On the equivalence between scarce-state-transition viterbi decoding and syndrome decoding of convolutional codes

When a scarce state transition (SST) Viterbi decoder is used to decode general nonsystematic convolutional codes (not included among quick look‐in (QLI) codes), metrics based on the maximum a posteriori probability (MAP) estimation method must be computed in order for the main decoder to operate under the criterion of minimizing the decoding error probability. In this case, however, it becomes necessary to extend the original code trellis structure by introducing augmented trellis states in order to incorporate the newly induced correlation among the apparent information sequence.This paper shows that the extended trellis degenerates into the original one as the channel error probability q approaches one‐half. By performing an equivalent transformation of metrics, it is shown also that the branch metrics derived based on the MAP estimation method converge to those computed using the conventional one as q approaches one‐half.

Maximum likelihood decoding of convolutional codes by Viterbi decoding method is an effective error correcting technique. However, little study on Viterbi decoding of high rate codes has been done since the number of paths entering each trellis state increases as the code rate increases. This paper presents a new maximum likelihood decoding of convolutional codes of rate (n ‐ 1)/n using a trellis. the trellis is drawn according to the state transitions of the syndrome former of the code, and has only one or two paths entering each state rather than 2n‐1 paths as in the case of conventional trellises. Thus, we can replace the 2n‐1‐ary comparisons at each state needed in the conventional Viterbi decoding for the code of rate (n ‐ 1)/n by binary comparisons. the implementation of maximum likelihood decoders for high rate convolutional codes is simplified greatly by this approach. Moreover, this decoding method shows the same performance as that of conventional Viterbi decoding method from the viewpoint of selecting the maximum likelihood code sequence.

Convolutional coding and Viterbi decoding, along with binary phase-shift keyed modulation, is presented as an efficient system for reliable communication on power limited satellite and space channels. Performance results, obtained theoretically and through computer simulation, are given for optimum short constraint length codes for a range of code constraint lengths and code rates. System efficiency is compared for hard receiver quantization and 4 and 8 level soft quantization. The effects on performance of varying of certain parameters relevant to decoder complexity and cost is examined. Quantitative performance degradation due to imperfect carrier phase coherence is evaluated and compared to that of an uncoded system. As an example of decoder performance versus complexity, a recently implemented 2-Mbit/s constraint length 7 Viterbi decoder is discussed. Finally a comparison is made between Viterbi and sequential decoding in terms of suitability to various system requirements.

We introduce the notion of innovations for Viterbi decoding of convolutional codes. First, we define a kind of innovation corresponding to the received data, i.e., the input to a Viterbi decoder. Then, the structure of a scarce-state-transition (SST) Viterbi decoder is derived in a natural manner. It is shown that the newly defined innovation is just the input to the main decoder in an SST Viterbi decoder and generates the same syndrome as the original received data does. A similar result holds for quick-look-in codes as well. In this case, however, the precise innovation is not defined. We see that this innovation-like quantity is related to the linear smoothed estimate of the information. The essence of innovations approach to a linear filtering problem is first to whiten the observed data, and then to treat the resulting simpler white-noise observations problem. In our case, this corresponds to the reduction of decoding complexity in the main decoder in an SST Viterbi decoder. We show that the distributions related to the main decoder (i.e., the input distribution and the state distribution in the code trellis for the main decoder) are much biased under moderately noisy conditions. We see that these biased distributions actually lead to the complexity reduction in the main decoder. Furthermore, it is shown that the proposed innovations approach can be extended to maximum-likelihood decoding of block codes as well.

