For iterative soft-decision decoding algorithms for binary linear block codes, error performance and computational complexity are very important factors.In this thesis, suÆcient conditions of the optimality of decoded codeword and a suÆcient condition which is used for ruling-out some useless iterations of bounded distance decoding which reduces the computational complexity of iterative soft-decision decoding algorithms are shown.New iterative soft-decision decoding algorithms which uses the suÆcient conditions of the optimality of decoded codeword to achievegood error performance with small computational complexity are also shown.First, the suÆcient conditions are derived based on: (1) partial knowledge of the distance pro le of the code, and (2) previously generated candidate codewords.When the numberof previously generated candidate codewords is greater than 1, the conditions presented here are less stringent than those derived by Taipale and Pursley [4] and Kaneko et.al.[5].The condition based on three previously generated candidate codewords is the rst such s u Æ c i e n t condition that has ever been derived.It is shown by computer simulation that these suÆcient condions reduce the computational complexity of iterative decoding algorithms without degradation of error performance.Second, a suÆcient condition to rule-out some useless test error patterns is derived.In an iterative decoding algorithm, such as Chase Type-II decoding algorithm[2] and its improved versions, candidate codewords for a received vector are generated
For iterative soft-decision decoding algorithms for binary linear block codes, error performance and computational complexity are very important factors.In this thesis, suÆcient conditions of the optimality of decoded codeword and a suÆcient condition which is used for ruling-out some useless iterations of bounded distance decoding which reduces the computational complexity of iterative soft-decision decoding algorithms are shown.New iterative soft-decision decoding algorithms which uses the suÆcient conditions of the optimality of decoded codeword to achievegood error performance with small computational complexity are also shown.First, the suÆcient conditions are derived based on: (1) partial knowledge of the distance pro le of the code, and (2) previously generated candidate codewords.When the numberof previously generated candidate codewords is greater than 1, the conditions presented here are less stringent than those derived by Taipale and Pursley [4] and Kaneko et.al.[5].The condition based on three previously generated candidate codewords is the rst such s u Æ c i e n t condition that has ever been derived.It is shown by computer simulation that these suÆcient condions reduce the computational complexity of iterative decoding algorithms without degradation of error performance.Second, a suÆcient condition to rule-out some useless test error patterns is derived.In an iterative decoding algorithm, such as Chase Type-II decoding algorithm[2] and its improved versions, candidate codewords for a received vector are generated
This paper presents a new low-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test. The initial candidate codeword is generated by a simple decoding method. The subsequent candidate codewords, if needed, are generated by a chain of low-weight trellis searches, one at a time. Each search is conducted through a low-weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested. This improvement is then used as the next candidate codeword for a test of optimality. The decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low-weight trellis search results in a repetition of a previously generated candidate codeword. A divide-and-conquer technique is also presented for codes that are not spanned by their minimum-weight codewords. The proposed decoding algorithm has been applied to some well-known codes of lengths 48, 64, and 128. Simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the (128, 29, 32) RM code with a significant reduction in computational decoding complexity.
This paper presents an approach to soft-decision decoding for a (n, k) binary linear block code. This approach achieves near-optimal to optimal performance for any signal-to-noise ratio value. The proposed decoding is based on the reordering of the received symbols according to their reliability measure and can be applied to any binary linear code. The basic idea is to generate a sequence of codewords such that there will be a high probability that the next codeword is closer to the received vector. In this algorithm the information provided by the soft-decisions is used to generate information sets utilized in decoding. A fast procedure checks whether a given set of k positions is an information set. A sequence of codewords is reconstructed using a sequence of information sets. Each codeword reconstructed is compared with the received word and the closest one is selected. Hence, the decoding algorithm is an iterative procedure designed to enhance the performance of the usual soft-decision decoding, since with each iteration of the procedure, real vectors successively closer to the received vector are examined. A high performance stop rule is utilized to reduce the number of generated information sets, stopping the decoding process when a codeword is closest to the received sequence.
