# Video over DSL with LDGM Codes for Interactive Applications
## 1 Introduction
Interleaving of packets in order to reduce the impact of error bursts also has a latency implication, again owing to the need to accumulate sufficient data before interleaving can take place. In addition, whenever the latency budget is large, the video-sending rate becomes \"bursty\", which can lead to congestion and ultimately to packets being dropped from buffers. Therefore, some of the results presented in this paper, examine the trade-off between error-repair capability and the latency arising from a choice of FEC method. As it is, because the packet loss pattern, rather than the number of packets lost, actually affects video distortion, other results examine the video delivered after using our recommended low-latency channel coder. LDPC codes present rapid decoding owing to the sparseness of their parity check matrix (refer to Section 2). However, in general the generator matrix created from the parity check matrix is not necessarily sparse and, hence, encoding time can be very high. To reduce encoding latency, Low-Density Generator Matrix (LDGM) codes [13], with, a sparse generator matrix, are attractive candidates. They can be used with relatively smaller block sizes, unlike LDPC codes, which are implemented with block sizes of about 1000 for best recovery performance. [PERSON] [14] has demonstrated that the encoding latency of systematic erasure codes is linearly dependent on the block size, for sufficiently large packets. Therefore, for block sizes of 200, as herein, one can expect a one fifth reduction in encoding time. The decoding speed still linearly depends on the block size but also linearly depends on the number of packets lost, that is, there is a channel dependent element. However, unmodified, LDGM codes have a non-zero error probability that is independent of the code block length, _i.e._, high error floors (see Section 2.2 for potential solutions to this problem). On the other hand, unlike RS codes, decoding can be iteratively refined through a belief-propagation algorithm (also known as a sum-product or iterative probabilistic decoding algorithm), rather than having to wait for all the data before decoding can begin. Thus, start-up latency is reduced, which is important for real-time streaming. Because in both [15] and [16], LDPC was selected as most suitable for Real-time Transport Protocol (RTP) video streaming compared to other channel codes, the possibilities for its reduced cousin, LDGM, are promising. Notice that in order to avoid legal complexity, this paper also confines itself to regular LDPC and LDGM codes (ones with a constant number of equations defining each code symbol). For an irregular LDPC code with apparently an associated patent refer to [17]. In this paper, we now consider the relevance of LDGM codes for video communication with shorter block lengths, whereas work in [13] considered their relevance for general-purpose data communication with larger block lengths. The remainder of this paper is organized as follows. Section 2 reviews the advantages and disadvantages of various channels codes suitable for protection of real-time video streams. Section 3 describes the methodology employed in evaluating the application of LDGM FEC. Section 4 is a comparison across those codes in terms of the trade-offs to be made across the dimensions of latency, error recovery, severity of error conditions, and resulting video distortion. In Section 5 we review related research in this area. Finally, Section 6 makes some concluding remarks before discussing future developments of this research.