Iterative Decoding Based on Error Pattern Correction

An Iteratively Decodable Tensor Product Code with Application to Data Storage

The error pattern correcting code (EPCC) can be
constructed to provide a syndrome decoding table targeting the
dominant error events of an inter-symbol interference channel at
the output of the Viterbi detector. For the size of the syndrome
table to be manageable and the list of possible error events to
be reasonable in size, the codeword length of EPCC needs to
be short enough. However, the rate of such a short length code
will be too low for hard drive applications. To accommodate the
required large redundancy, it is possible to record only a highly
compressed function of the parity bits of EPCC’s tensor product
with a symbol correcting code. In this paper, we show that the
proposed tensor error-pattern correcting code (T-EPCC) is linear
time encodable and also devise a low-complexity soft iterative
decoding algorithm for EPCC’s tensor product with q-ary LDPC
(T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC
achieves almost similar performance to single-level qLDPC with
a 1/2 KB sector at 50% reduction in decoding complexity.
Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of
1/2 KB single-level qLDPC at the same decoder complexity.

ORDER STATISTICS FOR CORRELATED NON-IDENTICALLYDISTRIBUTED RANDOM VARIABLES

This paper deals with a problem in which the joint statistics of a set of N random variables are known. Based on this knowledge, we derive the joint probability density function
(PDF) of the L largest random variables ( L<= N ). The N random variables will be assumed to be correlated and non-identically-distributed. Problems typical to this one are normally encountered in the performance analysis of a certain class of receivers used in multipath fading channels with correlated and unbalanced diversity branches. In this application, the receiver has access to N signal-to-noise ratio (SNR) random variables, and it has to make a symbol decision based on the largest L SNR’s. This class of receivers is widely known as generalized selection combining (GSC) receivers.

Probability of error analysis of predetection generalized selection combining receivers with correlated unbalanced Nakagami branches

In this paper we determine the probability of error of a predetection generalized selection combining (GSC)
receiver with correlated and unbalanced diversity branches in a Nakagami-m multipath fading channel.We start by
finding the joint probability density function (PDF) of the decision variables. This involves the derivation of the
joint PDF of the L largest random variables (L maxima) of an input population of N>L correlated nonidentically
distributed random variables, based on the statistics of the input population. The results obtained are then used in
the derivation of the error probabilities of noncoherent FSK (NCFSK) and DPSK receivers