Exact density evolution of protograph Low Density Parity Check (LDPC) codes over the Binary Erasure Channel (BEC) is considered. Upper bounds on the threshold are derived and expressed as single-variable minimizations. A simplified version of the upper bound is expressed in closed form in terms of the degrees of the nodes in the protograph. By maximizing the upper bound, useful conditions are derived for optimizing protographs to get thresholds close to capacity bounds. Using these conditions, a randomized construction method for good small-sized protographs is presented. © 2015 IEEE.

Andrew Edwin Thangaraj

Department of Electrical Engineering

Bins

Forward error correction

Satellite communication systems

Binary erasure channel

Construction method

Density evolution

Optimized designs

PROTOGRAPH

PROTOGRAPH LDPC CODES

PROTOGRAPH LOW DENSITY PARITY CHECK CODES (LDPC)

Upper bound

Codes (symbols)

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IIT Madras

Threshold upper bounds and optimized design of protograph LDPC codes for the Binary Erasure Channel

7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015

For certain degree-distribution pairs with non-zero fraction of degree-two bit nodes, the bit-error threshold of the standard ensemble of Low Density Parity Check (LDPC) codes is known to be close to capacity. However, the degree-two bit nodes preclude the possibility of a block-error threshold. Interestingly, LDPC codes constructed using protographs allow the possibility of having both degree-two bit nodes and a block-error threshold. In this paper, we analyze density evolution for protograph LDPC codes over the binary erasure channel and show that their bit-error probability decreases double exponentially with the number of iterations when the erasure probability is below the bit-error threshold and long chain of degree-two variable nodes are avoided in the protograph. We present deterministic constructions of such protograph LDPC codes with girth logarithmic in blocklength, resulting in an exponential fall in bit-error probability below the threshold. We provide optimized protographs, whose block-error thresholds are better than that of the standard ensemble with minimum bit-node degree three. These protograph LDPC codes are theoretically of great interest, and have applications, for instance, in coding with strong secrecy over wiretap channels. © 2013 IEEE.

Fulltext

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Journal	Data powered by Typeset7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015
Publisher	Data powered by TypesetInstitute of Electrical and Electronics Engineers Inc.
Open Access	No