This dissertation deals with maximum-likelihood soft-decision decoding as well as suboptimal soft-decision decoding of linear block codes. We present three new decoding algorithms: $MA\sp*D,\ H\sp*,$ and Directed Search. The first algorithm, $MA\sp*D,$ is an instance of Algorithm $A\sp*$ that conducts heuristic search through a code tree of the transmitted code when the decoding problem is transformed into a problem of graph-search through a code tree. $MA\sp*D$ takes into consideration more properties of the code and is considerably more efficient than the original $A\sp*$ decoding algorithm presented by Han, Hartmann, and Chen in 1993. The second algorithm, $H\sp*,$ is a new decoding algorithm that determines the value of every component of a minimum-cost codeword by estimating the cost of the minimum-cost codeword, which has a fixed value at one of the k most reliable, linearly independent bit positions. The suboptimal version of this algorithm is combined with other decoding algorithms to reduce the search space during the decoding process. The third algorithm, Directed Search, is designed to enhance the performance of soft-decision decoding by searching in continuous space. This approach explores the search space between a given vector and the received vector and finds the codeword closest to the received vector in the space explored. We also present a novel and efficient hybrid decoding algorithm for (n, k) linear block codes. It hybridizes $MA\sp*D,\ H\sp*,$ and Directed Search algorithms, utilizing their strengths to make the decoding more efficient. Simulation results for this hybrid algorithm are presented for the (104,52) binary-extended quadratic residue code and for the (128,64), the (256, 131), and the (256, 139) binary-extended BCH codes. This hybrid algorithm can efficiently decode the (104,52) binary extended quadratic residue code and the (128,64) code for any signal-to-noise ratio and has near-optimal to optimal performance. Previously, no practical decoder could decode these two codes with such a performance for all signal-to-noise ratio ranges.
The number of iterations of an iterative optimal or suboptimal decoding scheme for binary linear block codes without any effect on its error performance can be reduced by testing a sufficient condition on the optimality of a candidate codeword. The least stringent sufficient condition on the optimality of a decoded codeword is investigated under the assumption that the available information on the code is restricted to (1) the minimum weight or the distance profile and (2) for a given positive integer h, h or fewer already generated candidate codewords. The least stringent sufficient conditions of optimality for 1/spl les/h/spl les/3 are presented. Cond/sub 1/ is the same as the one given by Taipale and Pursley (1991), Cond/sub 2/ is less stringent than the one given by Kaneko, Nishijima, Inazumi and Hirasawa (see IEEE Trans. Inform. Theory, vol.IT-40, no.3, p.320, 1994), and Cond/sub 1/ and Cond/sub 2/ are derived from Cond/sub 3/ as special cases. These conditions can be used effectively to save computer simulation time for evaluating the error probability for maximum likelihood decoding.
This dissertation presents a novel approach to soft decision decoding for binary linear block codes. The basic idea of this approach is to achieve a desired error performance progressively in a number of stages. For each decoding stage, the error performance is highly bounded and the decoding is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved. As a result, more flexibility in the trade-off between performance and decoding complexity is provided. The proposed decoding is based on the reordering of the received symbols according to their reliability measure. In the dissertation, we evaluate the statistics of the noise after ordering. Based on these statistics, we derive two monotonic properties which dictate the reprocessing strategy. Each codeword is decoded in two steps: (1) hard-decision decoding based on reliability information and (2) reprocessing of the hard-decision decoded codeword in successive stages until the desired performance is achieved. The reprocessing is based on the monotonic properties of the ordering and is carried out using a cost function. A new resource test highly related to the reprocessing strategy is introduced to reduce the number of computations for each reprocessing stage. For short codes of lengths N ≤ 32 or medium codes with 32 < N ≤ 64 with rate R ≥ 0.6, near-optimum bit error performance is achieved in two stages of reprocessing with at most a computation complexity of o(K2) constructed code-words, where K is the dimension of the code. For longer codes, three or more reprocessing stages are required to achieve near-optimum decoding. However, most of the coding gain is obtained within the first two reprocessing stages for error performances of practical interest. The proposed decoding algorithm applies to any binary linear code, does not require any data storage and is well suitable for parallel processing. Furthermore, the maximum number of computations required at each reprocessing stage is fixed, which prevents buffer overflow at low SNR. Further reductions of the number of computations based on probabilistic or decomposable properties of the code considered are also investigated. The generalization of the algorithm to other channels is discussed. Finally, the discrete time channel associated with the AWGN model after ordering is greatly simplified. This simplification allows an important reduction of the number of computations required to evaluate the theoretical error performance of any algorithm based on a partial or total ordering.