A Comparison of ARA- and Protograph-Based LDPC Block and Convolutional Codes

Abstract

Abstract-ARA-and protograph-based LDPC codes are capable of achieving error performance similar to randomly constructed codes while enjoying several implementation advantages as a result of their structure. LDPC convolutional codes can be derived from these codes through an unwrapping process. In this paper, we review the unwrapping process as well as the pipeline decoder that allows continuous decoding of LDPC convolutional codes. Computer simulations are then used to demonstrate that the unwrapped convolutional codes achieve a "convolutional gain" in error performance. We conjecture that this is due to the concatenation of many constraint lengths worth of received symbols in the pipeline decoding process. The consequences of this improved performance are examined in terms of factors related to decoder implementation: processor size, memory requirements, and decoding delay (latency). Finally, given identical protograph kernels, we compare derived block and convolutional codes based on the above measures.

LDPC codes from voltage graphs

“…In an entirely different context, various researchers have looked at constructing families of LDPC codes by taking random lifts of a specially chosen base graph, or "protograph", yielding the so-called "protograph codes" [24], [6], [7], [19]. The idea exploited in these constructions is that the properties of the base graph may shed light on the properties of the covering graphs, and therefore on the resulting codes.…”

Asymptotically good LDPC convolutional codes based on protographs

“…The convolutional counterpart of LDPC block codes was introduced in [4], and LDPC convolutional codes have been shown to have certain advantages compared to LDPC block codes of the same complexity [5], [6]. In this paper, we use ensembles of tail-biting LDPC convolutional codes derived from a protograph-based ensemble of LDPC block codes to obtain a lower bound on the free distance of unterminated, asymptotically good, periodically time-varying LDPC convolutional code ensembles, i.e., ensembles that have the property of free distance growing linearly with constraint length.…”

Deriving Good LDPC Convolutional Codes from LDPC Block Codes

“…In order to compare these codes based on a given decoding processor (hardware) complexity, we consider a block code of length n = ν s (see [40] and [41]). The above timevarying convolutional code for r = 31 has constraint length ν s = (m s + 1) · c = 155, and hence approximately the same processor complexity as the quasi-cyclic block code of length n = 155 in Figure 7 and the time-invariant convolutional code with ν s = 145 in Figure 7, but it achieves large gains compared to both of these codes.…”

“…As was done in [41] 0.63 dB, and several of its punctured versions. Figure 9 shows simulation results for the obtained block and convolutional codes.…”

“…In particular, we consider the computational complexity, hardware complexity, decoder memory requirements, and decoding delay. More details on the various comparisons described in this section can be found in [30], [40], [41].…”