This paper presents two efficient Viterbi decoding-based suboptimal algorithms for tailbiting codes. The first algorithm, called the wrap-around Viterbi algorithm. (WAVA), falls into the circular decoding category. It...
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This paper presents two efficient Viterbi decoding-based suboptimal algorithms for tailbiting codes. The first algorithm, called the wrap-around Viterbi algorithm. (WAVA), falls into the circular decoding category. It processes the tailbiting trellis iteratively, explores the initial state of the transmitted sequence through continuous Viterbi decoding, and improves the decoding decision with iterations. A sufficient condition for the decision to be optimal is derived. For long tailbiting codes, the WAVA gives essentially optimal performance with about one round of Viterbi trial. For short- and medium-length tailbiting codes, simulations show that the WAVA achieves closer-to-optimum performance with fewer decoding stages compared with the other suboptimal circular decoding algorithms. The second algorithm, called the bidirectional Viterbi algorithm (BVA), employs two Wrap-around Viterbi decoders to process the tailbiting trellis from both ends in opposite directions. The surviving paths from the two decoders are combined to form composite paths once the decoders meet in the middle of the trellis. The composite paths at each stage thereafter serve as candidates for decision update. The bidirectional process improves the error performance and shortens the decoding latency of the unidirectional decoding with additional storage and computation requirements. Simulation results show that both proposed algorithms effectively achieve practically optimum performance for tailbiting codes of any length.
The structure of bidirectional syndrome decoding for binary rate (n-1)/n convolutional codes is investigated. It is shown that for backward decoding based on the trellis of a syndrome former H-T, the syndrome sequence...
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The structure of bidirectional syndrome decoding for binary rate (n-1)/n convolutional codes is investigated. It is shown that for backward decoding based on the trellis of a syndrome former H-T, the syndrome sequence must be generated in time-reversed order using an extra syndrome former H*(T), where H* is a generator matrix of the reciprocal dual code of the original code. It is also shown that if the syndrome bits are generated once and only once using H-T and H*(T): then the corresponding two error sequences have the intersection of v(1) x n error symbols, where v(1) is the memory length of H-T.
The main drawback of sequential decoding is the variability of its decoding effort which could cause decoding erasures. We propose and analyze in this correspondence an efficient bidirectional sequential decoding (BSD...
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The main drawback of sequential decoding is the variability of its decoding effort which could cause decoding erasures. We propose and analyze in this correspondence an efficient bidirectional sequential decoding (BSD) technique to alleviate this drawback. In the proposed BSD, two decoders are used;one is called a forward decoder (FD), and is used to search the tree from forward direction;while the other is called a backward decoder (ED), and is used for the backward search of the tree. Forward decoding and backward decoding are performed simultaneously, and stop whenever FD and ED merge at a common encoder state somewhere in the tree. The relationships between backward coding and forward coding are examined in detail. Good rate 1/2 convolutional codes, with memory m ranging from 2 to 25, suitable for bidirectional decoding found through extensive computer search, are provided. These codes possess the same distance properties from both forward and backward directions. It is found by means of extensive computer simulations as well as a heuristic argument that the advantage of BSD appears as a substantial decrease of the computational variability of sequential decoding. Our findings suggest that the Pareto exponent of unidirectional sequential decoding (USD) can be practically doubled by using BSD.
bidirectional suboptimal breadth-first decoding of convolutional codes is an attractive technique for slowly varying and quasi-static fading channels as it restricts the extent of decoding errors due to correct path l...
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bidirectional suboptimal breadth-first decoding of convolutional codes is an attractive technique for slowly varying and quasi-static fading channels as it restricts the extent of decoding errors due to correct path loss to very heavy noise or interference regions. This paper compares the performance of such a decoding scheme to the Viterbi algorithm over wide-band TDMA indoor radio links where equalization and space diversity are also used to combat dispersive fading and cochannel interference. On the basis of equal computational complexity and equal decoding delay, suboptimal, breadth-first, bidirectional decoding of a long constraint length convolutional code is shown to be superior to Viterbi decoding of a shorter constraint length code. Furthermore, this advantage increases as the outage criterion (in terms of bit error rate) becomes more stringent which makes bidirectional decoding particularly attractive for data applications and makes channel coding a more attractive alternative to increasing the space diversity order at the receiver.
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