Sequential decoding

About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.

Truncation Error Probability in Viterbi Decoding

Abstract: An upper bound on the bit error probability due to truncation of the path length in Viterbi decoding is obtained for any given convolutional code. This bound is then used to determine the path length at which the additional error probability due to truncation becomes negligible compared to the maximum likelihood decoding error probability. These results are tested by simulation using several short constraint length codes.

Achieving the Han-Kobayashi inner bound for the quantum interference channel by sequential decoding

Abstract: In this paper, we study the power of sequential decoding strategies for several channels with classical input and quantum output. In our sequential decoding strategies, the receiver loops through all candidate messages trying to project the received state onto a `typical' subspace for the candidate message under consideration, stopping if the projection succeeds for a message, which is then declared as the guess of the receiver for the sent message. We show that even such a conceptually simple strategy can be used to achieve rates up to the mutual information for a single sender single receiver channel called cq-channel henceforth, as well as the standard inner bound for a two sender single receiver multiple access channel, called ccq-MAC in this paper. Our decoding scheme for the ccq-MAC uses a new kind of conditionally typical projector which is constructed using a geometric result about how two subspaces interact structurally. As the main application of our methods, we construct an encoding and decoding scheme achieving the Chong-Motani-Garg inner bound for a two sender two receiver interference channel with classical input and quantum output, called ccqq-IC henceforth. This matches the best known inner bound for the interference channel in the classical setting. Achieving the Chong-Motani-Garg inner bound, which is known to be equivalent to the Han-Kobayashi inner bound, answers an open question raised recently by Fawzi et al. (arXiv:1102.2624). Our encoding scheme is the same as that of Chong-Motani-Garg, and our decoding scheme is sequential.

Iterated soft-decision decoding of block codes

Abstract: Systems and methods for augmenting the performance of iterative soft decision-in soft decision-out decoding of block codes with extrinsic information based on multiple parity equations inherent to the block codes. Cyclic shifting of codewords may be applied in the context of iterative soft decision-in soft decision-out decoding to maximize the usefulness of a parity equation corresponding to any particular codeword bit. Soft decisions are determined on a bit-by-bit basis in response to multi-bit symbol measurements. This allows the use of relatively inexpensive bit-based decoders for decoding of multi-bit symbols.

Comparison of LDPC block and LDPC convolutional codes based on their decoding latency

Abstract: We compare LDPC block and LDPC convolutional codes with respect to their decoding performance under low decoding latencies. Protograph based regular LDPC codes are considered with rather small lifting factors. LDPC block and convolutional codes are decoded using belief propagation. For LDPC convolutional codes, a sliding window decoder with different window sizes is applied to continuously decode the input symbols. We show the required E b /N 0 to achieve a bit error rate of 10−5 for the LDPC block and LDPC convolutional codes for the decoding latency of up to approximately 550 information bits. It has been observed that LDPC convolutional codes perform better than the block codes from which they are derived even at low latency. We demonstrate the trade off between complexity and performance in terms of lifting factor and window size for a fixed value of latency. Furthermore, the two codes are also compared in terms of their complexity as a function of E b /N 0 . Convolutional codes with Viterbi decoding are also compared with the two above mentioned codes.

Syndrome Decoding of Reed–Solomon Codes Beyond Half the Minimum Distance Based on Shift-Register Synthesis

Abstract: In this paper, a new approach for decoding low-rate Reed-Solomon codes beyond half the minimum distance is considered and analyzed. The maximum error correcting radius coincides with the error correcting radius of the Sudan algorithm published in 1997. However, unlike the Sudan Algorithm, the approach described here is not a list decoding algorithm, and is not based on polynomial interpolation. The algorithm in this paper is rather syndrome based, like classical algebraic decoding algorithms. The computational complexity of the new algorithm is of the same order as the complexity of the well-known Berlekamp-Massey algorithm. To decode errors beyond half the minimum distance, the new decoder is allowed to fail for some high-weight error patterns with a very small probability.