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.

We study low-delay error correction codes for streaming recovery over a class of packet-erasure channels that introduce both burst-erasures and isolated erasures. We propose a simple, yet effective class of codes whose parameters can be tuned to obtain a tradeoff between the capability to correct burst and isolated erasures. Our construction generalizes previously proposed low-delay codes which are effective only against burst erasures.We establish an information theoretic upper bound on the capability of any code to simultaneously correct burst and isolated erasures and show that our proposed constructions meet the upper bound in some special cases. We discuss the operational significance of column-distance and column-span metrics and establish that the rate 1/2 codes discovered by Martinian and Sundberg [IT Trans. 2004] through a computer search indeed attain the optimal column-distance and column-span tradeoff.Numerical simulations over a Gilbert-Elliott channel model and a Fritchman model show significant performance gains over previously proposed low-delay codes and random linear codes for certain range of channel parameters.

Abstract-The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several known column Hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction involves finding a class of superregular matrices that preserve this property after multiplication with non-singular block diagonal matrices in the ground field.

Abstract-The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several known column Hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction involves finding a class of superregular matrices that preserve this property after multiplication with non-singular block diagonal matrices in the ground field.

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