Layered Constructions for Low-Delay Streaming Codes

Abstract

We propose a new class of error correction codes for low-delay streaming communication. We consider an online setup where a source packet arrives at the encoder every M channel uses, and needs to be decoded with a maximum delay of T packets. We consider a sliding-window erasure channel -C(N, B, W ) -which introduces either up to N erasures in arbitrary positions, or B erasures in a single burst, in any window of length W . When M = 1, the case where source-arrival and channel-transmission rates are equal, we propose a class of codes -MiDAS codes -that achieve a near optimal rate. Our construction is based on a layered approach. We first construct an optimal code for the C(N = 1, B, W ) channel, and then concatenate an additional layer of parity-check symbols to deal with N > 1. When M > 1, the case where source-arrival and channel-transmission rates are unequal, we characterize the capacity when N = 1 and W ≥ M (T + 1), and for N > 1, we propose a construction based on a layered approach. Numerical simulations over Gilbert-Elliott and Fritchman channel models indicate significant gains in the residual loss probability over baseline schemes. We also discuss the connection between the error correction properties of the MiDAS codes and their underlying column distance and column span.

Column Rank Distances of Rank Metric Convolutional Codes

“…A convolutional code always admits a minimal encoder, i.e., in row reduced form 1 . The sum of the row degrees of a minimal encoder attains its minimum among all the encoders of C. Such sum is usually denoted by δ and called the degree of C. A rate k/n convolutional code C of degree δ is called an (n, k, δ) convolutional code [10].…”

“…These ideas gave rise to the area of multi-shot network coding. Although the potential of using multi-shot network coding was already observed in the seminal paper [5], only recently this interesting approach has been investigated [1,7,15,17].…”

“…Adapting this class of codes to the context of networks brought about the notion of rank metric convolutional codes and interestingly there has been little research on these codes, see [1,[6][7][8]17]. The work in [17] was pioneer in this direction by presenting the first class of rank metric convolutional codes together with a decoding algorithm able to deal with errors, erasures and deviations.…”

“…The work in [17] was pioneer in this direction by presenting the first class of rank metric convolutional codes together with a decoding algorithm able to deal with errors, erasures and deviations. However, the results were only valid for unit memory convolutional codes and in [1,[6][7][8] (see also the references therein) an interesting and more general class of rank metric convolutional codes was introduced to cope with network streaming applications.…”

Convolutional codes with maximum column sum rank for network streaming

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