage) ele- ment in SMM and path memory cell (PMC) of PM, an area- e ﬃ cient high-speed interleaved Viterbi decoder architecture for interleaved **convolutional** **code** is obtained. In this archi- tecture, we can get the throughput **rate** of the Viterbi decoder as high as the operating clock speed. Since the decoding la- tency of the state-parallel Viterbi decoder with register ex- change path memory structure is the same as the decoding depth, the decoding latency of the interleaved Viterbi de- coder is increased by I × DD. Therefore, the decoding la- tency of proposed architecture is the decoding depth mul- tiplied by the interleaving degree, that is, decoding latency = DD × I. Since interleaved **convolutional** coding scheme uses extra delay (A), its overall decoding latency becomes DD × I + A.

Show more
3.2 Minimal trellis for systematic recursive encoders Originally, minimal trellises have been constructed for codes, not for matrices (or encoders). However, the con- vention that the upper branches refer to the information bit 0 and the lower branches refer to the information bit 1 yields a particular encoding which, in general, is not systematic. We note that the association of solid/dashed branches with codeword bits can not be changed, as any change in this regard would result in a trellis which would no longer represent the **convolutional** **code**. However, by enforcing a diﬀerent convention on the association of the branches to the information bits, only a diﬀerent encoding for the same **code** is obtained.

Show more
The major simu lation para meters of OFDM system have been assumed as follow. FFT point is 64 (i.e . 64- subcarriers), modulation technique is QPSK, , 16-symbols cyclic pre fix, and **convolutional** **code** with **code** **rate** 1/3. Two channel models have been assumed. AWGN channel and multipath fading channel model (3 paths, frequency selective, Doppler shift=20Hz, Rayle igh). In case of fading channel, ma ximal ratio channel equalizer is assumed. In addition, other para meters inc luding o versampling factor (IF=1 &2), number of iterations (n = 4), c lipping rat io (CR= 6dB), and number of PTS groups (V = 4) have been considered in our simulation. The overall perfo rmance of OFDM system has been evaluated and investigated with and without the proposed PAPR approach (CRCF_ PTS). The simulation results are shown in Fig.5 through Fig.8.

Show more
Abstract- We propose a pre-computation architecture incorporated with T-algorithm for VD, which can effectively reduce the power consumption without degrading the decoding speed much. A general solution to derive the optimal pre- computation steps is also given in the paper. The Add Compare Select (ACS) unit in path metric unit is designed to reduce the latency of ACS loop delay by using Modified Carry Look Ahead Adder and Digital Comparator. We also consider the design of Survivor Memory Unit (SMU) which combines the advantages of both Register Exchange method and Trace Back method, to reduce the decoding latency and total area of the Viterbi decoder. The proposed Viterbi decoder design is described using Verilog HDL Implementation result of a VD for a **rate**-3/4 **convolutional** **code** used in a TCM system shows that compared with the full trellis VD, the precomputation architecture reduces the power consumption without performance loss, while the degradation in clock speed is negligible.

Show more
Optical interleave division multiple access technology (IDMA) is used in recent communication system to cope up with higher **code** **rate**, longer traffic intensity as well as superior interference rejection capability. In present article the qualitative performance of OIDMA is analyzed using random and tree interleavers and optimum selection of interleavers are decided by comparing BER performance of random and tree interleavers. **Convolutional** coding technique is used here for error correction purpose. **Code** **rate** has been changed by varying number of Ex-OR gates in encoder design. The memory elements which decide the constraint length is kept fixed. **Code** **rate** variation of fixed constraint length **convolutional** **code** has been incorporated in encoder design and effect of qualitative performance of OIDMA has been observed and BER is calculated for different users.

Show more
Abstract. In 2012, Lyubashevsky introduced a new framework for building lattice-based signature schemes without resorting to any trapdoor (such as GPV [6] or NTRU [7]). The idea is to sample a set of short lattice elements and construct the public key as a Short Integer Solution (SIS for short) instance. Signatures are obtained using a small subset sum of the secret key, hidden by a (large) Gaussian mask. (Information leakage is dealt with using rejection sampling.) Recently, Persichetti proposed an efficient adaptation of this framework to coding theory [12]. In this paper, we show that this adaptation cannot be secure, even for **one**-time signatures (OTS), due to an inherent difference between bounds in Hamming and Euclidean metrics. The attack consists in rewriting a signature as a noisy syndrome decoding problem, which can be handled efficiently using the extended bit flipping decoding algorithm. We illustrate our results by breaking Persichetti’s OTS scheme built upon this approach [12]: using a single signature, we recover the secret (signing) key in about the same amount of time as required for a couple of signature verifications.

Show more
10 Read more

Channel encoder used in the communication system to detect and correct the bit errors due to the channel impairments at the receiver. Choosing the encoder/decoder types that detect and correct large numbers of bits enhance the performance of the communication system. The coding algorithm used in this paper is series concatenated hamming /**convolutional** encoder/decoder levels. This algorithm enhances the system performance by reducing BER at a suitable SNR and low simulation time. The simulation time for the hamming/**convolutional** algorithm is less than the simulation time for two **convolutional** cascaded encoders. Increasing the encoder/decoder stages increase the complexity and consume much time in simulation without any effective decreasing in BER. The future scope for this work is applying the proposed channel codding algorithm on the image, voice and video as an input signal.

Show more