Adding RLL Properties to Four CCSDS LDPC Codes without Increasing Their Redundancy

Abstract

This paper presents the construction of Run Length Limited (RLL) Error Control Codes (ECCs) from four Low Density Parity Check (LDPC) Codes specified by Consultative Committee for Space Data Systems (CCSDS). The obtained RLL-ECCs present a practical alternative to the CCSDS codes with pseudorandomizers. Their advantage is that the maximal runlengths of equal symbols in their codeword sequences are guaranteed, which is not the case if the common approach with pseudo-randomizers is used. The other advantages are that no additional redundancy is introduced into encoded codewords and that the encoding and decoding procedures of the original error control CCSDS codes do not have to be modified in the following cases. In the first case if hard decoding is used and the transmission channel can be modeled as a Binary Symmetric Channel (BSC) or in the second case if soft decoding and coherent Binary Phase Shift Keying (BPSK) 158 P. Farkaš, M. Rakús modulation is used and the appropriate transmission channel model is an Additive White Gaussian Noise (AWGN) channel.

On adding security to RLL - LDPC CCSDS codes without additional redundancy

“…In [6] it was shown that RLL properties can be implemented into the standard codes [7] without additional redundancy and without the need to change the decoding procedures if some round conditions are valid [8]. The method is based on adding vectors called modifiers to encoded codewords with reordered symbols.…”

“…(2) GF and both will have length  . In (6) the index  denotes a key which is an element from a set  denoted as keyspace.…”

“…The LDPC codes defined by Eqns. (1-3) have b-intervals of the same length 8 [6]. Therefore, we can first estimate the number of combinations in which an uneven number of ones can be placed into the positions in the modifier corresponding to only one b-interval denoted N…”

“…Recently in [6] it was shown that RLL properties can be implemented into the CCSDS-LDPC codes specified in [7]. This can be done without additional redundancy and in some circumstances without the need to change the decoding procedures for the original error correcting codes [8].…”

“…This can be done without additional redundancy and in some circumstances without the need to change the decoding procedures for the original error correcting codes [8]. The approach presented in [6] was based on adding a so-called modifier to the encoded codewords with reordered symbols at the transmitting side. The influence of these changes can be eliminated at the receiver in the cases presented in [8].…”