An erasure-free sequential decoding algorithm for trellis codes, called the buffer looking algorithm (BLA), is introduced. Several versions of the algorithm can be obtained by choosing certain parameters and selecting a resynchronization scheme. These can be categorized as block decoding or continuous decoding, depending on the resynchronization scheme. Block decoding is guaranteed to resynchronize at the beginning of each block, but suffers some rate loss when the block length is relatively short. The performance of a typical block decoding scheme is analyzed, and we show that significant coding gains over Viterbi decoding can be achieved with much less computational effort. A resynchronization scheme is proposed for continuous sequential decoding. It is shown by analysis and simulation that continuous sequential decoding using this scheme has a high probability of resynchronizing successfully. This new resynchronization scheme solves the rate loss problem resulting from block decoding. The channel cutoff rate, demodulator quantization, and the tail's influence on performance are also discussed. Although this paper considers only the decoding of trellis codes, the algorithm can also be applied to the decoding of convolutional codes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Viterbi decoding algorithm with a scarce-state transition-type circuit configuration, namely the probability selecting states (PSS) mode decoder, is presented. The algorithm has reduced complexity compared to a conventional Viterbi decoder. It is shown that this method has three advantages over the general Viterbi algorithm: it is suitable to the quick look-in code, it applies the optimum decoding in a PSS-type decoder, and it makes full use of the likelihood concentration property. The bit-error-rate (BER) performance of a r=1/2, k=7 (147,135) code and PSS-type Viterbi decoder approximates the optimum performance of the standard Viterbi decoder and reduces the hardware of the conventional Viterbi decoder to about half.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this study, a power-efficient very large-scale integration (VLSI) implementation for the convolutional code decoder is presented. Based on the state transparent convolutional code definition, the receiving codewords are classified into non-erroneous and erroneous segments separately. Different from the conventional Viterbi decoder (VD), the authors use a low-complexity decoder, denoted as bit reverse decoder, to recover the non-erroneous segments using reverse operation with a little power consumption and present the segment-based VD to decode the erroneous codeword segments. Then, the clock-gating technique is employed to switch between segment-based VD and bit reverse decoder for power saving. To further reduce the power consumption, the authors group registers into several segments in the survivor memory unit of the segment-based VD and also apply clock gating to each segment individually. According to the number of consecutive erroneous codeword segments, the corresponding numbers of register segments in the survivor memory unit are enabled and other register segments are clock-gated to reduce the switching activities. Besides, our design determines the start and terminal states of the survivor path to obtain correct results of erroneous segments without bit-error rate degradation. As compared with other decoders, our design requires less power without decreasing the decoding performance.

Convolutional code is a coding scheme used in communication systems including deep space communications and wireless communications.It provides an alternative approach to block codes for transmission over a noisy channel.The block codes can be applied only for the block of data.The Convolutional coding has an advantage over the block codes in that it can be applied to a continuous data stream as well as to blocks of data.Viterbi decoder employed in digital wireless communication plays a rife role in the overall power consumption of trellis coded modulation decoder.Power reduction in Viterbi decoder could be achieved by reducing the number of states.A pre-computation architecture with T-algorithm was implemented for this purpose, and when we compare this result with full Trellis Viterbi decoder, this approach significantly reduces power consumption without degrading decoding speed.Convolutional encoding with viterbi decoding is a powerful FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by Additive White Gaussian Noise (AWGN).It operates on data stream and has memory that uses previous bits to encode.The Viterbi Algorithm (VA) is proposed, used for decoding a bit stream that has been encoded using FEC code.The Convolutional encoder adds redundancy to a continuous stream of input data by using a linear shift register.A pre-computation architecture with Viterbi algorithm is implemented for this purpose, Viterbi (Convolutional) encoder and Viterbi decoder are designed and implemented using FPGA technology, which are the essential blocks in digital communication systems.It is particularly suited to a channel in which the transmitted signal is corrupted mainly by AWGN.The Viterbi decoder of Constraint length 7 and code rate ½ is considered.The design is implemented using verilog on Xilinx Spartan 3E and advanced Spartan 6 board and the results and Comparisons are presented.

Packet loss is a common phenomenon in current image processing (IP) networks. Current network protocols manage this problem by retransmitting the lost packets. However, the delay due to the retransmission of the lost packets may be inappropriate for many real-time applications. Therefore, a better approach to resolve this problem is to recover the lost data from the received packets using some error control coding scheme. The conventional error control coding is based on a tandem source and channel coding framework, where the message signal is first compactly represented using a rate-distortion criterion, and then, the error correcting bits are appended to it. As an alternative, joint source-channel codes that can perform as good as, or better than, the tandem source and channel coding are being considered. In particular, lowpass discrete Fourier transform (DFT) codes have been studied as joint source-channel codes. This paper is dedicated to the analysis of lowpass DFT codes with bursty erasures. The analysis aims at studying the performance of lowpass DFT codes when consecutive samples of a DFT codevector are erased due to packet losses. It is known that lowpass DFT codes are highly sensitive to quantization error when there are consecutive erasures. This phenomenon is studied in the context of syndrome decoding. Bursty erasures give rise to a syndrome-decoding matrix that has very large elements depending on the code parameters and the burst length. The size of the elements of the syndrome decoding matrix is studied by establishing various relationships between the syndrome decoding matrix and the parity and the generator polynomial coefficients. With a suitable model for the quantization error, the reconstruction error performance of lowpass DFT codes is analyzed and then applied to the case of bursty erasures. The paper also proposes a recursive syndrome decoding algorithm to improve on the normal syndrome decoding of lowpass DFT codes in the case of bursty erasures. The proposed algorithm aims at recovering the quantized values of the erased samples based on a cost computed using the statistics of the codevector and of the quantization error.

