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Efficient methods for encoding and decoding Half-Weight codes are disclosed and similar high density codes are disclosed. The efficient methods require at most 3(k-1)+h/2+1 XORs of symbols to calculate h Half-Weight symbols from k source symbols, where h i ...
This paper addresses the problem of the distributed delivery of correlated data sources with help of network coding. Network coding provides an alternative to routing algorithms and offers improved system performance, robustness and throughput, with no nee ...
In a data decoder for decoding data from received symbols received over a channel from an encoder, a method for decoding data wherein the received data includes erasures and includes source symbols and repair symbols organized into one or more source block ...
It is shown that given two copies of a q-ary input channel W, where q is prime, it is possible to create two channels W- and W+ whose symmetric capacities satisfy I(W-)
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In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed. In particular, Arıkan’s polarization technique applied individually to each user will polarize any m-user binary input MAC into a finite collection ...
The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find ...
Consider communication over a binary-input memoryless output-symmetric channel with low-density parity-check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...
This paper proposes a new class of low-density generator-matrix codes (LDGM) based on chaotic dynamical systems. The codes are designed by controlling symbolic dynamics and using linear convolutional codes. Analyzing the complex structure of chaotic system ...
We consider the asymptotic behavior of the polarization process for polar codes when the blocklength tends to infinity. In particular, we study the asymptotics of the cumulative distribution P(Z(n)
Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...
