In this paper, a time-variant decoding model of a convolutional network code (CNC) is proposed. New necessary and sufficient conditions are established for the decodability of a CNC at a node r with delay L. They only...
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In this paper, a time-variant decoding model of a convolutional network code (CNC) is proposed. New necessary and sufficient conditions are established for the decodability of a CNC at a node r with delay L. They only involve the first L + 1 terms in the power series expansion of the global encoding kernel matrix at r. Concomitantly, a time-variant decoding algorithm is proposed with a decoding matrix over the base symbol field. The present time-variant decoding model only deals with partial information of the global encoding kernel matrix, and hence potentially makes CNCs applicable in a decentralized manner.
The conventional theory of linear network coding (LNC) is only over acyclic networks. Convolutional network coding (CNC) applies to all networks. It is also a form of LNC, but the linearity is w.r.t. the ring of ratio...
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The conventional theory of linear network coding (LNC) is only over acyclic networks. Convolutional network coding (CNC) applies to all networks. It is also a form of LNC, but the linearity is w.r.t. the ring of rational power series rather than the field of data symbols. CNC has been generalized to LNC w.r.t. any discrete valuation ring (DVR) in order for flexibility in applications. For a causal DVR-based code, all possible source-generated messages form a free module, while incoming coding vectors to a receiver span the received submodule. An existing time-invariantdecoding algorithm is at a delay equal to the largest valuation among all invariant factors of the received submodule. This intrinsic algebraic attribute is herein proved to be the optimal decoding delay. Meanwhile, time-variant decoding is formulated. The meaning of time-invariantdecoding delay gets a new interpretation through being a special case of the time-variant counterpart. The optimal delay turns out to be the same for time-variant decoding, but the decoding algorithm is more flexible in terms of decodability check and decoding matrix design. All results apply, in particular, to CNC.
We introduce an implementation-friendly binary message-passing decoding method for low-density parity-check (LDPC) codes that does not require the degree information of variable nodes or degree dependent parameters. F...
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We introduce an implementation-friendly binary message-passing decoding method for low-density parity-check (LDPC) codes that does not require the degree information of variable nodes or degree dependent parameters. For hard-decision decoding, given its low-complexity, the implementation cost for variable node degree information is an important consideration. We develop an estimation method for the extrinsic error probability (EEP) as well as its analysis. The proposed method offers similar performance as the existing methods for time-invariantdecoding in most cases, while it facilitates efficient circuit implementations of the LDPC decoder.
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