The authors propose a novel control channel quality improvement scheme for satellite communication systems using a majority decision method over convolutional coding and Viterbi decoding channels. To improve majority decision performance, which is degraded by burst errors due to Viterbi decoding in conventional serial transmission methods, a parallel transmission method is proposed. The performance of the parallel and serial transmission methods has been analyzed, and experimenta have been carried out using rate 1/2 convolutional encoding and Viterbi decoding (constraint length 4 and 7). It is shown that the parallel transmission method has about 10/sup 10/ times lower block error performance at P/sub e/=1*10/sup -4/ than the conventional method. >

For pt. I see ibid. vol.46, p.1592-1601 (1998). Soft-decision maximum-likelihood decoding of convolutional codes over GF(q) can be accomplished via searching through an error-trellis for the least weighing error sequence. The error-trellis is obtained by a syndrome-based construction. Its structure lends itself particularly well to the application of expedited search procedures. The method to carry out such error-trellis-based decoding is formulated by four algorithms. Three of these algorithms are aimed at reducing the worst case computational complexity, whereas by applying the fourth algorithm, the average computational complexity is reduced under low to moderate channel wise level. The syndrome decoder achieves substantial worst case and average computational gains in comparison with the conventional maximum-likelihood decoder, namely the Viterbi decoder, which searches for the most likely codeword directly within the code.

This paper discusses the impact of flexibility when designing a Viterbi decoder for both convolutional and TCM codes. Different trade-offs have to be considered in choosing the right architecture for the processing blocks and the resulting hardware penalty is evaluated. We study the impact of symbol quantization that degrades performance and affects the wordlength of the rate-flexible trellis datapath. A radix-2-based architecture for this datapath relaxes the hardware requirements on the branch metric and survivor path blocks substantially. The cost of flexibility in terms of cell area and power consumption is explored by an investigation of synthesized designs that provide different transmission rates. Two designs are fabricated in a digital 0.13-mum CMOS process. Based on post-layout simulations, a symbol baud rate of 168 Mbaud/s is achieved in TCM mode, equivalent to a maximum throughput of 840 Mbit/s using a 64-QAM constellation.

Tighter upper bounds on the error event and the bit error probabilities, respectively, for maximum-likelihood decoding of binary convolutional codes on the binary symmetric channel are derived from upper bounds previously published by Viterbi [1]. The measured bit error rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_b</tex> for a constraint length 3 decoder has been plotted versus the channel transition probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> and shows close agreement with the improved bound on the bit error probability.

This paper addresses the implementation and performance of hybrid-ARQ error control on a coherent slowly fading Ricean channel. Using a convolutional code with soft-decision Viterbi decoding for error correction, there are two methods for realizing the simultaneous error detection capability which characterizes hybrid-ARQ error control: (1) a two code approach which pre-encodes the information based on a high rate CRC code and performs error detection on the output of the Viterbi decoder, (2) a single code approach which modifies the Viterbi decoder to reject packets with low reliability during the Viterbi decoding process. The resulting analysis shows that the two code method is more robust than single code method with the most significant performance advantages realized for Rayleigh fading. The two code approach provides acceptable error rate performance and offers a throughput characteristic which is not as sensitive to changes in the average SNR as the single code approach. Since the implementational complexity of the two methods is comparable, the two code method is the preferred implementation for hybrid-ARQ on flat fading channels.

Advanced technology was needed for this within the cap of bandwidth, due to new developments in wireless networking and the increasing requirement of high data levels by consumers. One of the promising solutions is a system with 60 GHz Ultra-Wideband (UWB) that supports a data rate of up to 7 Gbps, considered 10 times faster than the Wi-Fi 802.11n data rate. The system uses advanced modulation modulations and coding systems called adaptive modulation and coding (AMC). However, inappropriate modulation level selection and coding rate can lead, in the event of radio frequency interference and a multi-way decline, to a low data rate. In fact, if non-optimum decoder due to the code’s restriction duration was chosen, more output loss occurs. In this paper, we will present explain about the OFDM technology. Also, we will discuss 60 GHZ Frequency Band and all their advantage. So, we will explain the OFDM-UWB systems and convolutional coding and viterbi decoding.