| 1. |
- Rathi, Vishwambhar, et al.
(författare)
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Performance analysis and design of two edge-type LDPC codes for the BEC wiretap channel
- 2013
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 59:2, s. 1048-1064
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Tidskriftsartikel (refereegranskat)abstract
- We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are binary erasure channels (BEC). A code construction method is proposed using two edge-type low-density parity-check (LDPC) codes based on the coset encoding scheme. Using a single edge-type LDPC ensemble with a given threshold over the BEC, we give a construction for a two edge-type LDPC ensemble with the same threshold. If the given single edge-type LDPC ensemble has degree two variable nodes, our construction gives rise to degree one variable nodes in the code used over the main channel. This results in zero threshold over the main channel. In order to circumvent this problem, the degree distribution of the two edge-type LDPC ensemble is numerically optimized. We find that the resulting ensembles are able to perform close to the boundary of the rate-equivocation region of the wiretap channel. Further, a method to compute the ensemble average equivocation of two edge-type LDPC ensembles is provided by generalizing a recently published approach to measure the equivocation of single edge-type ensembles for transmission over the BEC in the point-to-point setting. From this analysis, we find that relatively simple constructions give very good secrecy performance.
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| 2. |
- Si, Zhongwei, et al.
(författare)
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Rate-Compatible LDPC Convolutional Codes Achieving the Capacity of the BEC
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 58:6, s. 4021-4029
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a new family of rate-compatible regular low-density parity-check (LDPC) convolutional codes. The construction is based on graph extension, i.e., the codes of lower rates are generated by successively extending the graph of the base code with the highest rate. Theoretically, the proposed rate-compatible family can cover all the rational rates from 0 to 1. In addition, the regularity of degree distributions simplifies the code optimization. We prove analytically that all the LDPC convolutional codes of different rates in the family are capable of achieving the capacity of the binary erasure channel (BEC). The analysis is extended to the general binary memoryless symmetric channel, for which a capacity-approaching performance can be achieved. Analytical thresholds and simulation results for finite check and variable node degrees are provided for both BECs and binary-input additive white Gaussian noise channels. The results confirm that the decoding thresholds of the rate-compatible codes approach the corresponding Shannon limits over both channels.
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