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Re-proving Channel Polarization Theorems

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A Class of Generalized RS-Codes with Faster Encoding and Decoding Algorithms

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In this paper we study a particular class of generalized Reed-Solomon codes and introduce encoding and decoding algorithms for such codes that speed up current hardware implementations by a factor p wherein p can be any divisor of the size of the multiplic ...

Ieee2013

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Polarity-Balanced Codes

Balanced bipolar codes consist of sequences in which the symbols ‘−1’ and ‘+1’ appear equally often. Several generalizations to larger alphabets have been considered in literature. For example, for the q-ary alphabet {−q+1,−q+3, . . . , q−1}, known concept ...

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A Lower Bound on Achievable Rates by Polar Codes with Mismatch Polar Decoding

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In this paper we show that mismatched polar codes over symmetric B-DMCs symmetrized under the same permutation can achieve rates of at least I (W, V) bits whenever I (W, V) > 0, where W denotes the communication channel, V the mismatched channel used in th ...

Ieee2013

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Shannon, in his seminal work, formalized the transmission of data over a communication channel and determined its fundamental limits. He characterized the relation between communication rate and error probability and showed that as long as the communicatio ...

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We consider the problem of determining the tradeoff between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the ...

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We introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. As opposed to standard product codes, we do not require that a ...

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Iterative detection and decoding (IDD) in multiple-input multiple-output (MIMO) wireless systems is known to achieve near channel capacity. The high computational complexity of IDD, however, poses signiﬁcant challenges for practical implementations (in ter ...

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Polar Codes for the m-User Multiple Access Channel

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In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arikan's polarization technique applied individually to each user transforms independent uses of an m-user binary input MAC into su ...

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